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http://limw.realmonterotondoscalo.it/triangle-proofs-card-sort-activity-answer-key.html
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docx), PDF File (. Isosceles and Equilateral Triangles. 25 mm, 1 mm, 0. Action! Pairs Æ Investigation. Similar Triangles Worksheet Show Answers. A mental health assessment is when a professional -- like your family doctor, a psychologist, or a psychiatrist -- checks to see if you might have a mental problem and what type of treatment may. You can use the Triangle Midsegment Theorem. be/6saYBeHzArE Still struggling with proofs? Here is a link to a video that may help. com is the place to go to get the answers you need and to ask the questions you want. ANSWERS is a crossword puzzle answer. Lesson 1: Construct an Equilateral Triangle. This empowers people to learn from each other and to better understand the world. You can find the answer to a clue using the letters you already know and even see all the other clues we have seen that point to the same answer. 4_trig_applications_cw CW FILLED IN. Best answer: When you have evolved to eat grass and outrun your predators then advantages of grasslands is 1) a food source 2) good ground to run from predators from over say mountain areas 3) easier to see predators coming over say forest areas. answer to station 7. First, Create a random triangle on a piece of patty papers. 2 chart, other students are responsible for questioning the pair for their reasoning as well as for clarity. The NRICH Project aims to enrich the mathematical experiences of all learners. The must sort the triangles into categories depending on the type of triangle - whether they are right-angled, acute or scalene. Answer Keys Click on the file name to access the file: If you have difficulty accessing the Google doc via the link, you may download the appropriate PDF file attached to the bottom of this page. Adjust the triangle above by dragging any vertex. Geometry Worksheet Triangle Congruence Proofs Name: Date: Block: 1) Given: BD ⊥ AB, BD ⊥ DE, BC DC≅ Prove: ∠A ≅ ∠E. My Geometry students loved this! This Classifying Triangles card sort worksheet activity was the perfect activity for my Middle School Math & High School Geometry students to practice sorting triangles by their angle and side measurements. Let's look at our new figure. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment. Measure each side length to the nearest tenth of a centimeter. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. Abstract In this interview for Think magazine (April ’’92), Richard Paul provides a quick overview of critical thinking and the issues surrounding it: defining it, common mistakes in assessing it, its relation to communication skills, self-esteem, collaborative learning, motivation, curiosity, job skills for the future, national standards, and assessment strategies. Best answer: When you have evolved to eat grass and outrun your predators then advantages of grasslands is 1) a food source 2) good ground to run from predators from over say mountain areas 3) easier to see predators coming over say forest areas. Students had to figure out if the triangles with Equilateral, Isosceles, or Scalene. Figure 7: Indian proof of Pythagorean Theorem 2. A must-read for English-speaking expatriates and internationals across Europe, Expatica provides a tailored local news service and essential information on living, working, and moving to your country of choice. Continue proofs packet ; Now writing proofs from scratch. For the last five terms in the list, modify the vocabulary card to include examples, non-examples, and relationships between the angles. This activity for congruent triangles helps my students so much! It is great triangle congruence proofs practice and works so much better than a worksheet. Students need a copy of the sorting mat and cards with the directions. They reflect on these choices, and apply their learning by creating their own equations and tables of values that fall into each category. For instance, the teacher might ask:. This lesson applies the Pythagorean Theorem and teaches the foundational skills required to proceed to lesson 2, Origami Boats - Pythagorean Theorem in the real world Resource ID 49055. YES! Now is the time to redefine your true self using Slader's free Geometry Common Core answers. Use these 40 task cards with your students to help them practice solving word problems with PYTHAGOREAN THEOREM. Activity: On a paper mark two points Y and Z and join them to form a straight line. Congruent Triangles Snap! A Matching Activity. Houghton Mifflin provides answer keys online as well as for printable resources. ____ neither congruent nor similar to Triangle 1. Two-column proof - a formal proof that contains statements and reasons organized in two columns. Activity 4: Read this text about Pythagoras. A triangle has three sides and three angles. Welcome to Prezi, the presentation software that uses motion, zoom, and spatial relationships to bring your ideas to life and make you a great presenter. Start with a right triangle with legs $$a$$ and $$b$$ and hypotenuse \(c. This lesson should not be taught until the students have a knowledge of standard MAFS. The NRICH Project aims to enrich the mathematical experiences of all learners. Prove theorems about lines and angles. Module 1 embodies critical changes in Geometry as outlined by the Common Core. This self-checking maze has 11 problems involving finding the area of triangles. Learn about indirect characterization with this printable worksheet on making inferences and understanding character traits. com worksheets… Read More. You can find the answer to a clue using the letters you already know and even see all the other clues we have seen that point to the same answer. Measuring Segments - Worksheets, Quizzes, Guided Notes and other resources to help teachers teach Measuring Segments. Answer keys are available with a purchase in paperback, softcover or hardcover books. They reflect on these choices, and apply their learning by creating their own equations and tables of values that fall into each category. Planning Guide. Congruent Triangle Postulates Congruent Triangle Sort A Wednesday, January 18th: Congruent Triangles B/C Common Sides/Overlapping Triangles Thursday, January 19th: Congruent Triangles Task Cards Friday, January 20th: Congruent Triangles Task Cards Monday, January 23rd: Proofs Practice Tuesday, January 24th: CPCTC Proofs Begin HW (Due Thursday. Procedure Trigonometry is a branch of mathematics dealing with relationships between the angles and sides of triangles. New Special Right Triangles Worksheet Answers High from Similar Triangles Worksheet , source: latinopoetryreview. Intensify practice with this compilation of area of a triangle worksheets featuring skills like finding the area of scalene, isosceles and equilateral triangles, find the missing base or height, find the area with measures offered as integers, decimals, fractions and algebraic expressions to mention just a few. This is an intro activity to parallel lines and transversal relationships. The basic proof problems involving similar triangles will ask you to prove one of three things: the triangles are similar, a proportion is true, or a product is true. Start studying Springboard Geometry Unit 2 - Activities 12 & 13: Flowchart Proofs & Properties of Triangles. One area of knowledge in geometry is simple identification of shapes, and learning the names for shapes with a certain number of sides is a rote activity. The PowerPoint begins with an opening ques. be/6saYBeHzArE Still struggling with proofs? Here is a link to a video that may help. Answer Key 238 Preface. Worksheet 6. Answer: ANSWERS. Division For Grade 3. Scoots are a way for students to practice math skills on the move. Intensify practice with this compilation of area of a triangle worksheets featuring skills like finding the area of scalene, isosceles and equilateral triangles, find the missing base or height, find the area with measures offered as integers, decimals, fractions and algebraic expressions to mention just a few. In this video, learn how photographers use dilations to print the same photograph in larger or smaller sizes. By having students choose their own statements, they can't determine where they need to go just to have an equal number in each corner. Fundamental theorems are important foundations for the rest of the material to follow. Mathematics. I also adjust by having students work alone or with a partner. Area of a Triangle Worksheets. Or go to the answers. If a parallelogram contains at least one right angle, then it is a rectangle (definition). Find the answer to your question Find the answer to your question. Use MathJax to format equations. Children can learn the names and properties of different types of triangles as well as how to recognise them. Now cut the triangle in half as shown. Whole Class Math Congress As pairs share the answers from the BLM 4. Click here for Answers to Grown Up Proofs WS Wednesday 10/1 - Proof Review Short Proof Quiz Homework: Chapter 2 Review Worksheet Click here for Chapter 2 Review KEY Click here for Grown Up Proofs #2/3 WS Key Thursday 10/2 - Review Chapter 2 Homework: Chapter 2 Quick Review . Pre-Proof Warm-ups with Definitions Worksheet Five Pack - What conclusion does each problem lead you to? Similarity of Triangles with Similarity Proofs Worksheet Five Pack - I thought this was a cool way to do it. Procedure Trigonometry is a branch of mathematics dealing with relationships between the angles and sides of triangles. Actuator 8. Median, Altitude, and Angle Bisectors of a Triangle. If you don't see any interesting for you, use our search form on bottom ↓. Coordinate Geometry Proofs Worksheets- Includes math lessons, 2 practice sheets, homework sheet, and a quiz!. For quadrilaterals, being able to differentiate between a parallelogram (including the special case of the square), rhombus and a trapezoid are important skills. Alfred Kinsey was born on June 23, 1894, in Hoboken, New Jersey, the son of Sarah Ann (née Charles) and Alfred Seguine Kinsey. Additional notes The Pocket Money Clues should be cut out and placed in an envelope. Similar Triangles Sorting Activity FREEBIE! This similar triangles activity gets kids thinking about how to prove triangles are similar or how they are NOT similar. Also, congruent triangle proofs are so much richer and more interesting if the students already know their parallel lines and transversals angle relationships. Use a simple classification key to identify an unknown organism SPI 0807. GCSE Similar Triangles. Students will identify criteria for similarity and congruence of triangles, develop facility with geometric proofs (variety of formats), and use the concepts of similarity and congruence to prove theorems involving lines, angles, triangles, and other polygons. Saturday Jobs (worksheets) Objectives Solve simple problems involving ratio. be/6saYBeHzArE Still struggling with proofs? Here is a link to a video that may help. triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Search Tips. Their task is to answer. Use the Shape Sort Cards: Quadrilaterals pages in the Student Activity Book to make shapes with ordered pairs. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Read about triangles, do dot-to-dots, draw them, color them, and write the names of things with a triangular shape. Shop Target for free two-day shipping or free same-day store pick-up, plus free and easy returns. Best answer: It has been good and necessary to Americans in some forms. Parallel Lines and Transversals Worksheet - Free download as Word Doc (. In this investigation, we compare the larger triangle to the smaller triangle but. This activity for congruent triangles helps my students so much! It is great triangle congruence proofs practice and works so much better than a worksheet. 6 Materials. You will then compare the posters from the different groups and draw conclusions about which triangles are congruent, which triangles are not congruent and why. Coordinate Geometry Proofs Worksheets- Includes math lessons, 2 practice sheets, homework sheet, and a quiz!. Complete the following proof by giving the missing statements and reasons. Instant access to millions of Study Resources, Course Notes, Test Prep, 24/7 Homework Help, Tutors, and more. Trigonometry Word Problems Worksheet - Answers. In this activity you will create triangles based on given conditions and display them on a poster. The Bingo card and problems on the following pages are for playing Bingo using the concept of complex numbers. com Similar Triangles Sorting Activity FREEBIE! This similar triangles activity gets kids thinking about how to prove triangles are similar or how they are NOT similar. Intensify practice with this compilation of area of a triangle worksheets featuring skills like finding the area of scalene, isosceles and equilateral triangles, find the missing base or height, find the area with measures offered as integers, decimals, fractions and algebraic expressions to mention just a few. the long term damage he is. com: iPlay, iLearn Baby Sit to Stand Walkers Toys, Kids Activity Center, Toddlers Musical Fun Table, Lights and Sounds, Learning, Birthday Gift for 9, 12, 18. Bob Daemmrich/The Image Works. The NRICH Project aims to enrich the mathematical experiences of all learners. Ideal for quizzes, online testing & exams. Search filters applied In the Search field, type mail. A 9 uM UaDd0e4 3w 6iat 4hH qI0n 1fZi jn ji et LeI OGve Bocm de Et9r IyW. Key: Applications of Similar PolygonsNote: In problem #1, the answer should be 480 ft. At Chegg we understand how frustrating it can be when you’re stuck on homework questions, and we’re here to help. answer key to practice 1-3 (yesterday's homework) answer to station 1. 25 mm, 1 mm, 0. 2 Answer Key Day 4 - Matching Cards Matching Theorems & Postulates Day 4 - Proving Triangles Congruent. I have included some misconceptions to catch some out and also give possible class discussi. It seemed like the logical way to structure the course. If the diagonals of a parallelogram are congruent, then it is a rectangle. PRACTICE: Triangle Proofs Worksheet Part 2 Wednesday, 11/14/12 or Thursday, 11/15/12. exterior angle of a triangle theorem. Related SOL G. Separate the Angle, Segment and Equality Cards into three shuffled piles, with cards face down. ) How can we estimate the height of a building?. Students need a copy of the sorting mat and cards with the directions. proofs involving similar triangles worksheet answers generated on lbartman. And here's the magic square worksheets page. World History Tests Answer Key contains a copy of the student tests with answer overprints for easy grading. This is an intro activity to parallel lines and transversal relationships. 6 Explain a proof of the Pythagorean Theorem and its converse. It does not follow from this that the number of degrees in triangles may be more or less than 180. Key: Applications of Similar PolygonsNote: In problem #1, the answer should be 480 ft. two angles and the non-included side of another triangle, then the triangles are congruent Hypotenuse – Leg Postulate (HL): If a hypotenuse and a leg of one right triangle are congruent to a hypotenuse and a leg of another right triangle, then the triangles are congruent Right Angle Theorem (R. Present students with the Triangle Sort activity sheet (attached), and explain that they will be sorting the triangles based on the measure of their angles and the length of the sides. If two triangles are similar, this means the corresponding sides are in proportion. Unit 4 test study guide congruent triangles answer key gina wilson. Card activity - give the extraneous information; Classwork grade! HW: Triangle Congruence Practice #1; Wednesday, March 15 Intro to proofs with congruent triangles; In class we will do some examples together; HW: 1-18 - I will announce some problems the kids can cross out. Inspire your students with thousands of free teaching resources including videos, lesson plans, and games aligned to state and national standards. 36 m 45 m 27 m 4. These are the ways I have run this activity: • Place 2 cards at each station and have students move in groups of 3-4 from station to station after approximately 3 minutes. Now that you have found out how much energy was released by the Solar flare, you will estimate how strong the magnetic field was inside the coronal loop. ©4 f2x0 x1M1W xK LuWtZat uSQolfut9w 0a zroe M 8L TL IC X. You will need to use the Triangle Sum Theorem to find missing angle measures, find the scale factors, and don't {forget the rules about vertical angles!}. review answers with the class. If a parallelogram contains at least one right angle, then it is a rectangle (definition). For instance, the teacher might ask:. Proving one or more of these pairs of triangles congruent (with SSS, SAS, ASA, AAS, or HLR) will likely be an important part of the proof. a link the to answer key. Peer evaluation Text Analysis More Incredible Inferences C. Let's look at our new figure. (This way you only have to copy one set of cards) • Students work in pairs and are given a card set. Before you can ever start with proofs your students need to have a clear understanding of what makes sides and angles of triangles congruent. If a parallelogram contains at least one right angle, then it is a rectangle (definition). AM2) Underlined word is the answer. Awesome work! Hazel, London UK. answer to station 8. vocab in proofs review sheet answer key. Welcome to Prezi, the presentation software that uses motion, zoom, and spatial relationships to bring your ideas to life and make you a great presenter. Learners put the puzzle together to create a complete picture of Pythagoras. Students had to figure out if the triangles with Equilateral, Isosceles, or Scalene. • Lessons 7-4 and 7-5 Use trigonometric ratios to solve right triangle problems. Whole Class Æ Discussion Discuss lines of symmetry and how this relates to the type of triangle. Interactive Mathematics Activities for Arithmetic, Geometry, Algebra, Probability, Logic, Mathmagic, Optical Illusions, Combinatorial games and Puzzles. The PowerPoint begins with an opening ques. Intensify practice with this compilation of area of a triangle worksheets featuring skills like finding the area of scalene, isosceles and equilateral triangles, find the missing base or height, find the area with measures offered as integers, decimals, fractions and algebraic expressions to mention just a few. Instant access to millions of Study Resources, Course Notes, Test Prep, 24/7 Homework Help, Tutors, and more. The heart of the module is the study of transformations and the role transformations play in defining congruence. The two angles that are not adjacent, or next to, the exterior angle of the triangle are called remote interior angles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. Topic: Proofs Involving Congruent Triangle - Worksheet 1 1 Given: AB ≈ BC &
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2020-01-19 19:59:21
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https://proofwiki.org/wiki/Definition:Cauchy_Distribution
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# Definition:Cauchy Distribution
## Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \R$.
$X$ is said to have a Cauchy distribution if it has probability density function:
$\map {f_X} x = \dfrac 1 {\pi \gamma \paren {1 + \paren {\frac {x - x_0} \gamma}^2} }$
for some $\gamma > 0$.
This is written:
$X \sim \Cauchy {x_0} \gamma$
## Also see
• Results about the Cauchy distribution can be found here.
## Source of Name
This entry was named for Augustin Louis Cauchy.
## Technical Note
The $\LaTeX$ code for $\Cauchy {x_0} {\gamma}$ is \Cauchy {x_0} {\gamma} .
When either of the arguments is a single character, it is usual to omit the braces:
\Cauchy {x_0} \gamma
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2020-07-10 18:44:08
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https://datascience.stackexchange.com/questions/80221/creating-an-unclassified-class-in-random-forest
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# Creating an "unclassified" class in Random Forest
I am trying to classify satellite based images by creating a region of interest and then classifying according to it.
I am using a Jupyter notebook using python to do that.
I used a Random forest classifier and got a nice model and result, but the problem is that the image is "over classified" meaning that all the pixels et value and force to be classified.
I would like to define level of similarity that a pixel has to have in order to be classified, otherwise, it will not get any class.
For example, the black suppose to be asphalt:
However, in the RGB, you can see it's not asphalt:
Is there any way to define in random forest or any other algorithm "level os similarity"? (For example something similar to n-D angle to match pixels to reference like ised in SAM, but under random forest, or another algorithm that allows define that)
My end goal: to get "unclassified" values based on similarity level to the calibration data
It seems you can use RandomForest to get probabilities of being in both class by using predict_proba(X).
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2022-10-01 17:50:18
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http://www.gradesaver.com/textbooks/science/physics/physics-for-scientists-and-engineers-a-strategic-approach-with-modern-physics-3rd-edition/chapter-13-newton-s-theory-of-gravity-exercises-and-problems-page-373/16
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## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)
(a) The radius of the planet is $1.80\times 10^7~m$ (b) The rocket needs a minimum speed of 9.41 km/s to escape from the planet.
(a) We can find the radius $R$ of the planet. Let $M$ be the mass of the planet which is twice the mass of the earth. We know that the free-fall acceleration on the earth is $g = 9.80~m/s^2$. $\frac{G~M}{R^2} = \frac{1}{4}~g$ $R^2 = \frac{4~G~M}{g}$ $R = \sqrt{\frac{4~G~M}{g}}$ $R =\sqrt{\frac{(4)(6.67\times 10^{-11}~m^3/kg~s^2)(2)(5.98\times 10^{24}~kg)}{9.80~m/s^2}}$ $R = 1.80\times 10^7~m$ The radius of the planet is $1.80\times 10^7~m$ (b) We can use the equation for escape speed to find the escape speed from this planet. $v_{esc} = \sqrt{\frac{2~G~M}{R}}$ $v_{esc}=\sqrt{\frac{(2)(6.67\times 10^{-11}~m^3/kg~s^2)(2)(5.98\times 10^{24}~kg)}{1.80\times 10^{7}~m}}$ $v_{esc} = 9.41\times 10^3~m/s$ $v_{esc} = 9.41~km/s$ The rocket needs a minimum speed of 9.41 km/s to escape from the planet.
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2018-04-20 18:47:01
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https://brilliant.org/problems/algeometery/
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# Algeometery!!
Algebra Level 4
Find the total number of real solution(s) of the equation below. $\sin \pi x = |\ln|x||$
×
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2017-01-18 07:55:36
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https://www.advanceduninstaller.com/Adobe-AIR-5e95e9f9db3ad6d7561b54818ca5c4f1-application.htm
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Publishers
Adobe AIR contains of the executables below. They occupy 338.13 KB (346240 bytes) on disk.
• Adobe AIR Application Installer.exe (126.88 KB)
• Adobe AIR Updater.exe (100.38 KB)
• airappinstaller.exe (52.38 KB)
• template.exe (58.50 KB)
The current web page applies to Adobe AIR version 2.7.0.19480 only. For more Adobe AIR versions please click below:
...click to view all...
Adobe AIR has the habit of leaving behind some leftovers.
Directories found on disk:
• C:\Program Files (x86)\Common Files\Adobe AIR
Usually, the following files remain on disk:
• C:\Program Files (x86)\Common Files\Adobe AIR\sentinel
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\airappinstaller.exe
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\digest.s
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\NPSWF32.dll
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\setup.swf
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\stylesNative.swf
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\template.exe
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\template.msi
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\Thawte Root Certificate.cer
• C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Resources\WebKit.dll
Registry that is not removed:
• HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products\761B3BDFAF4FD16479F68236405AB7A2
Use regedit.exe to remove the following additional values from the Windows Registry:
• HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products\761B3BDFAF4FD16479F68236405AB7A2\ProductName
Adobe AIR is an application by Adobe Systems Incorporated. Sometimes, users want to erase this application. Sometimes this is easier said than done because deleting this by hand requires some knowledge regarding Windows program uninstallation. One of the best SIMPLE solution to erase Adobe AIR is to use Advanced Uninstaller PRO. Here is how to do this:
1. If you don't have Advanced Uninstaller PRO on your Windows system, install it. This is good because Advanced Uninstaller PRO is a very efficient uninstaller and all around utility to clean your Windows computer.
• set up Advanced Uninstaller PRO
2. Start Advanced Uninstaller PRO. It's recommended to take some time to get familiar with Advanced Uninstaller PRO's design and number of features available. Advanced Uninstaller PRO is a very good package of tools.
3. Press the General Tools button
4. Activate the Uninstall Programs button
5. A list of the applications installed on the PC will appear
6. Scroll the list of applications until you locate Adobe AIR or simply activate the Search field and type in "Adobe AIR". If it exists on your system the Adobe AIR app will be found automatically. Notice that after you select Adobe AIR in the list of applications, some data regarding the program is made available to you:
• Safety rating (in the lower left corner). The star rating tells you the opinion other users have regarding Adobe AIR, ranging from "Highly recommended" to "Very dangerous".
• Opinions by other users - Press the Read reviews button.
• Details regarding the application you want to uninstall, by clicking on the Properties button.
7. Click the Uninstall button. A confirmation page will show up. Confirm the removal by clicking Uninstall. Advanced Uninstaller PRO will then remove Adobe AIR.
8. After uninstalling Adobe AIR, Advanced Uninstaller PRO will ask you to run an additional cleanup. Click Next to perform the cleanup. All the items of Adobe AIR which have been left behind will be detected and you will be asked if you want to delete them. By uninstalling Adobe AIR with Advanced Uninstaller PRO, you can be sure that no Windows registry items, files or directories are left behind on your computer.
Your Windows system will remain clean, speedy and able to serve you properly.
Disclaimer
The text above is not a piece of advice to uninstall Adobe AIR by Adobe Systems Incorporated from your PC, we are not saying that Adobe AIR by Adobe Systems Incorporated is not a good application. This page simply contains detailed info on how to uninstall Adobe AIR supposing you decide this is what you want to do. The information above contains registry and disk entries that other software left behind and Advanced Uninstaller PRO stumbled upon and classified as "leftovers" on other users' computers.
2016-06-19 / Written by Daniel Statescu for Advanced Uninstaller PRO
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2020-04-02 06:10:26
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http://openstudy.com/updates/55eb9e45e4b0819646d9a1b5
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## amyna one year ago diffrentiate: g(x)=4^3x^2 Thank you for your help!
1. amyna
|dw:1441504840472:dw|
2. triciaal
differentiate power raised to a power think we can do substitution
3. triciaal
|dw:1441505133978:dw|
4. Astrophysics
Try logarithms
5. triciaal
maybe the log function
6. triciaal
right on time huh
7. Astrophysics
Haha :P
8. amyna
lol i dont understand. what you wrote, is that the correct way to do this problem or not?
9. beginnersmind
Nah. Start by rewriting |dw:1441505728153:dw|
10. amyna
oh okay so you have to use logs and rewrite it. is this true for all problems that may look similar to this?
11. beginnersmind
Generally base e is easier to deal with. And changing bases only changes the exponent by a constant factor. So it almost always helps.
12. amyna
ok thanks!
13. amyna
wait then how do i solve it after rewriting it? lol i forgot how to do that part!
14. beginnersmind
Use the chain rule.
15. amyna
ok thanks. i think i got it from here
16. amyna
no i don't get it. i don't know how to solve it. i tried using the chain rule
17. beginnersmind
Hm, you might need to review the chain rule then. I can go through this example if you want but I don't think it will be much help in general.
18. beginnersmind
@amyna
19. amyna
yes please! i would greatly appreciate that! :)
20. freckles
$y=(f(x))^{g(x)} , \text{ assume } f(x)>0 \\ \\ \text{ take } \ln( ) \text{ of both sides } \\ \ln(y)=\ln((f(x))^{g(x)}) \\ \ln(y)=g(x) \ln(f(x)) \text{ by use of power rule for logarithms } \\ \\ \text{ now differentiate both sides } \\ \frac{y'}{y}=g'(x) \cdot \ln(f(x))+g(x) \cdot \frac{f'(x)}{f(x)} \\ \text{ by a whole bunch of rules :p } \\ \text{ left hand side I just used chain rule } \\ \text{ right hand side I used product rule and chain rule }$ $y'=\{g'(x) \ln(f(x))+g(x) \frac{f'(x)}{f(x)} \} y \\ \text{ note: this step I just multiplied both sides by } y$ $\text{ now remember } y=(f(x))^{g(x)} \\ \text{ so make this replacement and you are done} \\$
21. beginnersmind
Ok, I'll try to explain how to apply the chain rule. You might want to look at this lesson from MIT OCW as well: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-11-chain-rule/ You look at $$e^{(ln4)*3*x^2}$$. If it was e^x the derivative would be e^x. But now the exponent is a function of x. So the result is e to that function of x _multiplied by the derivative of that function_. So $$[e^{g(x)}]' = g'(x)* e^{g(x)}$$ In this case g(x) = (ln4)*3*x^2 g'(x) = (ln4)*6*x so the final result is $(ln4)*6x*e^{ln4*3*x^2}$ which you can rewrite as $(ln4)*6x*4^{ln4*3*x^2}$ using the same idea with logarithms that we started with.
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2017-01-17 03:39:26
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https://math.stackexchange.com/questions/3012355/plotting-a-solution-of-a-differential-equation-with-sagemath/3074671
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# Plotting a solution of a differential equation with Sagemath
I need to solve a differential equation. The solution will depend on $$t$$ and $$q$$, and I need to define that $$q$$ piecewise depending on $$t$$.
var('k,Tmax,Tmin,w,T0,q'); T=function('T')(t); Te=function('Te')(t);
assume(k>0); assume(Tmax>Tmin); Te(t)=(Tmax+Tmin)/2+(Tmax-Tmin)/2*sin(w*t);
Now this is the differential equation solution:
sol=desolve(diff(T(t),t)-q+k*(T(t)-Te(t)),[T,t],[0,T0]);
The solution with $$q=0$$ for example would be
sol.subs(Tmax=21.6,Tmin=15.2,k=0.024,q=0,T0=15.6,w=pi/12);
but I need that q to be a model for a heater that's on from 8 AM to 22 PM, and off from 22 PM to 8 AM. So I need to define a $$q$$ function that if $$t mod 24$$ is between $$8$$ and $$22$$ its value is $$0.0504$$, and $$0$$ otherwise. Something like this
$$q(t)=\begin{cases}0.0504 \quad\ \ \ \ \ \ \ if \quad t\ mod\ 24 \in[8,22] \\ 0 \ \ \qquad \qquad otherwise\end{cases}$$
I've been trying with the piecewise function but it's not plotting anything, I always get error messages.
You can express $$q(t)$$ as a sum of differences of step functions. Also, it's more efficient to solve the differential equation numerically. I assume you want to plot the solution for some number of days (which can be specified in the code).
days=3
Tmax=21.6; Tmin=15.2; k=0.024; T0=15.6; w=pi/12
var('t');
Te=(Tmax+Tmin)/2+(Tmax-Tmin)/2*sin(w*t)
We define $$q(t)$$:
q = 0.0504*sum(unit_step(t-8-d*24) - unit_step(t-22-d*24) for d in range(days))
plot(q,t,0,days*24)
We define the ODE (also the one with $$q(t)=0$$, to compare):
T=function('T')(t);
ode0 = diff(T,t) == -k*(T-Te)
ode1 = diff(T,t) == q-k*(T-Te)
Finally we solve and plot:
sol0=desolve_rk4(ode0, T, ivar=t, ics=[0,T0], step=0.1, end_points=[0,days*24], output='plot', xmin=0,xmax=days*24)
sol1=desolve_rk4(ode1, T, ivar=t, ics=[0,T0], step=0.1, end_points=[0,days*24], output='plot', xmin=0,xmax=days*24, color='red')
sol0 + sol1
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2019-04-26 16:06:57
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http://www.scholarpedia.org/article/Interface_free_energy
|
# Interface free energy
Curator and Contributors
1.00 - Charles Pfister
Interface free energy is the contribution to the free energy of a system due to the presence of an interface separating two coexisting phases at equilibrium. It is also called surface tension. The content of the article is the definition and main properties of the interface free energy from first principles of statistical mechanics.
## Interface free energy in statistical mechanics
### Definition of the interface free energy
Consider a physical system at equilibrium in a vessel $$V$$ at a first order phase transition point with bulk phases $$A$$ and $$B\ .$$ The interface is the common boundary of the two phases when they coexist in $$V\ .$$ At the macroscopic scale, when the length of the vessel $$V$$ is the reference length, a flat interface perpendicular to a unit vector $${\mathbf n}$$ is described mathematically by a plane perpendicular to $${\mathbf n}\ ;$$ above this plane the state of the system is specified by the value of the order-parameter of one of the phases, and below by that of the other phase. The interface free energy $$\tau({\mathbf n})$$ is the free energy of that interface (per unit area). The way of defining $$\tau({\mathbf n})$$ is quite general and can be applied in principle to most systems; its origin can be traced back to the monumental work of J.W. Gibbs, On the Equilibrium of Heterogeneous Substances (1875-1878). The basic postulate is that the various contributions to the overall free energy $$F(V)$$ (taking into account the interactions of the system with the walls) can be separated into the bulk free energy, which is proportional to the volume of $$V\ ,$$ and a term proportional to the surface of $$V$$ (up to a negligible correction term). Thus, at a point of first order phase transition, when only phase $$A$$ is present, $F_A(V)=-\frac{1}{\beta}\ln Z_A(V)=f_{{\rm bulk} }(A)|V| + f_{{\rm wall} }(A)|\partial V|+ o(|\partial V|)$ where $$Z_A(V)$$ denotes the partition function of the system for phase $$A\ ,$$ $$\beta$$ the inverse temperature, $$|V|$$ the volume of $$V$$ and $$|\partial V|$$ the area of the boundary $$\partial V$$ of the vessel. A similar expression holds when phase $$B$$ is present. Under specific conditions it is possible to obtain macroscopic inhomogeneous states with a planar interface separating the two coexisting bulk phases. In such cases there is an additional contribution to the free energy and the postulate is that the free energy can be written as $F_{AB}(V)=-\frac{1}{\beta}\ln Z_{AB}(V)=f_{{\rm bulk} }(AB)|V| + f_{{\rm wall} }(AB)|\partial V|+ \tau({\mathbf n})|I({\mathbf n})|+ o(|\partial V|)$ with $f_{{\rm wall} }(AB)=\alpha f_{{\rm wall} }(A)+ (1-\alpha)f_{{\rm wall} }(B).$ The term $$|I({\mathbf n})|=O(|\partial V|)$$ is the area of the interface in $$V$$ perpendicular to the unit vector $${\mathbf n}$$ and $$\alpha$$ is the proportion of the walls of $$V$$ in contact with phase $$A\ .$$ At a first order phase transition point $$f_{{\rm bulk} }(AB)=f_{{\rm bulk} }(A)=f_{{\rm bulk} }(B)\ ,$$ and if the postulate is correct, one eliminates the terms $$f_{{\rm wall} }(AB)\ ,$$ $$f_{{\rm wall} }(A)$$ and $$f_{{\rm wall} }(B)$$ by considering the ratio of partition functions $\tag{1} -\frac{1}{\beta}\ln\frac{Z_{AB}(V)}{Z_A(V)^{\alpha}Z_B(V)^{1-\alpha}}=\tau({\mathbf n})|I({\mathbf n})|+ o(|\partial V|).$
An obvious difficulty is that $$\tau({\mathbf n})$$ is defined only when there is phase coexistence. This is why in many situations one proceeds differently in Physics. One models directly the interface in order to bypass these problems and then the interface free energy is simply identified with the free energy of the model for which one has standard methods for evaluating it. This is often an adequate way to proceed, but it cannot be applied always, for example when one is studying how the coexisting phases are spatially distributed inside the vessel $$V\ .$$
### Macroscopic states and interface free energy in Ising model
The ideas of the preceding section are implemented for the Ising model for which the mathematical results are the most complete. We expose the main results for three-dimensional Ising model. The two-dimensional case is also of interest. The model is defined on $\Lambda_{LM}:=\{t=(t_1,t_2,t_3)\in{\mathbf Z}^3\,{:}\; \max(|t_1|,|t_2|)\leq L\,,\;|t_3|\leq M \}.$ The energy of the system is equal to $H_{LM}(\underline{\sigma})=-\frac{1}{2} \sum_{t\in\Lambda_{LM}}\sum_{t^\prime\in\Lambda_{LM}}J(t,t^\prime)\,\sigma(t)\sigma(t^\prime) -\sum_{t\in\Lambda_{LM}}h\,\sigma(t)$ with coupling constants $$J(t,t^\prime)=0\ ,$$ except if $$t,t^\prime$$ are nearest neighbors, in which case $$J(t,t^\prime)=J>0\ .$$ An inhomogeneous magnetic field $$J^\prime \eta(t)\ ,$$ which acts only on the spins located at the boundary of the box $$\Lambda_{L,M}\ ,$$ models the interaction of the system with the walls, which is defined by $W_{LM}^\eta(\underline{\sigma}):=-\sum_{t\in\partial\Lambda_{LM}}J^\prime\eta(t)\sigma(t).$ Here $$\partial\Lambda_{LM}:=\{t\in\Lambda_{LM}\,:\,|t_3|=M\; \text{or}\; \max(|t_1|,|t_2|)=L \}$$ and $$J^\prime>0\ ;$$ the value of $$\eta(t)$$ is fixed, either $$\eta(t)=1$$ or $$\eta(t)=-1\ .$$ Different kinds of walls are modeled by choosing different values for $$\eta(t)$$ and for the coupling constant $$J^\prime\ .$$ The overall energy of the system is $$H_{LM}+W_{LM}^\eta\ .$$ According to statistical mechanics the free energy of the system is the logarithm of the partition function $$Z_{LM}^\eta\ ,$$ $F_{LM}^\eta(\beta,h,J^\prime):=-\beta^{-1}\ln Z_{LM}^\eta\quad\text{with}\quad Z_{LM}^\eta=\sum_{\underline{\sigma}^\prime}{\rm e}^{-\beta(H_{LM}(\underline{\sigma}^\prime)+W_{LM}^\eta(\underline{\sigma}^\prime))}\,.$ At the thermodynamical limit the bulk free energy per spin $f_{{\rm bulk} }(\beta,h)=\lim_{L\rightarrow\infty}\frac{1}{(2L+1)^d}F_{LL}^\eta(\beta,h,J^\prime)$ is independent on the choice of $$J^\prime>0$$ and $$\eta\ .$$ It is well-known that the model exhibits a first order phase transition at $$h=0$$ and $$\beta>\beta_c(3)$$ ($$\beta_c(d)$$ is the inverse critical temperature of the $$d$$-dimensional Ising model, $$d\geq 2$$). At that transition the bulk free energy $$f_{{\rm bulk} }(\beta,h)$$ is not differentiable at $$h=0\ ,$$ the spin-flip symmetry of $$H_{LM}$$ is broken and there is a positive spontaneous magnetization $$m^*(\beta)\ ,$$ $0<m^*(\beta)=\frac{d}{dh}f_{{\rm bulk} }(\beta,h)|_{h=0^+}=-\frac{d}{dh}f_{{\rm bulk} }(\beta,h)|_{h=0^-}.$
From now on the external magnetic field $$h=0$$ and $$\beta>\beta_c(3)\ .$$ The coarse-grained description of the model at the macroscopic scale is obtained by taking the macroscopic limit. In this limit the state of the system is given by a magnetization profile. Let $$0<a<1$$ and for simplicity set $$L=M\ ;$$ the set $$\Lambda_{LL}$$ is partitioned into cubic cells $$C_i$$ of linear size $$L^a$$ and the averaged magnetization over $$C_i$$ is $m_{C_i}(\underline{\sigma}):=|C_i|^{-1}\sum_{t\in C_i}\sigma(t).$ All lengths are scaled by $$L^{-1}\ ,$$ so that the distance between neighboring spins becomes $$L^{-1}\ .$$ For each point $$x$$ of the macroscopic box $$V=\{(x_1,x_2,x_3)\in{\mathbf R}^d\,{:}\; |x_i|\leq 1\}$$ the magnetization profile is defined by $\rho_L(x|\underline{\sigma}):=m_C(\underline{\sigma})\quad\text{if}\; (Lx_1,Lx_2,Lx_3)\in C_i\,.$ The probability of the profile $$\rho_L(x|\underline{\sigma})$$ is the joint probability of the block-spins $$m_{C_i}(\underline{\sigma})$$ induced by the usual Gibbs measure. The macroscopic limit is obtained by taking the limit $$L^{-1}\rightarrow 0\ .$$ (In probability theory this corresponds to the regime of the law of large numbers.) For pure boundary conditions, that is $$\eta(t)\equiv+1\ ,$$ respectively $$\eta(t)\equiv -1\ ,$$
Figure 1: A mixed boundary condition.
the interactions with the walls favor the bulk phase with positive spontaneous magnetization $$m^*(\beta)\ ,$$ respectively negative magnetization $$-m^*(\beta)\ .$$ In the macroscopic limit the probability measure on the density profiles becomes concentrated on the unique magnetization profile $$\rho(x)\equiv m^*(\beta)\ ,$$ respectively $$\rho(x)\equiv -m^*(\beta)\ ,$$ for any value of $$J^\prime>0\ ;$$ this constant profile describes the macroscopic state of the $$+$$-phase, respectively $$-$$-phase, of the model. A mixed boundary condition is related to the emergence of a planar interface perpendicular to $${\mathbf n}=(n_1,n_2,n_3)\ ,$$ $\eta^{\mathbf n}(t):=+1\quad \text{if}\; t_1n_1+t_2n_2+t_3n_3\geq 0\quad\text{and}\quad \eta^{\mathbf n}(t):=-1\quad \text{if}\; t_1n_1+t_2n_2+t_3n_3< 0.$ Thus $$\eta^{{\mathbf n} }(t)=1$$ if and only if $$t$$ is above or in the plane $$\pi({\mathbf n})$$ perpendicular to $${\mathbf n}$$ and passing through the origin, otherwise $$\eta^{{\mathbf n} }(t)=-1\ .$$ Let $$Z_{LM}^{{\mathbf n} }:=Z_{LM}^{\eta^{\mathbf n} }\ ;$$ using the symmetry $$Z_{LL}^+=Z_{LL}^-$$ the interface free energy $$\tau({\mathbf n})$$ is defined by (1) and is given by $\tag{2} \tau({\mathbf n})=-\frac{1}{\beta|I({\mathbf n})|}\lim_{L\rightarrow\infty}\frac{1}{L^{d-1}}\ln\frac{Z_{LL}^{{\mathbf n} } }{Z_{LL}^+}.$
One can prove:
1. the limit (2) is independent on $$J^\prime\geq J\ ;$$
2. for $$\beta>\beta_c(3)$$ the function $$\tau({\mathbf n})$$ verifies the basic properties 1), 2) and 3) of an interface free energy (see below, next section);
3. in the macroscopic limit the measure on the density profiles is concentrated on the unique magnetization profile $\rho_{{\mathbf n} }(x):=+ m^*(\beta)\;\text{if}\; x\; \text{is above}\; \pi({\mathbf n}) \quad\text{and}\quad \rho_{{\mathbf n} }(x):=-m^*(\beta)\;\text{if}\; x\; \text{is above}\; \pi({\mathbf n})\,.$
The condition $$J^\prime\geq J$$ is important, because for some values of $$J^\prime<J$$ and $$\beta$$ the physics near the walls of the system is different: a surface phase transition may take place and portions of the interface may be pinned to the walls. As a consequence of this phenomenon, in the macroscopic limit the interaction of the system with the walls given by $$\eta^{\mathbf n}$$ may not induce an interface perpendicular to $${\mathbf n}$$. For example, in the two-dimensional case, the macroscopic state may have an interface making an angle with the vertical walls of the vessel, whose value is given by the Young-Herring equation, so that (2) may not be equal to $$\tau({\mathbf n})\ ,$$ or, if $$J^\prime$$ is small enough and the macroscopic box is a square, then the whole interface may even be pinned to the walls so that there is no interface through the macroscopic box and the magnetization profile is constant, either equal to $$m^*(\beta)$$ or to $$-m^*(\beta)\ .$$ In such cases the limit (2) depends on $$J^\prime\ .$$ The condition $$J^\prime\geq J$$ has a simple physical interpretation; it ensures that the walls of the box $$V$$ are in the complete wetting regime, so that the interface cannot be pinned to the walls. In the literature the standard choice for ferromagnetic models is $$J^\prime=J\ ,$$ so that (2) gives the correct definition of $$\tau({\mathbf n})\ .$$ These results illustrate the fact that one must avoid the possibility of pinning the interface to the walls when using definition (1). On the other hand any wall interactions, which induce a macroscopic state with an interface perpendicular to $${\mathbf n}$$ and such that otherwise (1) is independent of the chosen interactions, are admissible for defining the interface free energy.
Several other definitions for $$\tau({\mathbf n})$$ have been proposed for the Ising or similar models. Most of them involve a ratio of partition functions and are based on the same pattern leading to (2) (see references below). A possibility of avoiding the above problem with the walls is to suppress (partially) the walls of the system by taking (partial) periodic boundary conditions. Then one imposes a condition implying the existence of a single planar interface perpendicular to $${\mathbf n}\ .$$ There are also variants of (2) where one considers a box $$\Lambda_{LM}$$ instead of $$\Lambda_{LL}$$ and take first the limit $$M\rightarrow\infty$$ before taking $$L\rightarrow\infty\ .$$ When $$J^\prime<J$$ this limit may give a different answer as the limit (2). On the other hand, if $$J^\prime\geq J\ ,$$ then one can take the limits in any order, first $$L\rightarrow\infty$$ and then $$M\rightarrow\infty$$ or vice-versa, or simultaneously $$L\rightarrow\infty$$ and $$M\rightarrow\infty\ .$$ The reason is that the walls are in the complete wetting regime and the interface is not pinned to the walls.
The surface tension for the two-dimensional Ising model can be computed exactly. Onsager computed it for $${\mathbf n}=(0,1)\ ,$$ $\beta\tau((0,1))=2(K-K^*)\,,\;\beta>\beta_c(2)\quad\text{and}\quad \tau((0,1))=0\,,\;\text{otherwise,}$ where $$K^*$$ is defined by $$\exp(-2K^*)=\tanh K$$ and $$K=\beta J\ .$$ Onsager did not use the definition (2); the computation of $$\tau((0,1))$$ defined by (2) is due to Abraham and Martin-Löf. The full interface free energy has been computed by McCoy and Wu. In general it is not easy to show that reasonable definitions give the same value for $$\tau({\mathbf n})\ .$$
## Basic properties of the interface free energy
### Convexity of the interface free energy
Assume that $${\tau}({\mathbf n})>0$$ for each unit vector $${\mathbf n}$$ is given. By convention $$\tau({\mathbf n})\ ,$$ with $$\|{\mathbf n}\|=1\ ,$$ is the physical value of the interface free energy of an interface perpendicular to $${\mathbf n}\ .$$ It is convenient to extend the definition of $$\tau$$ to any $${\mathbf x}\ ,$$ as a positively homogeneous function, by setting $\tau({\mathbf x}):=\|{\mathbf x}\|\tau({\mathbf x}/\|{\mathbf x}\|)\,.$
Figure 2: 2D-Ising model, equilibrium shape $$W_{\tau}$$,$$J=1,\,\beta=3\ .$$
Let $$\langle\,{\mathbf x}|{\mathbf y}\,\rangle:=x_1y_1+x_2y_2+x_3y_3$$ be Euclidean scalar product. The convex set $$W_\tau\ ,$$ which is the intersection of the half-spaces $$H({\mathbf n})=\{{\mathbf x}\,:\,\langle\,{\mathbf x}|{\mathbf n}\,\rangle\leq \tau({\mathbf n})\}\ ,$$ $W_\tau=\{{\mathbf x}\,{:}\; \langle\, {\mathbf x}|{\mathbf n}\,\rangle\leq \tau({\mathbf n})\,,\;\forall\, {\mathbf n}\},$ is called the equilibrium shape because it gives the solution of the following isoperimetric problem. Let $$K$$ be a subset of $$\mathbf R^3$$ with $${\rm vol}(K)={\rm vol}(W_\tau)\ .$$ If inside $$K$$ there is phase $$A$$ and outside $$K$$ phase $$B\ ,$$ then the (surface) free energy associated with the boundary of $$K$$ is given by the surface integral ${\mathcal F}(\partial K)=\int_{\partial K}\tau(n)\,dS.$ Among all sets $$K$$ with $${\rm vol}(K)={\rm vol}(W_\tau)$$ the minimum of the surface integral is attained for, and only for, $$K=W_\tau$$ or a translate of $$W_\tau\ .$$ It is Wulff (1901) who gave the geometrical construction of the solution of this isoperimetric problem. This is why the set $$W_\tau$$ is also called Wulff crystal.
The main property of an interface free energy is its convexity: for two distinct phases $$A$$ and $$B$$ at equilibrium, the interface free energy is a continuous convex function, which is positive and sublinear, that is
1. $$\tau({\mathbf x})>0\quad {\mathbf x}\not=0\ ,$$
2. $$\tau(t{\mathbf x})=t\, \tau({\mathbf x})\quad\forall \,{\mathbf x}$$ and all $$t\geq 0\ ,$$
3. $$\tau({\mathbf x}+{\mathbf y})\leq\tau({\mathbf x})+\tau({\mathbf y})\quad \forall \,{\mathbf x},{\mathbf y}\ .$$
By a classical result of Minkowski the interface free energy $$\tau$$ is the support function of the convex set $$W_\tau\ ,$$ that is $\tau({\mathbf x})=\sup\{\langle\,{\mathbf x}|{\mathbf y}\,\rangle\,{:}\; {\mathbf y}\in W_\tau\}\,.$
The next simple thermodynamical argument shows the convexity of $$\tau\ .$$ Let $${\mathcal P}$$ be a right prism whose base is a triangle with vertices $$a,b,c$$ and whose length $$L$$ is very large. Let $$\ell_0\ ,$$ respectively $$\ell_1\ ,$$ $$\ell_2\ ,$$ be the side of the triangle opposite to the vertex $$c\ ,$$ respectively $$b\ ,$$ $$a\ .$$
Figure 3: The right prism $${\mathcal P}\ .$$
The length of the side $$\ell_i$$ is $$|\ell_i|$$ and $${\mathbf n}_i$$ is the outward unit normal to $$\ell_i$$ (in the plane of the triangle), so that $|\ell_0|{\mathbf n}_0+|\ell_1|{\mathbf n}_1+|\ell_2|{\mathbf n}_2=0.$ We set $${\mathbf n}:=-{\mathbf n}_0=|\ell_1|/|\ell_0|{\mathbf n}_1+ |\ell_2|/|\ell_0|{\mathbf n}_2\ .$$ In the plane spanned by $${\mathbf n}_1$$ and $${\mathbf n}_2$$ let $${\mathbf m_1}$$ and $${\mathbf m_2}$$ be reciprocal vectors to $${\mathbf n}_1$$ and $${\mathbf n}_2\ ,$$ $$\langle\,{\mathbf m_i}|{\mathbf n_j}\rangle=\delta_{ij}\ .$$ Then $\sum_{i=1}^2\frac{|\ell_i|}{|\ell_0|}\tau({\mathbf n}_i)= \langle\,\sum_{i=1}^2\tau({\mathbf n}_i){\mathbf m}_i|{\mathbf n}\,\rangle\equiv\langle\,{\mathbf z}|{\mathbf n}\rangle.$ The vector $${\mathbf z}=\sum_{i=1}^2\tau({\mathbf n}_i){\mathbf m}_i$$ belongs to the intersection of the boundaries of the half-spaces $$H({\mathbf n}_1)$$ and $$H({\mathbf n}_2)$$ since $$\langle\,{\mathbf z}|{\mathbf n}_i\,\rangle=\tau({\mathbf n}_i)\ .$$ Suppose that $$\langle\,{\mathbf z}|{\mathbf n}\rangle<\tau({\mathbf n})\ ;$$ then $L\ell_0\tau({\mathbf n})>L\ell_1\tau({\mathbf n}_1)+L\ell_2\tau({\mathbf n}_2)\,,$ and an interface perpendicular to $${\mathbf n}$$ can be deformed using the right prism $${\mathcal P}\ ,$$ with long enough length $$L\ ,$$ so that the deformed interface has a lower free energy. At equilibrium such a planar interface cannot exist since its free energy must be minimal. Notice also that the plane $$\{{\mathbf x}\,:\,\langle\,{\mathbf x}|{\mathbf n}\,\rangle=\tau({\mathbf n})\}$$ cannot intersect $$W_{\tau}\ .$$ Therefore at equilibrium, $\tag{3} |\ell_0|\tau({\mathbf n})\leq|\ell_1|\tau({\mathbf n}_1)+|\ell_2|\tau({\mathbf n}_2).$
Since $$\tau$$ has been defined as a positively homogeneous function, it is immediate to see that for all choices of $${\mathbf n}_1\ ,$$ $${\mathbf n}_2\ ,$$ $$\ell_1$$ and $$\ell_2$$ (3) is equivalent to $\tau({\mathbf x}+{\mathbf y})\leq\tau({\mathbf x})+\tau({\mathbf y})\quad \forall \,{\mathbf x},{\mathbf y}.$
By definition an interface perpendicular to $${\mathbf n}$$ is thermodynamically stable if $\tau({\mathbf x}+{\mathbf y})<\tau({\mathbf x})+\tau({\mathbf y})\quad \forall \,{\mathbf x},{\mathbf y}\; \text{linearly independent, such that}\; {\mathbf x}+{\mathbf y}={\mathbf n}\,.$ In general the choice of the normal to the interface does not matter, so that $$\tau({\mathbf n})=\tau(-{\mathbf n})\ .$$
### Stable interfaces and polar set of the equilibrium shape
Assume that $$\tau$$ is given, verifying properties 1), 2) and 3) above (but not necessarily that $$\tau({\mathbf n})=\tau(-{\mathbf n})$$). Under these assumptions $$W_\tau$$ is a bounded closed convex set with $$0$$ as an interior point. In convex analysis there is another natural set associated with $$W_\tau\ ,$$ which is the polar set $$W^*_\tau\ .$$ It is defined by the dual relationship between non-zero vectors $${\mathbf v}$$ and closed half-spaces $${\mathbf v}^*$$ containing the origin, $${\mathbf v}^*:=\{{\mathbf x}\,{:}\; \langle\,{\mathbf v}|{\mathbf x}\,\rangle\leq 1\}.$$ The polar dual or polar set $$W^*_\tau$$ of $$W_\tau$$ is $W_\tau^*:=\bigcap\{{\mathbf x}^*\,{:}\; {\mathbf x}\in W_\tau\}= \{{\mathbf u}\,{:}\; \langle\,{\mathbf x}|{\mathbf u}\,\rangle\leq 1\quad\forall\,{\mathbf x}\in W_\tau\}.$
Figure 4: 2D-Ising model, polar set $$W^*_{\tau}$$,$$J=1,\,\beta=3\ .$$
It is also a bounded closed convex set with $$0$$ as an interior point and $$W_\tau=W_\tau^{**}\ .$$ It is not difficult to show that $W^*_\tau=\{{\mathbf u}\,{:}\; \tau({\mathbf u})\leq 1\}\quad\text{and}\quad \tau({\mathbf x})=\min\{t\geq 0\,{:}\; {\mathbf x}/t\in W^*_\tau\}\,.$ These statements mean that $$\tau$$ is the gauge function of $$W^*_\tau\ .$$ Hence the interface free energy can be interpreted either as the support function of $$W_\tau\ ,$$ or as the gauge function of $$W^*_\tau\ .$$ The boundary $$\partial W^*_\tau$$ of the polar set is simply the level-$$1$$ surface of $$\tau\ .$$ Since $$(\partial W^*_\tau)^*= W_\tau^{**}$$ and $${\mathbf n}^*=H({\mathbf n})$$ for any $${\mathbf n}\in \partial W^*_\tau\ ,$$ the boundary points of $$W^*_\tau$$ give a natural labeling of the support planes of $$W_\tau\ .$$ Moreover, the extremal points of $$W_\tau^*$$ label precisely the support planes of $$W_\tau$$ which represent stable interfaces. Therefore the equilibrium shape can be written as $W_\tau=\{{\mathbf x}\,{:}\; \langle\,{\mathbf x}|{\mathbf n}\,\rangle\leq \tau({\mathbf n})\,,\;\forall\,{\mathbf n}\in{\rm ext}W_\tau^*\}\,.$ One can measure experimentally $$\tau({\mathbf n})$$ only for $${\mathbf n}\in {\rm ext}W_\tau^*\ .$$ All tangent planes of $$W_\tau$$ represent stable interfaces, but there are support planes of $$W_\tau$$ which are not tangent planes when $$W_\tau$$ has an edge or a corner and which represent also stable interfaces.
### Summary
Provided that one can construct a macroscopic state with a planar interface perpendicular to $${\mathbf n}\ ,$$ one can use formula (1) to define $$\tau({\mathbf n})\ .$$ The fundamental property of the interface free energy is that it is a convex function. The interface free energy can be measured experimentally at equilibrium only for the interfaces which are thermodynamically stable. By convention the physical value of the interface free energy $$\tau({\mathbf n})$$ is given for a unit vector $${\mathbf n}\ .$$ But, using the extension of $$\tau$$ as an homogeneous function, this function can be interpreted either as the support function of the equilibrium shape $$W_\tau=\{{\mathbf x}\,{:}\; \langle\,{\mathbf x}|{\mathbf n}\,\rangle\leq \tau({\mathbf n})\,,\;\forall\, {\mathbf n}\}\ ,$$ or as the gauge function of $$W^*_\tau=\{{\mathbf x}\,{:}\; \tau({\mathbf x})\leq 1\}\ .$$ Stable interfaces are labeled by the extremal points of $$W^*_\tau\ .$$
## Bibliographical notes
(Herring 1953) and (Rotman, Wortis 1984) are reviews of physics on interfaces and equilibrium shapes of crystals. The review (Abraham 1986) is a review about exact results. Comparisons of several definitions of the interface free energy are carefully discussed and references can be found there. The results of the computation of the interface free energy of the two-dimensional Ising model can be found in (Rotman, Wortis 1981). The macroscopic limit for the two-dimensional Ising model and the role of the wetting transition is discussed in (Pfister, Velenik 1999). Mathematical results on wetting phenomenon for Ising systems are in (Fröhlich, Pfister 1987). The up-to-date reference concerning proofs of existence and convexity of surface tension for ferromagnetic models is (Messager et al. 1992). The basic reference for the thermodynamical properties of $$\tau$$ is (Herring 1951). The argument proving the convexity of $$\tau$$ is adapted from (Herring 1951). Instead of the polar set Herring uses for studying $$\tau$$ the surface tension plot, which is the set of points $$\{{\mathbf x}\,{:}\; {\mathbf x}=\tau({\mathbf n})\,{\mathbf n}\,,\;\|{\mathbf n}\|=1\}\ .$$ This is the standard way of presenting $$\tau$$ in physics. One gets the surface tension plot from $$\partial W_\tau^*$$ by an inversion on the unit sphere (or the unit circle in dimension 2). Affine parts of $$\partial W_\tau^*$$ become spherical parts, or circular parts, of the surface tension plot. The theory of convex sets used for studying the interface free energy and its equilibrium shape is classical and due essentially to Minkowski. A good recent reference is chapters 1 and 2 of (Schneider 1993). An extended version of this article with further references can be found in (Pfister 2009).
## References
Abraham D.B. (1986): Surface Structures and Phase Transitions–Exact Results, pp. 1–74 in Phase Transitions and Critical Phenomena vol 10, eds Domb C., Lebowitz J.L., Academic Press, London.
Fröhlich J., Pfister C.-E. (1987): The wetting and layering transitions in the half–infinite Ising model, Europhys. Lett. 3, 845–852.
Herring C. (1951): Some Theorems on the Free Energies of Crystal Surfaces, Phys. Rev. 82, 87–93.
Herring C. (1953): The Use of Classical Macroscopic Concepts in Surface-Energy Problems, pp.5–81 in Structure and Properties of Solid Surfaces, eds. Gomer R., Smith C.S., The University of Chicago Press, Chicago.
Messager A., Miracle-Sole S., Ruiz J. (1992): Convexity Properties of the Surface Tension and Equilibrium Crystals, J. Stat. Phys. 67, 449–470.
Pfister C.-E. (2009): Interface free energy or surface tension: definition and basic properties, arXiv:0911.5232 (2009).
Pfister C.-E., Velenik Y. (1999): Interface, Surface Tension and Reentrant Pinning Transition in the 2D Ising Model, Commum. Math. Phys. 204, 269–312.
Rotman C., Wortis M. (1981): Exact equilibrium crystal shapes at nonzero temperature in two dimensions, Phys. Rev. B 11, 6274–6277.
Rotman C., Wortis M. (1984): Statistical mechanics of equilibrium crystal shapes: Interfacial phase diagrams and phase transitions, Phys. Rep. 103, 59–79.
Schneider R. (1993): Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications 44 (chapters 1 and 2), Cambridge University Press, Cambridge.
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2014-07-25 10:29:08
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http://mathhelpforum.com/calculus/12607-partial-derivatives-problem.html
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# Math Help - Partial derivatives problem
1. ## Partial derivatives problem
This was confusing me so any help would be appreciated!
For each of the following partial derivatives, give a possible F(x,y).
1) derivative with respect to y = x^2 divided by y
2) derivative with respect to y = xe raised to the xy
2. Originally Posted by clockingly
This was confusing me so any help would be appreciated!
For each of the following partial derivatives, give a possible F(x,y).
1) x^2 divided by y
2) xe raised to the xy
Is this the entire question?
3. Originally Posted by frenzy
Is this the entire question?
Ahhh sorry. Forgot to include
1) the derivative with respect to y = x^2 divided by y
2) the derivative with respect to y = xe^xy
I'll edit that first post.
4. Originally Posted by clockingly
Ahhh sorry. Forgot to include
1) the derivative with respect to y = x^2 divided by y
2) the derivative with respect to y = xe^xy
if d/dy F(x,y)=x^2/y
then
F(x,y) could be x^2*ln(y)
or x^2*ln(y)+sin(x^234)*e^(x^1/5)
or
x^2*ln(y)+g(x)
where g(x) does not depend on y
there are others
Or is there...hmmm.
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2014-03-09 19:04:25
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=18&t=47844
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## De Broglie Problem
$\lambda=\frac{h}{p}$
Doreen Liu 4D
Posts: 54
Joined: Wed Sep 11, 2019 12:17 am
### De Broglie Problem
A baseball must weigh between 5 and 5.25 ounces. What is the wavelength of a 5.15 ounce ball thrown at 92mph.
Can someone help me with this problem? Also, would I have to turn both the ounces and the miles/hour into SI units before I can start solving it?
Mansi_1D
Posts: 50
Joined: Fri Aug 02, 2019 12:15 am
### Re: De Broglie Problem
To find the wavelength, you would use h/mv equation. The mass is 5.15 ounce and velocity is 92mph. However, the mass has to be in kg and the velocity in m/s when you plug it into the equation, so yes you would have to convert them first.
Ananta3G
Posts: 62
Joined: Wed Sep 18, 2019 12:19 am
### Re: De Broglie Problem
The equation gives you an answer in meters so you would need to convert the velocity from mph to m/s first. Then, in order for Planck's constant's units, J/Hz to cancel out the other units, you need to convert the mass to Kg, otherwise you would have one mass in ounce but a unit that uses Kg which would stop the equation from working.
Ryan Chang 1C
Posts: 105
Joined: Sat Aug 24, 2019 12:17 am
### Re: De Broglie Problem
After converting the values, plugging in each value would look like this:
(6.626x10^-34 kg ms^2 s^-1)/(1.675x10^-27kg x 100x10^-12m) = 3.96x10^3m/s
Megan Jung 3A
Posts: 50
Joined: Thu Jul 11, 2019 12:17 am
### Re: De Broglie Problem
For this problem, you would have to convert oz to kg and mph to km/h
The conversion for oz to kg :
5.15oz(28.3g/10oz)(1kg/1000g)
The conversion for mph to km/h:
92mi/hr(1hr/3600sec)(1.609344km/mi)
From there, use De Broglie's Equation to solve for the wavelength
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2020-11-30 11:40:55
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https://maker.pro/forums/threads/twist-sensitive-resistor.7687/
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# twist sensitive resistor?
D
#### Dave
Jan 1, 1970
0
I have science project that involves measuring a small torque, or
twisting force.
Is there a torque sensitive resistor I can buy? Or perhaps a torque
sensitive capacitor? I can integrate it into an existing circuit if I
can find one.
Thanks, Dave
H
#### Henry Kolesnik
Jan 1, 1970
0
You could make a capacitor to be torque sensitive. Attach one plate to the
shaft and the other to a fixed point. The capacity will vary with the
torque.
C
Jan 1, 1970
0
R
#### Randy Day
Jan 1, 1970
0
Dave said:
I have science project that involves measuring a small torque, or
twisting force.
Is there a torque sensitive resistor I can buy? Or perhaps a torque
sensitive capacitor? I can integrate it into an existing circuit if I
can find one.
Thanks, Dave
HTH
J
#### JeffM
Jan 1, 1970
0
Henry Kolesnik top-posted:
You could make a capacitor to be torque sensitive.
Attach one plate to the shaft and the other to a fixed point.
The [capacitance] will vary with the torque.
That will measure angular displacement
(which may be an analog to torque),
but it doesn't measure force or radius.
..
..
J
#### JeffM
Jan 1, 1970
0
Is there a torque sensitive resistor I can buy?
Next time you post to multiple groups
post just ONCE
and put ALL the groups in which you want the question to appear
on the Groups line.
This allows EVERYONE who reads the question
to easily see ALL the solutions that are proposed.
..
..
..
Henry has already suggested a variable capacitor.
That can be an analog of torque
(as can a potentiometer--which is smaller and cheaper).
Both of these will likely require gearing
to get any kind of resolution
(leaving you with forward/backward lash).
..
..
A strain gauge measures force (which can also be an analog of torque).
J
#### Jonathan Kirwan
Jan 1, 1970
0
I have science project that involves measuring a small torque, or
twisting force.
How small is the torque? The magnitude such as between two small,
balanced and suspended masses and another pair of masses as in the
Cavendish experiment?
Is there a torque sensitive resistor I can buy? Or perhaps a torque
sensitive capacitor? I can integrate it into an existing circuit if I
can find one.
What is twisting? If it is the famous dumbbell experiment, for
example, you can just use a simple small-milliwatt 635nm diode laser
or better yet a HeNe laser and bounce it off of a tiny bit of mirror
attached to one of the suspended masses. You can easily align the
beam so that it reflects and then hits an exact point on a distant
ruler and when the suspended mass shifts slightly through some angle
X, the reflected beam will go though a deflection change of 2X. This
may be just fine if you are replicating Cavendish for a science
project.
Jon
J
#### Jamie
Jan 1, 1970
0
Dave said:
I have science project that involves measuring a small torque, or
twisting force.
Is there a torque sensitive resistor I can buy? Or perhaps a torque
sensitive capacitor? I can integrate it into an existing circuit if I
can find one.
Thanks, Dave
One of our machines at work has an optical pick up on on
each end of a drive shaft. when the machine is at idle (no torque)
the 2 opticals are perfectly aligned or near it. as the shaft starts
to twist under load, the drive side will get ahead of the output
side of the shaft thus causing the two opticals to miss align and
produce an offset of pulses ect./
also you could simply measure the load current on the drive device?
there are also things like load cells that use a capactive method.
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2022-10-01 17:52:33
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https://worldbuilding.stackexchange.com/questions/57311/what-adaptions-would-humans-obtain-if-they-lived-on-mars
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# What adaptions would humans obtain if they lived on Mars?
What adaptions would humans obtain if they lived on Mars? (eg. get taller/shorter because of gravity)
In a universe where humans terraformed mars to have breathable air and house some plants, what would happen to humans? Physically?
• For what we know, there might be no second generation at all. How do you want to prevent low gravity effects on fetus? As far as I remember, there is a suspicion it'll be fatal. Of course, no one tried this on actual humans. – Mołot Oct 2 '16 at 21:20
• This article suggests your colonists will be infertile, and if you overcome that, their children would be sterile. Not good, not good at all. – Mołot Oct 2 '16 at 21:30
I suspect that visual inspection of a Martian colonist would reveal no differences from standard Earth people. This is because humans are not going to sit around and wait to evolve. If they have the technology and will to Terraform Mars (or anyplace else, for that matter) they will also be augmenting themselves through biotechnology to live and thrive in that environment.
Terraforming eliminates the need to make very drastic external modifications anyway. The temperature and atmosphere are being changed to conform to the averages of Earth (by definition), so there is no need to grow an insulating fur coat, or develop extra sets of lungs, for example.
Only if you were to subject the colonist to detailed microscopic or forensic examination would differences become apparent. The Martian colonist will have their bone structure modified to maintain strength and density despite the lower gravity. Metabolic processes will be more efficient than on an unmodified human in order to maximize resources, especially near the beginning when everything needs to be imported. Balance and reflexes will be rewired to account for the lesser gravity, and perhaps there will be a need to increase the pigment melanin to account for the limited magnetic field and ozone on Mars and the high levels of ultraviolet radiation in the environment.
If Mars is colder than Earth on average, there might be selection towards the Inuit physique, maximizing volume while minimizing surface area. Once again, this would be a conscious choice engineered into the colonists by the first generation rather than natural selection working its wonders and allowing a dormant trait to reassert itself.
How this would be done is going to be through a combination of genetic engineering, microbiome tweaking and possibly some cyborg technology (at least until the genetic engineering part is perfected. Maybe first generation colonists can be identified by the cyborg implants they wear).
So short answer: people will not evolve to fit the environment, they will engineer themselves to live and thrive in the environment without changing their external appearances.
This is hard to answer since the mars changed over time. Even though we know the mars as a red desert without water or life, it is possible, that at some point there was water on mars. Research even shows riverbeds of rivers that once were present on the surface of mars. This could be related to the atmosphere of mars, which may have vanished due to hawking radiation or solar power. Great video about this topic is on the "TED" youtube channel. Heres a link.
If we would have developed on the mars we know, i guess we wouldn't have differnet lungs, since the air on mars is very differnet from earths, we would probably only consist of 5% water, this is a technique of some microbes to sustain extreme tempertatures ranging from -1K to 420K degrees.
They can withstand temperature ranges from 1 K (−458 °F; −272 °C) (close to absolute zero) to about 420 K (300 °F; 150 °C)
EDIT 1: Since gravity on mars is about a third of earths (0.376 g), we would have less muscles, but in return could be taller since the blood needs less energy to travel greater vertical distances. This also goes for trees and animals, i suspect trees could grow much higher since gravity wouldnt effect them in the way it does on earth, though this is only true if the trees, animals, and humans can adapt to the other envoiremental circumstances like extreme cold, etc. Interesting though is the fact that mars, despite beeing a dessert, is rather cold than hot "min: −143 °C avrg:−63 °C max:35 °C". The seasons on mars are pretty similar to earths, just about twice as long. The Seasonsonal as well as the day-night differences would be tremendous though, because without an atmosphere and without water, warmth is not really "stored" so every night or winter will be way coulder then a day or a summer and transitions would be rather quick, somthing like -6 o'clock :25°C - 7 o'clock: -10°C-. Yet another pretty big difference between earth and mars is the atmospheric pressure which is about 100 times lower than earths, i dont quite know how this would affect us though... Also birds would not be able to coordinate theyre flight and we wouldnt use compasses since mars has no magnetic field. A big roblem would be the periodic sandstorms, which we could maybe compensate with some form of non-visual orientation, or our eyes would be adaptet to sandstorms in another way. Civilisation could be focused around the polar caps, since they contain ice (thus water) maybe, travelling from north to southpole would be considered a difficult journey?
Great topic btw, if you are writing a story or sth along these lines, let me know ;) Hope this helps^^; ~Jan
• Guess i shouldve read th whole question huh? Whatever, it was fun to think about^^ – tankman175 Oct 2 '16 at 22:07
• In the case of seeing in sandstorms, they likely will have nictitating membranes aka transparent eyelids (camels have these). – Anketam Oct 2 '16 at 23:32
• Oh wow, yes that seems very likely. Gotta admit, biology is awesome. – tankman175 Oct 4 '16 at 19:02
• Thanks Anketam! :D Also tankman175, I am doing a story type thing about it, its called Beyond Humanity and its on my deviantart: inkgink.deviantart.com/journal/… – InkGink Oct 4 '16 at 22:15
• Oh so your are a fellow from deviantart! Ill make sure to read your story as soon as i find the time :D – tankman175 Oct 6 '16 at 21:14
Here are some of the possible effects.
1- Lower gravity: thinner bones (starting with the settler themselves)
2- Lower gravity: taller heights (starting after a couple of generations)
3- Lower gravity: lesser muscle mass (starting with the settlers themselves)
4- Thinner atmosphere: larger lungs (starting after a couple of generations)
5- Thinner atmosphere: weaker hearts (starting with the 2nd generation)
6- Lower gravity: weaker immunity (starting with the settlers themselves)
7- Lack of minerals in food: weaker physique, increase in chances of severe illness and death (starting with the 2nd generation)
8- CCl$_4$ in the dust: body wastes away to a slow, agonizing death (starting with the settlers themselves)
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2020-01-21 03:04:50
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https://zbmath.org/?q=an:0873.11036
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# zbMATH — the first resource for mathematics
Explicit $$4$$-descents on an elliptic curve. (English) Zbl 0873.11036
From the authors’ introduction: “The authors investigate how to find generators of an elliptic curve $$E (\mathbb{Q})$$ modulo $$2E (\mathbb{Q})$$ defined over $$\mathbb{Q}$$. As is usual, they can reduce this to the study of a certain homogeneous space $y^2= f(x,1), \tag{1}$ where $$f(X,Z)$$ is a binary quartic form with integer coefficients. One wishes to know whether equation (1) has a $$\mathbb{Q}$$-rational point and if so to exhibit one. One can often show that equation (1) has no $$\mathbb{Q}$$-rational point by local methods. However, even if (1) is everywhere locally soluble, it does not follow necessarily that a $$\mathbb{Q}$$-rational point exists; this failure of the “Hasse principle” is well-known and gives rise to an element of the Tate-Shafarevich group.”
The difficulty in practice arises therefore when a homogeneous space is everywhere locally soluble, but we cannot decide whether or not a $$\mathbb{Q}$$-rational point exists on it; this may happen either because such a point does not actually exist but we have serious difficulties in proving this fact, or because it does exist, but has a very large height (which means that it is impossible to discover this point by brute force computations). To deal with such troublesome homogeneous spaces, the authors consider further descent on equation (1) and propose an explicit method suitable for machine calculation. We quote again from the Introduction:
“This has been done before in the literature for special types of elliptic curves. However, we could find no general account which was of use for systematic machine computations. We explain an explicit method for performing such further descent and we show this is equivalent to constructing elements of order dividing 4 in the Tate-Shafarevich group of the elliptic curve.”
After the whole method is developed (in which some sophistication is, probably, unavoidable), the paper ends up with a section, labeled “Examples”. This occupies less than one page and contains just one example with as few details as possible. In the reviewer’s opinion, this is a drawback of the paper.
##### MSC:
11G05 Elliptic curves over global fields 14H52 Elliptic curves 11Y16 Number-theoretic algorithms; complexity
Full Text:
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2021-08-01 09:32:36
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http://www.freemathhelp.com/forum/archive/index.php/t-44665.html
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PDA
View Full Version : Help with simplifying 2/x^2 + 3/x + 1/x + 2
LMande
07-07-2006, 11:19 PM
2/x^2 + 3/x + 1/x+2
I'm supposed to add then simplify.
This is what I have so far..
I factored the denominator since it's an exponent.
2/(x+2)(x+1) + 3/x + 1/x+2
Is the common denominator X or x + 2 or am I WAY off?
Any help would be greatly appreciated.
stapel
07-08-2006, 12:35 AM
What you have posted means the following:
. . . . .\L \frac{2}{x^2}\,+\,\frac{3}{x} \,+\,\frac{1}{x}\,+\,2
Is this what you meant? Or did you mean the following:
. . . . .\L \frac{2}{x^2}\,+\,\frac{3}{x}\,+\, \frac{1}{x\,+\,2}
...or something else?
Also, are you using "X" and "x" to mean the same thing? (This would be contrary to mathematical practice, is why I ask.)
Thank you.
Eliz.
Denis
07-08-2006, 01:31 AM
Whoops...hit submit button twice :(
Denis
07-08-2006, 01:35 AM
2/x^2 + 3/x + 1/x+2
I'm supposed to add then simplify.
This is what I have so far..
I factored the denominator since it's an exponent.
2/(x+2)(x+1) + 3/x + 1/x+2
Is the common denominator X or x + 2 or am I WAY off?
Any help would be greatly appreciated.
Assuming you meant: 2/x^2 + 3/x + 1/(x+2) : that set of brackets is IMPORTANT
How in heck did you change x^2 to (x+2)(x+1) ?
(x+2)(x+1) = x^2 + 3x + 2 :shock:
Tuff luck: common denominator is x(x^2)(x+2)
[2(x(x+2)) + 3(x^2(x+2) + 1(x(x^2)] / [x(x^2)(x+2)]
Multiply 'em out, then simplify.
LMande
07-08-2006, 11:31 AM
Okay...
Eliz... it's the second one, but when I realized what it looks like typed out right it should be
(2/x^2 + 2x) + (3/x) + (1/x+2)
I hope I'm typing this in right. I'm really having a hard time "translating" this in computer language!!!
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2014-03-08 20:16:16
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https://www.researchgate.net/scientific-contributions/G-Stenborg-9001270
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G. Stenborg's research while affiliated with Johns Hopkins University and other places
Publications (160)
Article
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Although coronal mass ejections (CMEs) resembling flux ropes generally expand self-similarly, deformations along their fronts have been reported in observations and simulations. We present evidence of one CME becoming deformed after a period of self-similar expansion in the corona. The event was observed by multiple white-light imagers on 2021 Janu...
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The Wide-field Imager for Solar Probe (WISPR) onboard Parker Solar Probe (PSP), observing in white light, has a fixed angular field of view, extending from 13.5∘ to 108∘ from the Sun and approximately 50∘ in the transverse direction. In January 2021, on its seventh orbit, PSP crossed the heliospheric current sheet (HCS) near perihelion at a distanc...
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Although coronal mass ejections (CMEs) resembling flux ropes generally expand self-similarly, deformations along their fronts have been reported in observations and simulations. We present evidence of one CME becoming deformed after a period of self-similarly expansion in the corona. The event was observed by multiple white-light imagers on January...
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The Wide-field Imager for Solar Probe (WISPR) onboard Parker Solar Probe (PSP), observing in white light, has a fixed angular field of view, extending from 13.5 degree to 108 degree from the Sun and approximately 50 degree in the transverse direction. In January 2021, on its seventh orbit, PSP crossed the heliospheric current sheet (HCS) near perih...
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We present an update to the first white-light detections of a dust trail observed closely following the orbit of asteroid (3200) Phaethon, as seen by the Wide-field Imager for the Parker Solar Probe instrument on the NASA Parker Solar Probe mission. Here, we provide a summary and analysis of observations of the dust trail over nine separate mission...
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Context. Recurrent, arc-shaped intensity disturbances were detected by extreme-ultraviolet channels in an active region. The fronts were observed to propagate along a coronal loop bundle rooted in a small area within a sunspot umbra. Previous works have linked these intensity disturbances to slow magnetoacoustic waves that propagate from the lower...
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The closest perihelion pass of Parker Solar Probe (PSP), so far, occurred between 2021 November 16 and 26 and reached ∼13.29 R ☉ from Sun center. This pass resulted in very unique observations of the solar corona by the Wide-field Instrument for Solar PRobe (WISPR). WISPR observed at least 10 coronal mass ejections (CMEs), some of which were so clo...
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Full-text available
Recurrent, arc-shaped intensity disturbances were detected by EUV channels in an active region. The fronts were observed to propagate along a coronal loop bundle rooted in a small area within a sunspot umbra. Previous works have linked these intensity disturbances to slow magnetoacoustic waves that propagate from the lower atmosphere to the corona...
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Full-text available
The closest perihelion pass of Parker Solar Probe (PSP), so far, occurred between 16 and 26 of November 2021 and reached ~13.29 Rsun from Sun center. This pass resulted in very unique observations of the solar corona by the Wide-field Instrument for Solar PRobe (WISPR). WISPR observed at least ten CMEs, some of which were so close that the structur...
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Full-text available
We present an update to the first white-light detections of a dust trail observed closely following the orbit of asteroid (3200) Phaethon, as seen by the Wide-field Imager for Parker Solar Probe (WISPR) instrument on the NASA Parker Solar Probe (PSP) mission. Here we provide a summary and analysis of observations of the dust trail over nine separat...
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We present the fine structure of the inner solar corona between 1.65 and 3.0 solar radii as revealed by the STEREO-A COR1 white-light coronagraph from 2008 June 20 to July 31. The COR1 imaging data were wavelet processed to enhance the intensity contrast of coronal features. The constructed limb synoptic maps at a range of altitudes show the evolut...
Article
We analyze the formation and three-dimensional (3D) evolution of two coronal mass ejections (CMEs) and their associated waves in the low corona via a detailed multi-viewpoint analysis of extreme-ultraviolet observations. We analyze the kinematics in the radial and lateral directions and identify three stages in the early evolution of the CME: (1) a...
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Visible light observations from the Wide-field Imager for Solar PRobe (WISPR) aboard the Parker Solar Probe (PSP) mission offer a unique opportunity to study the dust environment near the Sun. The existence of a dust-free zone (DFZ) around stars was postulated almost a century ago. Despite numerous attempts to detect it from as close as 0.3 au, obs...
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The Parker Solar Probe mission (PSP) has completed seven orbits around the Sun. The Wide-field Imager for Solar Probe (WISPR) on PSP consists of two visible light heliospheric imagers, which together image the interplanetary medium between 13.°5 and 108° elongation. The PSP/WISPR nominal science observing window occurs during the solar encounters,...
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Preprint
Slow waves are commonly observed on the entire solar atmosphere. Assuming a thin flux tube approximation, the cut-off periods of slow-mode magneto-acoustic-gravity waves that travel from the photosphere to the corona were obtained in Costa et al. (2018). In that paper, however, a typo in the specific heat coefficient at constant pressure $c_{\mathr... Preprint Full-text available The Wide-field Imager for Parker Solar Probe (WISPR) captures unprecedented white-light images of the solar corona and inner heliosphere. Thanks to the uniqueness of Parker Solar Probe's (PSP) orbit, WISPR is able to image locally'' coronal structures at high spatial and time resolutions. The observed plane of sky, however, rapidly changes becaus... Article Full-text available During its first solar encounter, the Parker Solar Probe (PSP) acquired unprecedented up-close imaging of a small Coronal Mass Ejection (CME) propagating in the forming slow solar wind. 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The characterization of these faint white-light structures gives us insight on the origin and acceleration of the slow solar wind. The vantage observing points provided by the SECCHI and LASCO instruments... Article The white-light STEREO/SECCHI images include light scattered by dust in orbit about the Sun (the F-corona). We analyzed the evolution of the symmetry axis of the F-corona between 2007 and 2012 in the elongation range covered by the STEREO-A/HI-1 instrument (4°–24° elongation) to characterize the plane of symmetry of the zodiacal dust cloud. The sym... Article Full-text available Coronal mass ejection (CME) events are among the main drivers of geomagnetic disturbances, and hence play a central role in the Sun–Earth system. Their monitoring and, in particular, the determination of their speed and direction of propagation are key issues for the forecasting of space weather near to Earth. We have implemented a method to track... Article We present the analysis of an unusual failed eruption captured in high cadence and in many wavelengths during the observing campaign in support of the VAULT2.0 sounding rocket launch. The refurbished Very high Angular resolution Ultraviolet Telescope (VAULT2.0) is a Ly$\alpha$($\lambda\$ 1216 \AA) spectroheliograph launched on September 30, 2014. T...
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White-light coronal and heliospheric imagers observe scattering of photospheric light from both dust particles (the F-Corona) and free electrons in the corona (the K-corona). The separation of the two coronae is thus vitally important to reveal the faint K-coronal structures (e.g., streamers, co-rotating interaction regions, coronal mass ejections,...
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Very high angular resolution ultraviolet telescope (VAULT2.0) is a Lyman-alpha (Lyα; 1216Å) spectroheliograph designed to observe the upper chromospheric region of the solar atmosphere with high spatial (<0.5′′) and temporal (8s) resolution. Besides being the brightest line in the solar spectrum, Lyα emission arises at the temperature interface bet...
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High-quality white-light images from the SECCHI/HI-1 telescope onboard STEREO-B reveal high-velocity evanescent clumps [HVECs] expelled from the coma of the C/2011 L4 [Pan-STARRS] comet. Animated images provide evidence of highly dynamic ejecta moving near-radially in the anti-sunward direction. The bulk speed of the clumps at their initial detecti...
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To contribute to the understanding of the physical mechanisms at work during the initial phase and early evolution of erupting prominences, we analyze combined observations from ground-based and space-borne instruments. We present two case studies, which occurred at two different phases of the solar cycle, namely on March 2, 2002 and on April 16, 2...
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We report on the role of small-scale, transient magnetic activity in the formation and evolution of solar coronal plumes. Three plumes within equatorial coronal holes are analyzed over the span of several days based on the Solar Dynamic Observatory (SDO)/Atmospheric Imaging Assembly 171 Å and 193 Å images and SDO/Helioseismic and Magnetic Imager li...
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The white light coronagraphs onboard SOHO (LASCO-C2 and -C3) and most recently STEREO (SECCHI -COR1 and -COR2) have detected a myriad of coronal mass ejections (CME). They are a key component of space weather and under certain conditions they can become geo-effective, hence the importance of their kinematic characterization to help predict their ef...
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2022-12-08 06:52:27
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https://hal.inria.fr/lirmm-01347027v2
|
Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable
2 G-SCOP_OC - OC
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
4 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : For planar graphs, we consider the problems of list edge coloring and list total coloring. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors. Total coloring is the problem of coloring the edges and the vertices while ensuring that two edges that are adjacent, two vertices that are adjacent, or a vertex and an edge that are incident receive different colors. In their list extensions, instead of having the same set of colors for the whole graph, every vertex or edge is assigned some set of colors and has to be colored from it. A graph is minimally edge or total choosable if it is list $\Delta$-edge-colorable or list $(\Delta +1)$-total-colorable, respectively, where $\Delta$ is the maximum degree in the graph. It is already known that planar graphs with $\Delta \geq 8$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable (Li Xu 2011), and that planar graphs with $\Delta \geq 7$ and no triangle sharing a vertex with a $C_4$ or no triangle adjacent to a $C_k (\forall 3 \leq k \leq 6)$ are minimally total colorable (Wang Wu 2011). We strengthen here these results and prove that planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable.
Keywords :
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.131-146
Domaine :
https://hal.inria.fr/lirmm-01347027
Contributeur : Coordination Episciences Iam <>
Soumis le : mardi 16 août 2016 - 17:08:10
Dernière modification le : jeudi 11 janvier 2018 - 06:27:28
Fichier
2586-9917-1-PB.pdf
Accord explicite pour ce dépôt
Identifiants
• HAL Id : lirmm-01347027, version 2
Citation
Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou. Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.131-146. 〈lirmm-01347027v2〉
Métriques
Consultations de la notice
191
Téléchargements de fichiers
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2018-01-21 03:17:09
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https://www.freemathhelp.com/forum/threads/i-don%E2%80%99t-really-know-where-to-put-this-under-please-help-6-25-38-7-33-93.113065/
|
#### Whackyballoon
##### New member
Hi this is probably really simple but if could some one could help this would be nice
6.25 -38 = 7-33.93
they are just ratios but I would like to know what the second unit should be if the first number is 9
eg 9-xxx = 6.25-38= 7-33.93
#### lev888
##### Junior Member
Ratios? Do you mean 6.25/38 = 7/33.93? Doesn't look right to me. Please verify and post your work.
#### Dr.Peterson
##### Elite Member
Hi this is probably really simple but if could some one could help this would be nice
6.25 -38 = 7-33.93
they are just ratios but I would like to know what the second unit should be if the first number is 9
eg 9-xxx = 6.25-38= 7-33.93
It would be really helpful if you explained the context; what you wrote means nothing, but knowing where the numbers come from could help us see what is really going on.
I'm guessing these are meant to be pairs of numbers from a table, like
Code:
6.25 38
7 33.93
9 ???
But I observe that 6.25 × 38 = 7 × 33.93, both being (about) 237.5. (presumably 33.93 is a rounded number, accounting for the slight difference.) So this is an inverse proportion (where the products are equal), not a direct proportion (in which the ratios would be equal). Your hyphens, which look as if they were subtractions, really get in the way of understanding.
Now you want to find a ??? such that 9 × ??? is also equal to 237.5. Can you do that?
#### JeffM
##### Elite Member
Hi this is probably really simple but if could some one could help this would be nice
6.25 -38 = 7-33.93
they are just ratios but I would like to know what the second unit should be if the first number is 9
eg 9-xxx = 6.25-38= 7-33.93
You have not got any helpful answers because (a) you have not done anything that we ask that you do before posting, and (b) your question makes no sense. You say your question is about ratios, but your equation seems to involve subtraction. Did you know that ratios are usually writen either as fractions or using colons?
I am guessing that you are saying 6.25 : 7 :: 33.93 : 38 or, what is the same thing, 6/7 = 33.93/38.
If that guess is right, I should point out that ratios are usually shown with positive integers so the normal way to express this is 625/700 = 3393/3800. More importantly, it is only APPROXIMATELY true.
$$\displaystyle \dfrac{3393}{3800} = 0.8928947 \ne 0.8928571 = \dfrac{625}{700}.$$
Now if I am anywhere close to what you are talking about, let us know. And, given that you posted this in intermediate algebra, is your question
$$\displaystyle \dfrac{625}{700} \approx \dfrac{x}{900} \text { or } \dfrac{625}{700} \approx \dfrac{900}{x} \text {?}$$
EDIT: I see that while I was writing, Dr. Peterson made a guess similar to mine but probably more complete. Please answer our questions so we can be more helpful.
Last edited:
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2019-04-20 06:26:06
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https://rubrix.readthedocs.io/en/master/tutorials/01-labeling-finetuning.html
|
# 🏷️ Label your data to fine-tune a classifier with Hugging Face#
In this tutorial, we’ll build a sentiment classifier for user requests in the banking domain as follows:
• 🏁 Start with the most popular sentiment classifier on the Hugging Face Hub (almost 4 million monthly downloads as of December 2021) which has been fine-tuned on the SST2 sentiment dataset.
• 🏷️ Label a training dataset with banking user requests starting with the pre-trained sentiment classifier predictions.
• ⚙️ Fine-tune the pre-trained classifier with your training dataset.
• 🏷️ Label more data by correcting the predictions of the fine-tuned model.
• ⚙️ Fine-tune the pre-trained classifier with the extended training dataset.
## Introduction#
This tutorial will show you how to fine-tune a sentiment classifier for your own domain, starting with no labeled data.
Most online tutorials about fine-tuning models assume you already have a training dataset. You’ll find many tutorials for fine-tuning a pre-trained model with widely-used datasets, such as IMDB for sentiment analysis.
However, very often what you want is to fine-tune a model for your use case. It’s well-known that NLP model performance usually degrades with “out-of-domain” data. For example, a sentiment classifier pre-trained on movie reviews (e.g., IMDB) will not perform very well with customer requests.
This is an overview of the workflow we’ll be following:
Let’s get started!
## Setup#
Rubrix, is a free and open-source tool to explore, annotate, and monitor data for NLP projects.
If you are new to Rubrix, check out the Github repository ⭐.
If you have not installed and launched Rubrix, check the Setup and Installation guide.
In this tutorial, we’ll use the transformers, datasets and sklearn libraries. We’ll also install ipwidgets for training progress bars.
[ ]:
%pip install transformers[torch] datasets sklearn ipywidgets -qqq
## Preliminaries#
For building our fine-tuned classifier we’ll be using two main resources, both available in the 🤗 Hub :
1. A dataset in the banking domain: banking77
2. A pre-trained sentiment classifier: distilbert-base-uncased-finetuned-sst-2-english
### Dataset: Banking 77#
This dataset contains online banking user queries annotated with their corresponding intents.
In our case, we’ll label the sentiment of these queries. This might be useful for digital assistants and customer service analytics.
Let’s load the dataset directly from the hub and split the dataset into two 50% subsets. We’ll start with the to_label1 split for data exploration and annotation, and keep to_label2 for further iterations.
[ ]:
from datasets import load_dataset
to_label1, to_label2 = banking_ds['train'].train_test_split(test_size=0.5, seed=42).values()
### Model: sentiment distilbert fine-tuned on sst-2#
As of December 2021, the distilbert-base-uncased-finetuned-sst-2-english is in the top five of the most popular text-classification models in the Hugging Face Hub.
This model is a distilbert model fine-tuned on SST-2 (Stanford Sentiment Treebank), a highly popular sentiment classification benchmark.
As we will see later, this is a general-purpose sentiment classifier, which will need further fine-tuning for specific use cases and styles of text. In our case, we’ll explore its quality on banking user queries and build a training set for adapting it to this domain.
Let’s load the model and test it with an example from our dataset:
[3]:
from transformers import pipeline
sentiment_classifier = pipeline(
model="distilbert-base-uncased-finetuned-sst-2-english",
return_all_scores=True,
)
to_label1[3]['text'], sentiment_classifier(to_label1[3]['text'])
[3]:
('Hi, Last week I have contacted the seller for a refund as directed by you, but i have not received the money yet. Please look into this issue with seller and help me in getting the refund.',
[[{'label': 'NEGATIVE', 'score': 0.9934700727462769},
{'label': 'POSITIVE', 'score': 0.0065299225971102715}]])
The model assigns more probability to the NEGATIVE class. Following our annotation policy (read more below), we’ll label examples like this as POSITIVE as they are general questions, not related to issues or problems with the banking application. The ultimate goal will be to fine-tune the model to predict POSITIVE for these cases.
### A note on sentiment analysis and data annotation#
Sentiment analysis is one of the most subjective tasks in NLP. What we understand by sentiment will vary from one application to another and depend on the business objectives of the project. Also, sentiment can be modeled in different ways, leading to different labeling schemes. For example, sentiment can be modeled as real value (going from -1 to 1, from 0 to 1.0, etc.) or with 2 or more labels (including different degrees such as positive, negative, neutral, etc.)
For this tutorial, we’ll use the original labeling scheme defined by the pre-trained model which is composed of two labels: POSITIVE and NEGATIVE. We could have added the NEUTRAL label, but let’s keep it simple.
Another important issue when approaching a data annotation project are the annotation guidelines, which explain how to assign the labels to specific examples. As we’ll see later, the messages we’ll be labeling are mostly questions with a neutral sentiment, which we’ll label with the POSITIVE label, and some other are negative questions which we’ll label with the NEGATIVE label. Later on, we’ll show some examples of each label.
## 1. Run the pre-trained model over the dataset and log the predictions#
As a first step, let’s use the pre-trained model for predicting over our raw dataset. For this, we will use the handy dataset.map method from the datasets library.
The following steps could be simplified by using the auto-monitor support for Hugging Face pipelines. You can find more details in the Monitoring guide.
### Predict#
[ ]:
def predict(examples):
return {"predictions": sentiment_classifier(examples['text'], truncation=True)}
# add .select(range(10)) before map if you just want to test this quickly with 10 examples
to_label1 = to_label1.map(predict, batched=True, batch_size=4)
Note
If you don’t want to run the predictions yourself, you can also load the records with the predictions directly from the Hugging Face Hub: load_dataset("rubrix/sentiment-banking", split="train"), see below for more details.
### Create records#
The following code builds a list of Rubrix records with the predictions.
[ ]:
import rubrix as rb
records = []
for example in to_label1.shuffle():
record = rb.TextClassificationRecord(
text=example["text"],
metadata={'category': example['label']}, # log the intents for exploration of specific intents
prediction=[(pred['label'], pred['score']) for pred in example['predictions']],
prediction_agent="distilbert-base-uncased-finetuned-sst-2-english"
)
records.append(record)
Before logging the records to Rubrix, we will upload them to the Hugging Face Hub. In this way we save a version of them with the predictions, so the next time we do this tutorial, we don’t have to run the pre-trained model again. You can do the same, once you annotated the dataset to effectively version your complete records.
[ ]:
dataset_rb = rb.DatasetForTextClassification(records)
dataset_ds = dataset_rb.to_datasets()
dataset_ds.push_to_hub("rubrix/sentiment-banking")
After pushing the dataset to the hub, you can simply retrieve it via load_dataset and rb.read_datasets.
[ ]:
dataset_ds = load_dataset("rubrix/sentiment-banking", split="train")
### Log#
Now let’s log the records to Rubrix to explore the dataset and label our first training set.
[ ]:
rb.log(name='labeling_with_pretrained', records=dataset_rb)
## 2. Explore and label data with the pretrained model#
In this step, we’ll start by exploring how the pre-trained model is performing with our dataset.
At first sight:
• The pre-trained sentiment classifier tends to label most of the examples as NEGATIVE (4.835 of 5.001 records). You can see this yourself using the Predictions / Predicted as: filter
• Using this filter and filtering by predicted as POSITIVE, we see that examples like “I didn’t withdraw the amount of cash that is showing up in the app.” are not predicted as expected (according to our basic “annotation policy” described in the preliminaries).
Taking into account this analysis, we can start labeling our data.
Rubrix provides you with a search-driven UI to annotated data, using free-text search, search filters and the Elasticsearch query DSL for advanced queries. This is especially useful for sparse datasets, tasks with a high number of labels, or unbalanced classes. In the standard case, we recommend you to follow the workflow below:
1. Start labeling examples sequentially, without using search features. This way you will annotate a fraction of your data which will be aligned with the dataset distribution.
2. Once you have a sense of the data, you can start using filters and search features to annotate examples with specific labels. In our case, we’ll label examples predicted as POSITIVE by our pre-trained model, and then a few examples predicted as NEGATIVE.
### Labeling POSITIVE examples#
After some minutes, we’ve labelled almost 5% of our raw dataset with more than 200 annotated examples, which is a small dataset but should be enough for a first fine-tuning of our banking sentiment classifier:
## 3. Fine-tune the pre-trained model#
In this step, we’ll load our training set from Rubrix and fine-tune using the Trainer API from Hugging Face transformers. For this, we closely follow the guide Fine-tuning a pre-trained model from the transformers docs.
First, let’s load the annotations from our dataset using the query parameter from the load method. The Validated status corresponds to annotated records.
[47]:
rb_dataset = rb.load(name='labeling_with_pretrained', query="status:Validated")
[47]:
inputs prediction prediction_agent annotation annotation_agent multi_label explanation id metadata status event_timestamp metrics search_keywords
0 {'text': 'I would like to cancel a purchase.'} [(NEGATIVE, 0.9997695088386536), (POSITIVE, 0.... distilbert-base-uncased-finetuned-sst-2-english POSITIVE rubrix False None 0002cbd9-b687-462a-bbd2-3130f4c88d8d {'category': 52} Validated None None None
1 {'text': 'What's up with the extra fee I got?'} [(NEGATIVE, 0.9968097805976868), (POSITIVE, 0.... distilbert-base-uncased-finetuned-sst-2-english NEGATIVE rubrix False None 0009f445-4844-4ccd-9ea8-207a1fb0e239 {'category': 19} Validated None None None
2 {'text': 'Do you have an age requirement when ... [(NEGATIVE, 0.9825802445411682), (POSITIVE, 0.... distilbert-base-uncased-finetuned-sst-2-english POSITIVE rubrix False None 0012e385-643c-4660-ad66-5b4339bb3999 {'category': 1} Validated None None None
### Prepare training and test datasets#
Let’s now prepare our dataset for training and testing our sentiment classifier, using the datasets library:
[ ]:
# create 🤗 dataset with labels as numeric ids
train_ds = rb_dataset.prepare_for_training()
[ ]:
from transformers import AutoTokenizer
# tokenize our datasets
tokenizer = AutoTokenizer.from_pretrained("distilbert-base-uncased-finetuned-sst-2-english")
def tokenize_function(examples):
tokenized_train_ds = train_ds.map(tokenize_function, batched=True)
[ ]:
# split the data into a training and evaluation set
train_dataset, eval_dataset = tokenized_train_ds.train_test_split(test_size=0.2, seed=42).values()
### Train our sentiment classifier#
As we mentioned before, we’re going to fine-tune the distilbert-base-uncased-finetuned-sst-2-english model. Another option will be fine-tuning a distilbert masked language model from scratch, but we leave this experiment to you.
[ ]:
from transformers import AutoModelForSequenceClassification
model = AutoModelForSequenceClassification.from_pretrained("distilbert-base-uncased-finetuned-sst-2-english")
Let’s configure the Trainer:
[ ]:
import numpy as np
from transformers import Trainer
from transformers import TrainingArguments
training_args = TrainingArguments(
"distilbert-base-uncased-sentiment-banking",
evaluation_strategy="epoch",
logging_steps=30,
)
def compute_metrics(eval_pred):
logits, labels = eval_pred
predictions = np.argmax(logits, axis=-1)
return metric.compute(predictions=predictions, references=labels)
trainer = Trainer(
args=training_args,
model=model,
train_dataset=train_dataset,
eval_dataset=eval_dataset,
compute_metrics=compute_metrics,
)
And finally, we can train our first model!
[ ]:
trainer.train()
## 4. Testing the fine-tuned model#
In this step, let’s first test the model we have just trained.
Let’s create a new pipeline with our model:
[ ]:
finetuned_sentiment_classifier = pipeline(
model=model.to("cpu"),
tokenizer=tokenizer,
return_all_scores=True
)
Then, we can compare its predictions with the pre-trained model and an example:
[ ]:
finetuned_sentiment_classifier(
'I need to deposit my virtual card, how do i do that.'
), sentiment_classifier(
'I need to deposit my virtual card, how do i do that.'
)
As you can see, our fine-tuned model now classifies this general questions (not related to issues or problems) as POSITIVE, while the pre-trained model still classifies this as NEGATIVE.
Let’s check now an example related to an issue where both models work as expected:
[ ]:
finetuned_sentiment_classifier(
'Why is my payment still pending?'
), sentiment_classifier(
'Why is my payment still pending?'
)
## 5. Run our fine-tuned model over the dataset and log the predictions#
Let’s now create a dataset from the remaining records (those which we haven’t annotated in the first annotation session).
We’ll do this using the Default status, which means the record hasn’t been assigned a label.
[ ]:
rb_dataset = rb.load(name='labeling_with_pretrained', query="status:Default")
From here, this is basically the same as step 1, in this case using our fine-tuned model:
Let’s take advantage of the datasets map feature, to make batched predictions.
[ ]:
def predict(examples):
texts = [example["text"] for example in examples["inputs"]]
return {
"prediction": finetuned_sentiment_classifier(texts),
"prediction_agent": ["distilbert-base-uncased-banking77-sentiment"]*len(texts)
}
ds_dataset = rb_dataset.to_datasets().map(predict, batched=True, batch_size=8)
Afterward, we can convert the dataset directly to Rubrix records again and log them to the web app.
[ ]:
records = rb.read_datasets(ds_dataset, task="TextClassification")
rb.log(records=records, name='labeling_with_finetuned')
## 6. Explore and label data with the fine-tuned model#
In this step, we’ll start by exploring how the fine-tuned model is performing with our dataset.
At first sight, using the predicted as filter by POSITIVE and then by NEGATIVE, we can observe that the fine-tuned model predictions are more aligned with our “annotation policy”.
Now that the model is performing better for our use case, we’ll extend our training set with highly informative examples. A typical workflow for doing this is as follows:
1. Use the prediction score filter for labeling uncertain examples.
2. Label examples predicted by our fine-tuned model as POSITIVE and then predicted as NEGATIVE to correct the predictions.
After spending some minutes, we labelled almost 2% of our raw dataset with around 80 annotated examples, which is a small dataset but hopefully with highly informative examples.
## 7. Fine-tuning with the extended training dataset#
In this step, we’ll add the new examples to our training set and fine-tune a new version of our banking sentiment classifier.
### Adding labeled examples to our previous training set#
Let’s add our new examples to our previous training set.
[ ]:
rb_dataset = rb.load("labeling_with_finetuned")
train_ds = rb_dataset.prepare_for_training()
tokenized_train_ds = train_ds.map(tokenize_function, batched=True)
[ ]:
from datasets import concatenate_datasets
train_dataset = concatenate_datasets([train_dataset, tokenized_train_ds])
### Training our sentiment classifier#
As we want to measure the effect of adding examples to our training set we will:
• Fine-tune from the pre-trained sentiment weights (as we did before)
• Use the previous test set and the extended train set (obtaining a metric we use to compare this new version with our previous model)
[ ]:
from transformers import AutoModelForSequenceClassification
model = AutoModelForSequenceClassification.from_pretrained("distilbert-base-uncased-finetuned-sst-2-english")
[ ]:
train_ds = train_dataset.shuffle(seed=42)
trainer = Trainer(
args=training_args,
model=model,
train_dataset=train_dataset,
eval_dataset=eval_dataset,
compute_metrics=compute_metrics,
)
trainer.train()
[ ]:
model.save_pretrained("distilbert-base-uncased-sentiment-banking")
## Summary#
In this tutorial, you learned how to build a training set from scratch with the help of a pre-trained model, performing two iterations of predict > log > label.
Although this is somehow a toy example, you will be able to apply this workflow to your own projects to adapt existing models or building them from scratch.
In this tutorial, we’ve covered one way of building training sets: hand labeling. If you are interested in other methods, which could be combined with hand labeling, checkout the following:
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2022-12-05 11:38:37
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https://www.sparrho.com/item/measurement-of-dollarv0dollar-production-ratios-in-dollarppdollar-collisions-at-dollarsqrts-09dollar-and-7tev/89f87e/
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# Measurement of $V^0$ production ratios in $pp$ collisions at $\sqrt{s} = 0.9$ and 7\,TeV
Research paper by LHCb Collaboration, R. Aaij, B. Adeva, M. Adinolfi, C. Adrover, A. Affolder, Z. Ajaltouni, J. Albrecht, F. Alessio, M. Alexander, G. Alkhazov, P. Alvarez Cartelle, A. A. Alves, S. Amato, Y. Amhis, et al.
Indexed on: 13 Jul '11Published on: 13 Jul '11Published in: High Energy Physics - Experiment
#### Abstract
The $\bar{\Lambda} / \Lambda$ and $\bar{\Lambda} / K^0_\mathrm{S}$ production ratios are measured by the LHCb detector from $0.3\,\mathrm{nb}^{-1}$ of $pp$ collisions delivered by the LHC at $\sqrt{s} = 0.9$\,TeV and $1.8\,\mathrm{nb}^{-1}$ at $\sqrt{s} = 7$\,TeV. Both ratios are presented as a function of transverse momentum, $p_\mathrm{T}$, and rapidity, $y$, in the ranges {$0.15 < p_\mathrm{T} < 2.50\,\mathrm{GeV}/c$} and {$2.0<y<4.5$}. Results at the two energies are in good agreement as a function of rapidity loss, $\Delta y = y_\mathrm{beam} - y$, and are consistent with previous measurements. The ratio $\bar{\Lambda} / \Lambda$, measuring the transport of baryon number from the collision into the detector, is smaller in data than predicted in simulation, particularly at high rapidity. The ratio $\bar{\Lambda} / K^0_\mathrm{S}$, measuring the baryon-to-meson suppression in strange quark hadronisation, is significantly larger than expected.
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2021-06-23 15:44:55
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https://analystprep.com/study-notes/cfa-level-2/using-p-es-to-obtain-terminal-value-in-multistage-dividend-discount-models/
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# Using P/Es to Obtain Terminal Value in Multistage Dividend Discount Models
When estimating the terminal value, analysts use price multiples such as P/Es and P/Bs to estimate terminal values. There are two significant approaches to computing terminal values based on multiples:
### I. Terminal Price Multiples based on Fundamentals
The terminal value is computed as the product of the justified multiple and the estimate of earnings.
\begin{align*}\text{Terminal value}_{\text{n}}&=\text{Justified leading P⁄E}\times \text{Forecasted earnings}_{(\text{n}+1)}\\ \text{Terminal value}_{\text{n}}&=\text{Justified trailing P⁄E}\times \text{Forecasted earnings}_ {(\text{n})}\end{align*}
### ii. Terminal Price Multiples based on Comparables
The terminal value is computed as the product of the benchmark multiple and the estimate of earnings.
\begin{align*}\text{Terminal value}_{\text{n}}&=\text{Benchmark leading P⁄E}\times \text{Forecasted earnings}_{(\text{n}+1)}\\ \text{Benchmark value}_{\text{n}}&=\text{Justified leading P⁄E}\times \text{Forecasted earnings}_ {(\text{n})}\end{align*}
The benchmark value could be the:
• Median industry P/E.
• Average industry P/E.
• Average of own past P/E.
An advantage of the price multiples approach is that it is grounded in market data, unlike the Gordon growth model that is based on multiple estimates and is very sensitive to changes in these estimates.
A disadvantage is that if the benchmark value is mispriced, the estimate of the terminal value will also reflect this mispricing.
#### Example: Estimating Terminal Value
Consider the following information:
$$\small{\begin{array}{l|l}\textbf{Values for subject firm} & \\ \hline\text{Required rate of return} & 10\% \\ \hline\text{EPS forecast in year five} & 1.4\\ \end{array}}$$
$$\small{\begin{array}{l|l}\textbf{Values for peer group} & \\ \hline \text{Mean dividend payout ratio} & 0.35 \\ \hline \text{Mean ROE} & 6\% \\ \hline \text{Median P/E} & 8\\ \end{array}}$$
Using P/Es to determine terminal value using the Gordon Growth model:
\begin{align*}\text{D}_5&= \text{EPS}_5\times\text{Dividend payout ratio}\\&=1.4 \times0.35\\&=0.49\end{align*}
\begin{align*}\text{Retention ratio}&=1-\text{Dividend payout ratio}\\&=1-0.35\\&=0.65\end{align*}
\begin{align*}\text{g}&=\text{Retention ratio} \times\text{ROE}\\&=0.65 ×6\%\\&=3.9\%\end{align*}
\begin{align*}\text{V}_5&=\frac{\text{D}_5(1+\text{g})}{\text{r}-\text{g}}\\&=\frac{0.49(1.039)}{0.10-0.039}\\&=8.35\end{align*}
Using P/Es to determine terminal value using comparables:
\begin{align*}\text{V}_5&= \text{P⁄E}\times\text{EPS}_5\\&=8×1.4\\&=11.20\end{align*}
## Question
Consider the following information:
$$\small{\begin{array}{l|l}\textbf{The required rate of return} & 14\% \\ \hline\text{EPS forecast for year six} & 2.5 \\ \hline\text{ROE} & 7\% \\ \hline\text{Dividend payout ratio} & 30\%\\ \end{array}}$$
The terminal value in year value is closest to:
1. 75.
2. 9.
3. 24.
### Solution
The correct answer is C.
\begin{align*}\text{g}&=\text{Retention ratio}\times\text{ROE}\\ \\ \text{Retention ratio}&=1-\text{Dividend payout ratio}\\ &=1-0.30=0.70\\ \\ \text{g}&=0.70\times0.07\\&=4.9\%\\ \\ \text{D}_6&= 2.5 \times0.30\\&=0.75\\ \\ \text{V}_5&=\frac{0.75}{0.14-0.049}\\&=8.24\end{align*}
Reading 25: Market-Based Valuation: Price and Enterprise Value Multiples
LOS 25 (l) Calculate and explain the use of price multiples in determining terminal value in a multistage discounted cash flow (DCF) model.
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2023-03-23 18:17:02
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https://nigerianscholars.com/past-questions/economics/question/248100/
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Home » » Cross elasticity of demand can be mathematically expressed as the
# Cross elasticity of demand can be mathematically expressed as the
### Question
Cross elasticity of demand can be mathematically expressed as the
### Options
A)
$$\frac{\text{% change in quantity of commodity X}}{\text{% change in quantity of commodity Y}}$$
B)
$$\frac{\text{% change in quantity demanded}}{\text{% change in price}}$$
C)
$$\frac{\text{% change in quantity demanded of commodity X}}{\text{% change in price of commodity Y}}$$
D)
$$\frac{\text{% change in quantity demanded}}{\text{% change in income}}$$
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2022-08-17 00:57:38
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https://math.stackexchange.com/questions/420136/finding-the-major-and-minor-axis-vertices-for-an-ellipse-given-two-conjugate-dia/420153
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# Finding the major and minor axis vertices for an ellipse given two conjugate diameters?
I've been googling, searching forums and looking in my old algebra/trig books to try to understand how to find the end points to the major and minor axis of an ellipse given the end points of two conjugate diameters (assume ellipse centered at the origin). I want to be able to recast an ellipse given that data into a form acceptable for use in an SVG diagram which requires the major(x) and minor(y) axis radii. I can calculate any rotation necessary from the major axis end point.
See for example the below image. I have conjugate points P and Q and need to find (a) and (b). Example showing conjugate points P and Q (I couldn't upload an image(rep !> 10 yet)).
I hope someone here can help shed some light on this for me.
• Do you have any question for which you want to find end points of axis? – iostream007 Jun 14 '13 at 9:56
• Can you just elaborate with the example? – Rusty Jun 14 '13 at 9:59
• Here's how Pappus did it. – David Mitra Jun 14 '13 at 10:12
Perhaps added since this question was answered, Wikipedia has good information on this problem. There is an interesting geometric construction which contrasts with the algebraic solutions offered here: Rytz's construction.
(I have been told to add information to the answer rather than just posting links. Unfortunately as my rep is less than 50 I can't make comments yet)
The setting in which I found Rytz's construction useful was in drawing the elevation of a circle in a plan oblique projection. In this case, as in the other conjugate tangent problems that arise in parallel projection, the ellipse is tangent to the midpoints of the edges of a parallelogram. This is a slightly more constrained and regular situation than the diagram referenced in the original question, though a tangent parallelogram could easily be constructed around the ellipse shown in that image.
Rytz's construction is apparently the last refinement of a long series of solutions to this problem, starting with Pappus. It relies on the fact that conjugate diameters are affine images of perpendicular diameters of a circle. In particular, the perpendiculars from the foci to any tangent intersect the tangent on the auxiliary circle, the circle centered at the centre of the ellipse with the major axis as diameter. As I understand it Rytz's construction is a carefully minimized (in terms of number of steps) derivative of the earlier techniques, intended for practical use in drafting, etc.
So that we're clear on definitions: A pair of diameters of an ellipse are conjugate if (and only if) the tangents at the endpoints of one diameter are parallel to the other diameter.
Let $P(a \cos\theta, b \sin\theta)$ be a point on an ellipse in standard position (for now). The tangent line at $P$ has slope vector $(-a\sin\theta, b\cos\theta)$; because this can be written $(a\cos(\theta+\pi/2), b\sin(\theta+\pi/2))$, we see that it is also the position vector of a point, say $Q$, on the ellipse. The diameter through $P$ is conjugate to the diameter through $Q$.
Therefore, if we have $P(p_x, p_y)$ and $Q(q_x, q_y)$ as endpoints of conjugate diameters of an ellipse in standard position (with $\angle POQ < \pi$ a counterclockwise angle), we can write:
\begin{align} p_x = \phantom{-}a \cos\theta &\qquad p_y = b \sin\theta \\ q_x = -a\sin\theta &\qquad q_y = b\cos\theta \end{align} for some $\theta$, so that $$a^2 = p_x^2 + q_x^2 \qquad\qquad b^2 = p_y^2 + q_y^2 \qquad\qquad (\text{and}\quad p_x q_y - p_y q_x = a b)$$
If the ellipse in question is rotated, things are a little more complicated.
We take $P$ and $Q$ to be the images of $(a\cos\theta, b\sin\theta)$ and $(-a\sin\theta, b\cos\theta)$ under rotation by angle, say, $\phi$. Using an appropriate rotation matrix, we have
\begin{align} p_x = \phantom{-}a \cos\theta \cos\phi - b \sin\theta \sin\phi &\qquad p_y = \phantom{-}a \cos\theta \sin\phi + b \sin\theta \cos\phi \\ q_x = -a \sin\theta \cos\phi - b \cos\theta \sin\phi &\qquad q_y = -a \sin\theta \sin\phi + b \cos\theta \cos\phi \end{align}
These provide relations
\begin{align} p_x^2 + p_y^2 + q_x^2 + q_y^2 &= a^2 + b^2 &=: r \\ p_x q_y - p_y q_x &= a b &=: s \end{align} (The latter actually re-captures a result, cited by Isaac Newton, that all "bounding parallelograms" of an ellipse have the same area.)
Thus, \begin{align} a + b &= \sqrt{a^2 + b^2 + 2 a b} = \sqrt{r + 2 s} \\ |a - b| &= \sqrt{a^2 + b^2 - 2 a b} = \sqrt{r - 2 s} \end{align} so that $$\{a,b\} = \frac{1}{2}\left(\sqrt{r + 2 s} \pm \sqrt{r - 2 s}\right)$$
Taking $a \ge b$, we eliminate the ambiguity: $$a = \frac{1}{2}\left(\sqrt{r+2s} + \sqrt{r-2s}\right) \qquad\qquad b = \frac{1}{2}\left(\sqrt{r+2s} - \sqrt{r-2s}\right)$$
We can (and should) solve for $\theta$ and $\phi$. Start by observing ... \begin{align} p_x^2 + p_y^2 = a^2\cos^2\theta+b^2\sin^2\theta &\qquad q_x^2 + q_y^2 = a^2\sin^2\theta+b^2\cos^2\theta \\ p_x^2 + q_x^2 = a^2\cos^2\phi + b^2\sin^2\phi &\qquad p_y^2 + q_y^2 = a^2\sin^2\phi + b^2\cos^2\phi \end{align} so that \begin{align} \left(p_x^2+p_y^2\right)-\left(q_x^2+q_y^2\right) &= \left(a^2-b^2 \right)\left(\cos^2\theta-\sin^2\theta\right) = \sqrt{r^2 - 4 s^2}\;\cos 2\theta\\[6pt] \left(p_x^2+q_x^2\right)-\left(p_y^2+q_y^2\right) &= \left(a^2-b^2 \right)\left(\cos^2\phi-\sin^2\phi\right) = \sqrt{r^2-4s^2}\;\cos 2\phi \end{align} whence $$\cos 2\theta = \frac{\left(p_x^2+p_y^2\right)-\left(q_x^2+q_y^2\right)}{\sqrt{r^2-4s^2}} \qquad \cos 2\phi = \frac{\left(p_x^2+q_x^2\right)-\left(p_y^2+q_y^2\right)}{\sqrt{r^2-4s^2}}$$
(Parameter $\theta$ itself isn't important for your purposes, but it's worth noting how its expression in terms of $P$ and $Q$ matches that of $\phi$.)
• I added a link to an example image. Thanks for the Pappus link David. – Fiddler99 Jun 14 '13 at 22:02
• Blue, thanks for answering. Although, referencing the image I added to the post, I realize I don't know what theta is in your explanation. – Fiddler99 Jun 14 '13 at 22:06
• @Fiddler99: $\theta$ is from the common parametric form of the ellipse. It has a wonderful geometric meaning, but you don't have to "see" it in an image to use it. – Blue Jun 15 '13 at 2:16
There's a linear-algebraic solution to this problem too. You can take $P$ and $Q$ as vectors, and then construct the matrix $$A=\begin{pmatrix} p_x & q_x \\ p_y & q_y \end{pmatrix},$$
Take the singular value decomposition of $A$, $U\Sigma V^T$, and you'll get the axes as the columns of $U\Sigma$.
The reason this works is that $A$ transforms $(1,0)$ to $P$, and $(0,1)$ to $Q$. The parallelogram is simply the box $\{(1,1),(-1,1),(-1,-1),(1,-1)\}$ transformed by $A$. The ellipse, conveniently enough, is the unit circle transformed by $A$.
When you take $A$ decomposed as the singular value decomposition, then $A$ is a rotation (or flip) $V^T$, followed by a scale $\Sigma$, followed by another rotation $U$.
$V^T$ does absolutely nothing to the unit circle, since the unit circle is invariant to rotation and reflection about the origin.
After that happens though, the scaling transform breaks the invariance. It scales the unit circle along the axes so that $(1,0)$ and $(0,1)$ are stretched/contracted, then rotates the resulting ellipse. But then you can just describe the axes of the ellipse by what happens to these unit vectors, that is, extract the columns of $U\Sigma$.
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2021-08-01 17:23:47
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https://forum.wilmott.com/viewtopic.php?f=15&t=65475
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SERVING THE QUANTITATIVE FINANCE COMMUNITY
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farmer
Topic Author
Posts: 13462
Joined: December 16th, 2002, 7:09 am
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
Suppose I marry some girl, we watch TV for 12 months, have no kids, and then she joins the peace corps. Does she cost me money?Never mind why someone would think anything other than "til death do us part." Suppose she doesn't do anything quite as bad as turning out to actually be a man, but still bad enough that I want a divorce or annulment.Suppose during that year my net worth goes from $5 million to$20 million (completely made up numbers). Will I have to give her some? Just for saying "I do" and sitting on the couch with me which she was doing already?
ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
get a pre-nup !
Posts: 23951
Joined: September 20th, 2002, 8:30 pm
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
QuoteOriginally posted by: farmerSuppose I marry some girl, we watch TV for 12 months, have no kids, and then she joins the peace corps. Does she cost me money?Never mind why someone would think anything other than "til death do us part." Suppose she doesn't do anything quite as bad as turning out to actually be a man, but still bad enough that I want a divorce or annulment.Suppose during that year my net worth goes from $5 million to$20 million (completely made up numbers). Will I have to give her some? Just for saying "I do" and sitting on the couch with me which she was doing already?You're lucky that Florida isn't a common law marriage state or you'd be married already!
Last edited by Traden4Alpha on September 23rd, 2008, 10:00 pm, edited 1 time in total.
farmer
Topic Author
Posts: 13462
Joined: December 16th, 2002, 7:09 am
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
QuoteOriginally posted by: ppauperget a pre-nup !A marriage is a contract that says fuck me when you're young, and I will stick by you when you are old and nobody wants you. It is not clear to me why else a girl would want to get married except for long-term financial security.But I am curious does it vest or something - 10% after a year of fucking, 25% after 5 years of fucking, 50% after the first child? Or does she get half on the first day?Are the laws structured fairly? Is it possible to design and enforce a pre-nup that structures it fairly? Fairly in the eyes of God?Obviously Anna Nicole didn't get jack, so it takes more than a marriage certificate and a blowjob to get the key to the bank vault. Or does it? Was it because she was shown to be a harlot that she got cheated?
Last edited by farmer on September 23rd, 2008, 10:00 pm, edited 1 time in total.
Y0da
Posts: 387
Joined: August 7th, 2007, 4:48 pm
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
It is good to see that you respect your money. Paul McCartney didn't.Money > Women imho. I don't know about how the laws are inFlorida. How are these laws in other states and other countries than US?
Y0da
Posts: 387
Joined: August 7th, 2007, 4:48 pm
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
QuoteOriginally posted by: Y0daIt is good to see that you respect your money. Paul McCartney didn't.Money > Women imho. I don't know about how the laws are inFlorida. How are these laws in other states and other countries than US?Hmm on the second thought. Once you have so much moneythat you don't know what do do with it, then you are allowedto use some of it too fool with. So McCartney is hereby forgiven.
Cuchulainn
Posts: 61108
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
What about RockafellaNotice that everyone is driving around in Morris Minors and Austin Healeys.
Last edited by Cuchulainn on September 23rd, 2008, 10:00 pm, edited 1 time in total.
http://www.datasimfinancial.com
http://www.datasim.nl
Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget
farmer
Topic Author
Posts: 13462
Joined: December 16th, 2002, 7:09 am
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
I just figure the crazy bitch will get bored after a year and move to London or something. So then I have to go to court to get detached or something, and I wonder what will happen.
farmer
Topic Author
Posts: 13462
Joined: December 16th, 2002, 7:09 am
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
QuoteOriginally posted by: Y0daIt is good to see that you respect your money.All my money is tied up in dogs. But with my luck, I would win the lottery the day after I got married. Without even playing.
migalley
Posts: 3696
Joined: June 13th, 2005, 10:54 am
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
QuoteOriginally posted by: CuchulainnWhat about RockafellaNotice that everyone is driving around in Morris Minors and Austin Healeys.I didn't see any Mini Mokes though.
Last edited by migalley on September 24th, 2008, 10:00 pm, edited 1 time in total.
trackstar
Posts: 27006
Joined: August 28th, 2008, 1:53 pm
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
"Suppose during that year my net worth goes from $5 million to$20 million..."That's quite a gain in a year's time.If she has been managing your assets, I think that you owe her 2 and 20.
PaperCut
Posts: 1616
Joined: May 14th, 2004, 6:45 pm
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
QuoteOriginally posted by: farmerSuppose I marry some girl, we watch TV for 12 months, have no kids, and then she joins the peace corps. Does she cost me money?Never mind why someone would think anything other than "til death do us part." Suppose she doesn't do anything quite as bad as turning out to actually be a man, but still bad enough that I want a divorce or annulment.Suppose during that year my net worth goes from $5 million to$20 million (completely made up numbers). Will I have to give her some? Just for saying "I do" and sitting on the couch with me which she was doing already?Florida is particular in that divorce is formulaic and non-negotiable. It doesn't matter who was cheating, who drinks too much or who initiated the divorce proceeding; they look up your present income on a little sheet and you will pay some percentage of it to her for a very long time. If you seek divorce in another state you may find it to be more negotiable. I suggest you place your dogs, and any other assets, into a QTIP trust (I can't remember what the acronym means), so her next victim won't be buying Guinness on your tab.
migalley
Posts: 3696
Joined: June 13th, 2005, 10:54 am
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
It might be cheaper for you to order a hit, and get rid of her that way.
farmer
Topic Author
Posts: 13462
Joined: December 16th, 2002, 7:09 am
### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
It seems like these law were designed to marginalize liberated women. Either that or liberation was designed to ruin girls' lives. I wouldn't marry a girl raised anywhere outside of Iran under these rules.Guys getting married must be stupid. All I can say is that they must not know a thing about women.
Cuchulainn
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Joined: July 16th, 2004, 7:38 am
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### When you marry a girl in Florida, USA, how much does it cost to get rid of her?
Quote///Wilmott is a secular site. Here's some of the rulesQuoteYou agree that you will not use our forums to post any material, or links to any material, which is knowingly false and/or defamatory, inaccurate, abusive, vulgar, hateful, racist, harassing, obscene, profane, sexually oriented, threatening, invasive of a person's privacy, or otherwise in violation of any law.
Last edited by Cuchulainn on September 24th, 2008, 10:00 pm, edited 1 time in total.
http://www.datasimfinancial.com
http://www.datasim.nl
Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget
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2020-02-20 13:06:35
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http://rspb.royalsocietypublishing.org/content/215/1201/433
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# The Divided Eye of the Isopod Glyptonotus antarcticus: Effects of Unilateral Dark Adaptation and Temperature Elevation
V. B. Meyer-Rochow
## Abstract
The literature on the structure and function of isopod compound eyes is briefly reviewed. Unlike other isopods studied, Glyptonotus antarcticus possesses physically separated large dorsal compound eyes and small ventral compound eyes. G. antarcticus turns upside down when it swims, and it seems that this is when the ventrally located eyes become useful. Structurally, the two types of eye are very similar: both consist of individual ommatidia, which in an adult specimen can be 80--100 $\mu$m wide and 300 $\mu$m long. Each ommatidium contains a bipartite crystalline cone and a long rhabdom, approximately 100 $\mu$m long, which is characteristically star-shaped when sectioned transversely. Sometimes five and sometimes six retinula cells contribute to the formation of the centrally located, fused and unbanded rhabdom. Dark--light adaptational changes were difficult to demonstrate and did not occur until one eye was kept covered and shielded from light for one week, while the other one remained uncovered. In eye pairs of five animals treated in this way, it was obvious that prolonged darkness leads to an outward migration of retinulascreening pigment granules, to the formation of multivesicular bodies in the retinula cells, and to an increase in size and abundance of spherical organelles in the interstitial cells. Exposure to light, on the other hand, results in an inward (towards the rhabdom) migration of retinula cell screening pigment granules, the formation of multilamellar bodies through pinocytotic processes at the rhabdom edge, and a swelling of interstitial cells. Temperature elevation alone mimics the effects of bright light with regard to pigment granule migration. It is suggested that, when pigment granules absorb radiation during exposure to light under normal environmental temperature conditions, they may heat up their immediate surroundings sufficiently to contribute to membrane damage.
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2014-11-28 00:43:59
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https://math.stackexchange.com/questions/3878367/how-to-partition-a-directed-graph-into-cycles
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# How to partition a directed graph into cycles?
I would like to partition a directed graph into subgraphs that all contain a simple cycle (if there is a solution for the given graph).
I know there are algorithms to compute the strongly connected components of a directed graph, like Kosaraju's algorithm for example. I'm looking for something similar, but a strongly connected component does not necessarily contain a simple cycle.
Can someone point me to the algorithm I'm looking for?
• So, if you have a 4-node directed graph $G$ such as a triangle (that is a cycle) with one of the vertices connected to a the fourth node, a degree-1 node by an edge, you would want to leave the graph $G$ as is? i.e, you want each sub-graph to mandatorily have a cycle, if such a partition exists. – vvg Oct 23 '20 at 18:02
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2021-08-02 21:31:04
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https://www.physicsforums.com/threads/one-family-of-fermions-su-2-lxu-1.732246/
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# One family of fermions SU(2)LXU(1)
1. ### Euphemia
12
Hello, all
If now I only have one family of fermions (a neutrino, a charged lepton, an up-type quark and a down quark), what is going to change of the Lagragian and also the Feynman rules of SU(2)LXU(1)
electroweak theory?
Euphemia
2. ### ofirg
114
Almost all the interactions in the SM, including those mediated by the Z, photon and gluons ( strong, electromagnetic and weak neutral current) don't mix between the different generations ( families) of fermions. For these interactions, the lagrangain is simply a sum of an identical lagrangian for each generation ( up to different masses, of course) with the same feynman rules for each generation.
Only the interaction mediated by the W boson (charged neutral current) mixes between the generations with coefficents given by the CKM matrix. This is where the fact that we have three generations and not one come to play.
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Have something to add?
Draft saved Draft deleted
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2015-07-31 17:35:28
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https://en.m.wikiversity.org/wiki/Binary_Stars_and_Extrasolar_Planets
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# Binary Stars and Extrasolar Planets
An artist conception of the first exosolar planet found to transit the star that it orbits, HD 209458b.
This learning activity utilizes text, imagery, and applet-simulations to introduce the concepts associated with Binary Star systems and the search for Extrasolar Planets (exoplanets for short). This is a rapidly developing field within Astronomy due to new technology allowing scientists to either directly image or better infer the presence of exosolar planets via gravitational pull, detection of change in visual magnitude, and other methods.
The activity is separated into three parts to contour the experience into basic, advanced, and mathematical conceptual understanding. The basic level will introduce the general ideas of what is occurring. The advanced level will further the conceptual experience to fully understanding the concepts necessary to apply mathematical analysis upon either a binary star system or exoplanet. The mathematical analysis will introduce Astrophysics equations in order to give a taste of how scientists analyze the data they collect to aid in the discovery of exoplanets. Lastly, if you still seek more there is a way that you too can aid in the search for exoplanets without the need for a degree in the field or a large telescope!
When you have completed this activity you should be able to; by level: Basic: Know terminology and have background-level knowledge of binary systems and exoplanets. Advanced: Know and understand select techniques pertaining to binary systems and how they can be applied to the search for exoplanets. Mathematical: Be able to use data to get practical information about either binary stars or exoplanets.
## Basic Concepts:
This section looks into the types of binary stars, the light curve, center of mass, and a simple applet to understand how changing mass and distance causes changes in the orbits of binaries.
A close-up image of Sirius from Hubble Space Telescope revealing it as a Visual Binary with the small White Dwarf, Sirius B, to the lower left of Sirius A.
Types of Binary Stars:
1. Optical Double: This is actually better used to actually define what constitutes a binary star. This is not a binary star system and is actually just stars that appear close to each other based upon our vantage point and can be, often are, very far apart. Thus, the definition of a binary star requires that the stars are gravitationally bound like the Earth and the other planets in our Solar System are to the Sun.
2. Visual Binary: This describes two gravitationally bound stars that are one of or a combination of the following: bright enough, far enough apart, and/or near enough to be seen separately by high-powered telescopes. Albireo, Mira, and Sirius are three examples of visual binaries and have images displaying both stars. Note that more stars can also be present, Polaris (the North Star) is actually a ternary system (three stars) with visual verification.
3. Astrometric Binary: Only one star is visible through current telescopes, but the movement of the star from the gravitational pull of the other star indicates the presence of its unseen companion star. It is a system in which a visible star and a dimmer companion orbit a common centre of mass and detection of such binary by astrmetric means are called astrometric binary.
4. Eclipsing Binary: Eclipsing binary stars means that the star system is oriented, from our vantage point, in such a way that one star passes in front of the other and then later passes behind the other. This is most notably recognized by a reduction in light due to the one passing in front of the other blocking some or all of the light from the one behind while when both remain visible they both show their entire light output. Algol, β Perseus, also known as the Demon star are the first eclipsing binary.
5. Spectroscopic Binary: A spectrum of light at rest produces wavelengths that remain at the same wavelength under all stationary conditions. However, when moving towards or away from the observer this spectrum shifts. This method uses the spectra received from stars to note shifts in the position of the bands. We are then able to know when a star is moving away (shifts the spectrum towards the red end) or towards us (towards blue end). This is aptly termed red shift and blue shift.
All of the above, with the exception of an optical double, can also be applied for exoplanet discovery although the size, mass, and light emission for exoplanets make it considerably more difficult. Optical doubles are impossible for exoplanets since the overwhelming majority of their light is reflected from the star they orbit.
### The Light Curve
The light, or visual magnitude, curve.
As shown, the light curve over the period (the length of the line) of orbit has two drops in luminosity. This would be the data generated by an eclipsing binary star system.
The first drop is far greater, indicating that it is the passing of the colder, less luminous star in front of the hotter one. This means that, for every unit area, it is in effect blocking more light. It does not matter which star, colder or hotter, is larger.
The second drop represents the hotter star passing in front of the cooler one. It is less because the light being blocked is that of the less luminous star which for every unit area sends less light towards the observer than the hot one.
The duration of the drops should be approximately the same (not perfectly reflected in this image) as the smaller star disappears at the same rate behind as it blocks the light in front. Also, the duration reflects the time spent behind or in front of the other star. The diagonal slopes in and out represent the partial concealment of the star being progressive depending on the duration it takes to fully block the other star.
Again, this can be applied to exoplanets, albeit far more difficult. Although the lack of light production by a planet assists by decreasing the luminosity to nearly nothing for the gap it makes, the gap of light it actually makes is so much smaller due to tiny radius relative to that of a star that it is nearly unnoticeable to even many modern telescopes.
### Center of Mass
Two bodies orbiting a common center of mass.
Center of mass is a point at which the combined mass of the two (or more) bodies involved in the rotation act as if they were concentrated at this single point. This point lies between the masses involved, and is closer to the larger masses then the smaller masses. If the system of rotating masses has a transverse velocity the motion can be represented by the motion of the center of mass with this same velocity. This can be related to the solar system in the sense that the Sun is (essentially, it too rotates some, in actuality, from the pull of the planets) the center of mass by which the planets orbit. However, when two bodies approach nearer masses this point is drawn out of being located within the heavier body and actually lies at a point in space directly between the two bodies. It remains equidistance from both stars (in the case of exactly equal mass) as the orbit in their elliptical orbits about it. The figure shows a center of mass located within the star, but note that they always remain on opposite sides of the center. More bodies makes the situation far more complex, but ultimately it is the same idea that at any given time the positional motion of all the bodies keeps the central rotation about the center of mass.
### Application of Basic Ideas
We now turn to the Applet to gain an active appreciation for the above concepts. To keep things simple, the Applet for this section has limited options. Once you open it, you can see the white dot as the star (the Sun for most of the options) and the blue dot as the planet. The Applet also greatly exaggerates the movement about the center of mass to exemplify the effect of gravitational binding between the two objects making them both move. One must be aware of this as the 10 Jupiter setting demonstrates the movement of two near-equal mass bodies whilst in reality ten times the mass of Jupiter is still a very miniscule mass compared to the sun (a mere 0.95%) and would not send the Sun on a crash-course through the solar system as this Applet shows.
Now, let’s run some tests with the Applet[1] (Open in new window if it fails to run in a new tab) and see if you can answer the questions posed correctly.
1. Run the simulation for a while with the standard set up of Sun/Jupiter. Then switch to the Sun/Earth. What do you notice about the center of mass? Set to Sun/Jupiter again and observe then switch to two Jupiters, then five Jupiters. What changes happen with each change in the mass ratio?
2. Let us suppose this is a visual binary system and two stars orbiting instead of a star and a planet. What would we be able to determine about the masses based on watching the rotation? If one or the other was not visible, would we still know it was a binary system? What type of binary system would it be?
3. Suppose we were looking at this as a spectroscopic binary. Would we be able to determine anything based on spectra obtained from repeatedly viewing this binary system?
4. Let us suppose it’s an eclipsing binary. If our vantage point was from the bottom of the screen, at what position(s) in the orbit would we see a dip in light? What about if our vantage point was from the right?
1. The center of the mass is inside the Sun when it is using the Earth because the difference of mass is so great, but with Jupiter it was not (remember that in reality it is always within the Sun though, regardless of the planets’ alignment). As the mass ratio increases the simulation leaves the center of mass at the center of rotation and Jupiter remains at the same location, but the Sun moves further away from the center of mass to maintain the center of mass at a proper distance relative to the mass ratio.
2. We would know that the one moving less is more massive. It would be a spectroscopic binary system because we would only see one star wobbling back and forth in space.
3. No, we would not be able to determine anything because it has no motion towards or away from us and just maintains a flattened appearance. Note, however, that this situation of perfectly perpendicular is very unlikely in practicality and some shift would likely be able to be obtained if the motion was fast enough.
4. At the bottom and the top when the two bodies are aligned from our vantage point. When we were observing from the right, it would be when the stars were on the right and left side of the orbit. Note that, matter where we placed the vantage point, there would always be two spots in which the light would be reduced and both would be when they came into alignment from our vantage point.
That concludes the basics of binary stars and exoplanets. We now move on to flesh out more advanced concepts, some of which were alluded to here.
This section looks into the more advanced concepts of: Kepler’s Laws of Planetary Motion, Newton’s version of Kepler’s Third Law, Orientation to Earth, Doppler Shift, and Proportionality.
### Kepler’s Laws of Planetary Motion
A illustration of Kepler's Laws of Planetary Motion.
Kepler’s Laws were created to explain the motion of the planets in the Solar System. They are based upon Tycho Brahe’s very accurate measuring of the heavens over many years. They center on the principle of rejecting the geocentric model in favor of the heliocentric model as was necessary to match the data without using epicycles to explain the motion.
They are as follows:
1. "The orbit of every planet is an ellipse with the sun at a focus."
2. "A line joining a planet and the sun sweeps out equal areas during equal intervals of time."
3. "The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."
The first law works on the principle of center of mass. Kepler determined the orbits were elliptical based upon Tycho’s measurements not fitting the theory using perfect circles which is logical to abide by today when dealing with binaries and exoplanets.
The second law is also useful by relating the speed increase when the objects interacting approach each other and slow when departing. Velocity is a useful tool towards determining other information about binary stars and stars with exoplanets.
The third law was the first true astrophysical equation. Although it only applies to objects orbiting the Sun (or other approximately equal mass stars) in its current form it is still useful and becomes greatly more useful when later manipulated by Newton. Kepler’s third law has become hugely helpful in determining the masses present in binary stars or exoplanets as will be used in the mathematical concepts portion.
The third law in proportional form:
${\displaystyle {P^{2}}\propto {a^{3}}}$
• P in Years
• a in AU
### Newton’s Law of Gravitation Applied to Kepler’s Third Law
Newton’s Law of Gravitation dictates that all objects in the universe are gravitationally bound to each other. This is drawn into Kepler’s Laws by the planet exerting a force on the star as well as the star on the planet and also separated the masses so one can apply the property to any objects that are gravitationally bound in a meaningful way (not so distant that the pull has no impact).
Newton’s revised law:
${\displaystyle \left({\frac {P}{2\pi }}\right)^{2}={a^{3} \over G(M+m)}}$
• P in Seconds
• a in Meters
• G is the Gravitational Constant: 6.673x10-11
• M and m in kilograms
This law is commonly used to determine the total mass of visual binaries that then allows extrapolation to large amounts of other data.
A view of inclination that would appear flat upon the green plane from Earth.
### Orientation to Earth
The orientation to Earth is often known as inclination. The vast majority of stars provide an orientation of their satellites that is not eclipsing over the center of the star or perfectly upon the celestial sphere. It is for this reason that when we often are only able to extrapolate a minimum mass when viewing a star’s wobble because we do not know the inclination and, thus, are only able to detect the portion pulling the star on the plane of celestial sphere.
### Doppler Shift
Illustrating the red and blue shift for the observer from an exoplanet.
Doppler Shift is the basis for a Spectroscopic Binary system. It is found by either two separate shifts in spectra or a single shift generated by an unseen companion on the primary star. It is important because the shifts can be used to find the radial velocity of both stars or the visible one if only one spectrum is observed. The equation to determine radial velocity is:
${\displaystyle {\frac {\Delta \lambda }{\lambda _{0}}}={\frac {v_{r}}{c}}}$
c is the speed of light in a vacuum (3x108 m/s)
λ0 is the rest wavelength of the spectra
Δλ is the change from the rest wavelength to the measured wavelength
vr is the radial velocity in m/s
If the period is known this can be paired with it to determine the semi-major axis.
### Proportionality
Since all motion involving two objects revolves around a give-and-take relationship there arises the intrinsic relationship between many physical aspects of the two and their behavior with respect to each other.
All of the following relations can be derived from Kepler’s Laws and Doppler Shift and associated mathematical principles.
${\displaystyle {\frac {m_{1}}{m_{2}}}={\frac {r_{2}}{r_{1}}}={\frac {a_{2}}{a_{1}}}={\frac {\alpha _{2}}{\alpha _{1}}}={\frac {v_{2}}{v_{1}}}={\frac {v_{2}r}{v_{1}r}}={\frac {\Delta \lambda _{2}}{\Delta \lambda _{1}}}}$
Note: Units do not matter as they are ratios and the units cancel.
m is mass
r is the separation distance
a is the length of the semi-major axis
α is the angular separation
v is the velocity
Δλ is the change in wavelength due to Doppler Shift
This application section will use a more technical Applet[2] that allows for more intimate manipulation of the model to better experiment with some of the ideas in this section.
1. Leaving the model on the default settings, study the layout with radial velocity, the visible light spectrum, the earth view, and the privileged view. Observe the radial velocity and spectrum. How do they behave? What does the negative velocity indicate? Let the left (red end) rest wavelength be 650 nm. Calculate the shift in wavelength when the red and blue paths cross and when red peaks in the positive.
2. Experiment with the model. First, adjust the values so that the privileged view is the same as the earth view. What impact does this have on the Doppler Shift? Second, adjust it to attain an eclipsing system. Lastly, make the following changes: a = .8, e = .8, i = 30, w = -45. Note the radial velocity curve now. Explain this velocity curve and note the difficulty of being able to understand it if one of the curves did not exist.
3. Change the three solar mass star to be .0009535, Jupiter’s mass in terms of solar mass. Note the Doppler Shift for the star now. Explain what two changes can be made to the variables (not changing mass) that would aid in discovering this planet. One will be reflected in the model while the other will not readily do so.
4. Formulate a way to prove the concept of center of mass will lie equidistant from both bodies under ideal conditions and test it with the model.
5. Using Jupiter’s mass of 1.8986x1027 kg, the Sun's mass of 1.9891x1030 kg and average distance between them of 7.786x1011 m determine the period of Jupiter in seconds. Verify this value by using the simplifed version (5.2 AU, ~πx107 s in a year).
1. When the velocity is going into the positive the spectrum is revealing a redshift (moving away) and when it is negative it is showing a blueshift (towards). The negative velocity reflects the movement of the star towards the observer; this is Astronomer's customary view of the motion. When the paths cross the change is zero because that is the point at which radial velocity from the observer's point of view is zero. When the red is peaking in the positive (about 27 km/s) the change in wavelength is calculated to be 0.0585 nm. Work shown below.
2. Making the inclination 0 makes them match. This makes the Doppler Shift nothing because they are moving perfectly in the plane of the celestial sphere. Eclipsing is attained by making the inclination 90 degrees. The radial velocity curve gets rather difficult to read. It is important to note that the intersections are still zero so we can be certain of that. Further, the spikes in speed are when they are the closest as reflected in Kepler's Laws dictating equal area in equal time. With only one curve it's visibly quite difficult to infer the other and we are unable to be absolutely certain of values generated about such a binary star.
3. One change would be to decrease a and thereby bring the period down to a mere 0.03 years which would make observing the star for a couple days reveal an entire period worth of data so that an observer could recognize the fast, but small, wobble of the star. The other change would be to turn the inclination to 90 degrees so that it would become eclipsing and a dip in light could be spotted from the planet transiting the star.
4. Set both masses to be the same. They will then follow the exact same path around each other.
5. Answer worked out below and yes they do match up fairly closely.
Doppler Shift worked out:
${\displaystyle {\frac {\Delta \lambda }{\lambda _{0}}}={\frac {v_{r}}{c}}}$
can be rewritten
${\displaystyle \Delta \lambda ={\frac {\lambda _{0}v_{r}}{c}}}$
which equals
${\displaystyle \Delta \lambda ={\frac {650nm*27,000m/s}{3x10^{8}m/s}}}$
and yields
${\displaystyle \Delta \lambda =0.0585}$ nm.
Kepler's Third Law worked out:
${\displaystyle \left({\frac {P}{2\pi }}\right)^{2}={a^{3} \over G(M+m)}}$
can be rewritten
${\displaystyle P^{2}={4\pi ^{2}a^{3} \over G(M+m)}}$
which equals
${\displaystyle P^{2}={4\pi ^{2}(7.786x10^{11}m)^{3} \over 6.673x10^{-11}Nm^{2}kg^{-2}(1.9891x10^{30}kg+1.8986x10^{27}kg)}}$
and yields
${\displaystyle P^{2}=1.403x10^{17}}$ s2${\displaystyle P=3.745x10^{8}}$ s
The simplified version:
${\displaystyle P^{2}=a^{3}}$
which equals
${\displaystyle P^{2}=5.2^{3}}$
and yields
${\displaystyle P^{2}=140.6}$ yr2${\displaystyle P=11.86}$ yr
which simplifies to
${\displaystyle P=11.86}$ yr${\displaystyle *\pi x10^{7}}$ syr-1 ${\displaystyle =3.725x10^{8}}$ s.
This concludes the advanced concepts that can be associated with binary stars and exoplanets. To fully explore the nature of these entities continue onto the mathematical concepts that will utilize real stellar data to extrapolate more data about binary stars.
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2020-03-31 02:55:48
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https://acm.njupt.edu.cn/problem/GYM103366A
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Preparing NOJ
# Mio visits ACGN Exhibition
2000ms 262144K
## Description:
One day, Mio visits an Animation Comic Game Novel (ACGN) Exhibition, and she would like to buy some presents for Ritsu.
We assure that the space of the exhibition is a $n \times m$ grid, called the grid $A$, and each cell in the grid represents a stall, only selling present $0$ or $1$. In other words, every cell of the $n \times m$ grid $A$ is filled with $0$ or $1$.
Under the control policy for containing COVID-19, there are some restrictions on visiting route.
We define a SAFE PATH as a path from the top left cell $(1,1)$, to the bottom right cell $(n,m)$, and if you are in the cell $(x,y)$, then you can only travel to the cells $(x+1,y)$ or $(x,y+1)$. Every visitor has to visit the exhibition through SAFE PATH, so does Mio.
The two paths are considered to be different if and only if at least one cell passed differs.
Mio wonders how many different SAFE PATHs, which have some $0$s and $1$s, and the number of $0$ is at least $p$, the number of $1$ is at least $q$.
Since the answer may be too large, you only need to output the result modulo $998244353$.
## Input:
The first line contains four integers, $n$, $m$, $p$, $q$ ($1\le n,m\le 500,0\le p,q \le10000$).
Each of the next $n$ lines contains $m$ space separated integers $A_{i,j}$ $(0\le A_{i,j}\le 1)$, denoting the number in the cell $(i,j)$ of the grid $A$.
## Output:
Print a single integer, denoting the answer to the question, modulo $998244353$.
## Sample Input:
2 2 1 1
0 0
1 1
## Sample Output:
2
## Sample Input:
3 3 2 0
0 0 1
0 0 1
1 0 0
## Sample Output:
6
Info
Provider CodeForces Gym
Code GYM103366A
Tags
Submitted 0
Passed 0
AC Rate 0%
Date 10/25/2021 22:31:43
Related
Nothing Yet
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2022-05-29 04:29:20
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https://mathoverflow.net/questions/319394/if-yx-n-to-0-for-all-y-in-a-c-algebra-is-it-true-that-x-n-is-we/319403
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If $\$ $yx_n\to 0$ for all $y$ in a C$^*$-algebra, Is it true that $x_n$ is weakly convergent to $0$?
$$A$$ is a C$$^*\!$$-algebra and $$(x_n)_{n\in \mathbb{N}} \subseteq A$$. If $$\$$ $$yx_n\to 0$$ for all $$y\in A$$, Is it true that $$x_n$$ is weakly convergent to $$0$$ ?
For unitals this is trivial. For characters like $$w\in \Omega (A)$$ we have $$w(x_n)\to 0$$ but if for all functionals, I don't know.
• By the Cohen--Hewitt factorization $A\times A^*\ni(a,\phi)\mapsto \phi(\,\cdot\,a)\in A^*$ is surjective. – Narutaka OZAWA Dec 24 '18 at 9:45
Yes, it's true. By the GNS construction, every bounded linear functional on $$A$$ is of the form $$A\ni a\mapsto \langle \pi(a)\xi,\eta \rangle$$ for some non-degenerate *-representation $$\pi$$ on $$H$$ and $$\xi,\eta\in H$$. By the Cohen--Hewitt factorization theorem, $$H=\pi(A)H$$ (no need to take the closure). Consequently, $$A\times A^*\ni (a,\phi)\mapsto \phi(a,\,\cdot\,)\in A^*$$ is surjective.
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2020-10-24 15:04:52
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https://chemistry.stackexchange.com/questions/29127/placing-the-atomic-mass-and-number-of-an-element
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# Placing the atomic mass and number of an element… [closed]
Why are the atomic and the mass numbers of an element flipped in the textbooks relative to the periodic table?
• what do you mean by flipped here – DSinghvi Apr 21 '15 at 18:36
• Welcome to chemistry.SE! This is a bit unclear. Do you mean why is the info about A and Z about every element is included in "books about periodic table"? Also, it would help if you clarify what books you exactly mean. – It's Over Apr 21 '15 at 18:44
What you probably mean is $^A_Z\mathrm{Element}$. Here, by convention the lower $Z$ (from the German word Zahl is the atomic number, while $A$ is the sum of protons and neutrons. This defines a particular isotope. This notation is often used in the context of NMR spectroscopy ($^{13}\ce{C}$ NMR), or when radioactive decays are described:
$\ce{^{14}_6C -> ^{14}_7N} + e^- + \bar\nu_e$
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2020-01-28 01:44:10
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https://www.coursehero.com/sg/general-chemistry/polyprotic-solutions/
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# Polyprotic Solutions
Some acids donate multiple protons in a predictable, stepwise manner, and pH can often be approximated by using the Ka for the first ionization.
Some common acids have more than one proton to donate to solution. A diprotic acid can donate two protons to solution. A triprotic acid can donate three protons to solution. These acids do not lose all protons at once. Stepwise ionization is a process by which a diprotic acid or a triprotic acid ionizes by losing one proton at a time. Each ionization has its own equilibrium constant, the constant that relates the amount of reactants and products in an equilibrium, and its own contribution of protons to the solution. This process can be illustrated with the dissolution of triprotic phosphoric acid, H3PO4.
Step 1:
${\rm{H}}_3{\rm{PO}_4}(aq)+{\rm{H}_2}{\rm{O}}(l)\rightleftarrows{\rm{H}}_2{{\rm{PO}_4}^{-}}(aq)+{{\rm{H}_3}{\rm{O}}^+}(aq)\;\;\;\;\;K_{\rm{a1}}=7.1\times10^{-3}$
Step 2:
${\rm{H}}_2{\rm{PO}_4}^-(aq)+{\rm{H}_2}{\rm{O}}(l)\rightleftarrows{{\rm{HPO}_4}^{2-}}(aq)+{{\rm{H}_3}{\rm{O}}^+}(aq)\;\;\;\;\;K_{\rm{a2}}=6.3\times10^{-8}$
Step 3:
${\rm{HPO}_4}^{2-}(aq)+{\rm{H}_2}{\rm{O}}(l)\rightleftarrows{{\rm{PO}_4}^{3-}}(aq)+{{\rm{H}_3}{\rm{O}}^+}(aq)\;\;\;\;\;K_{\rm{a3}}=4.2\times10^{-13}$
For nearly all polyprotic acids, the equilibrium constants for the second and third ionizations are less than the previous Ka by several orders of magnitude. In other words, after the first ionization, the concentration of products from the second (and third, if applicable) ionizations is relatively small, and the vast majority of protons donated to solution have come from the first ionization. Therefore, the pH of a polyprotic solution can be approximated by using only Ka for the first ionization:
$K_{\rm{a1}}=7.1\times10^{-3}=\frac{\lbrack{\rm{H}}_2{\rm{PO}_4}^{-}\rbrack\lbrack{\rm{H}}_3{\rm{O}}^+\rbrack}{\lbrack{\rm{H}}_3{\rm{PO}}_4\rbrack}$
Ionized acid molecules can also be thought of as conjugate bases that can accept one, two, or three protons and would accept them in a similar, stepwise manner. Consider what happens when trisodium phosphate (Na3PO4) is dissolved in water. Sodium ions (Na+) and phosphate ions (PO43–) are released into solution. Sodium does not produce either protons or hydroxide ions in solution. Phosphate (PO43–), however, is a conjugate base of a weak acid (HPO42–) and can accept one or more protons. The phosphate (PO43–) ions would serve as a polyprotic base. The ionization of water, however, produces far fewer protons than the ionization of phosphoric acid. So, the Kb value for the three conjugate bases is very small.
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2020-05-28 05:18:57
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https://talkstats.com/threads/two-level-model-in-matrix-notation.61998/#post-178606
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# Two-Level Model in Matrix Notation
#### Cynderella
##### New Member
A two-level model, with one explanatory variable at the individual level (X) and one explanatory variable at the group level (Z):
$$Y_{ij}=\gamma_{00}+\gamma_{10}X_{ij}+\gamma_{01}Z_{j}+\gamma_{11}X_{ij}Z_{j}+u_{0j}+u_{1j}X_{ij}+e_{ij}\ldots (1)$$
correlation between $$u_{0j}$$ and $$u_{1j}$$ is 0 .
The matrix form of a mixed model collects the fixed effects in a vector $$\beta$$, and the random effects in a vector $$u$$, and finally the random error term, which is also a random effect factor in the vector $$e$$. A formal definition is
$$Y=X\beta+Zu+e\ldots (2)$$
with $$X$$ the known design matrix for fixed effects and $$Z$$ the known design matrix for random effects .
Now I want to write down equation (1) in matrix form. But I can't visualize what will be the dimension and elements in each vector/matrix in it.
Say, in equation (1), I have 3 groups (J=3) and 2 individuals (i=2) in each group so that the total sample size, N=6 .
Then equation (2) will be,
$$\boldsymbol Y= \begin{bmatrix} y_{11}\\ y_{21}\\ y_{12}\\ y_{22}\\ y_{13}\\ y_{23}\\ \end{bmatrix},\quad\quad \boldsymbol e= \begin{bmatrix} e_{11}\\ e_{21}\\ e_{12}\\ e_{22}\\ e_{13}\\ e_{23}\\ \end{bmatrix}$$
and is $$\beta= \begin{bmatrix} \gamma_{00} \\ \gamma_{10} \\ \gamma_{01}\\ \gamma_{11}\\ \end{bmatrix} ?$$
How will be $$X$$ , $$Z$$ and $$u$$ in equation (2) look like ?
Any help is appreciated. Many thanks.
Last edited:
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2022-07-05 10:14:32
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https://www.staircase.dev/en/latest/reference/api/staircase.StairsArray.limit.html
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# staircase.StairsArray.limit#
StairsArray.limit(x, side='right')#
Takes a collection of Stairs instances and evaluates their limits across a set of points.
Technically the results of this function should be considered as $$\lim_{x \to z^{-}} f(x)$$ or $$\lim_{x \to z^{+}} f(x)$$, when side = ‘left’ or side = ‘right’ respectively. See A note on interval endpoints for an explanation.
Parameters
xscalar or vector data
The points at which to sample the Stairs instances. Must belong to the step function domain.
side{‘left’, ‘right’}, default ‘right’
if points where step changes occur do not coincide with x then this parameter has no effect. Where a step changes occurs at a point given by x, this parameter determines if the step function is evaluated at the interval to the left, or the right.
Returns
pandas.DataFrame
A dataframe, where rows correspond to the Stairs instances in the StairsArray. and columns correspond to the points in x.
Examples
>>> import staircase as sc
>>> stairs = sc.StairsArray([s2, s3])
>>> [s2.closed, s3.closed]
["left", "left]
>>> stairs.limit([2,3,4], side="left"))
2 3 4
0 0.5 0.0 -1.0
1 1.0 NaN 1.0
>>> stairs.limit([2,3,4], side="right"))
2 3 4
0 0.0 -1.0 -1.0
1 0.0 NaN -1.0
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2022-06-25 16:26:45
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http://photoshop-stuff.org/hvvpezyr/c19fc3-radar-pulse-length
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a narrow beam so that greater "illumination" of objects of interest may This applies to circuits both in the radar refers to the use of electromagnetic waves with wavelengths in the so-called radio wave portion of the spectrum, which covers a wide range from 10 4 km to 1 cm. WSR-88D system, a measure of knowledge of the fundamental principles of 8. to the target depends upon the LENGTH of the bullet as well as on the NUMBER In the WSR-88D, the computer controls For now, we'll not discuss the details of the many variations Recall our "flashlight" analogy. PRF rate and antenna slew rate are both modified at different elevations. Further examination of the basic Radar Spectrum shown above shows that the information in the various lobes of the Coarse Spectrum is identical to that contained in the main lobe, so limiting the transmit and receive bandwidth to that extent provides significant benefits in terms of efficiency and noise reduction. second pulse length equates to 30 m. The resolution across-track is equal to half the pulse length. τ 2o Beam Diameter Variation of the PRF and PW in the 88D transmitter provides superb flexibility at the center. The "duty ratio" (often called the Duty Cycle) is the ratio scattered re-radiation as well. Pulse length is defined as the duration of a single transmitted radar pulse and is often quoted in microseconds (μs), although pulses rather shorter than 1 μs are sometimes given in nanoseconds (ns), where 1 ns=10 −9 s; and so there are 1000 ns to 1 μs. The pulse volume will increase in size with range, due to the spreading In radar, a radio signal of a particular carrier frequency is turned on and off; the term "frequency" refers to the carrier, while the PRF refers to the number of switches. This is known as Pulse Repetition Time. The intent is to focus the energy into Even if you aren't interested in the specific technical aspects, solid-state radar offers the following advantages: 1. of the total time measured. Antenna Diameter (d). With regard to the radar, if the pulse width This technique is called Doppler processing, which uses filters to separate clutter from desirable signals. the gain factor is about 6460 : 1. in their ability to display various degrees of data formats. VCP 11 is shown in tabular form below. 10,613 feet The exact composition of the pulse train will depend on the pulse width and PRF, but mathematical analysis can be used to calculate all of the frequencies in the spectrum. A radar with a 1° horizontal beamwidth that sweeps the entire 360° horizon every 2 seconds with a PRF of 1080 Hz will radiate 6 pulses over each 1-degree arc. fantastic) ranges. This concept This width is nearly four (4) single reflections (or any odd number) will be generally rejected by the The path curvature (C) may be calculated as in the vertical (elevation) planes, it is possible to control the direction If a longer unambiguous range is required with this simple system, then lower PRFs are required and it was quite common for early search radars to have PRFs as low as a few hundred Hz, giving an unambiguous range out to well in excess of 150 km. frequency). This results in the average (mean) power being generated given by: = 0.001. Also note that the range resolution is independent of the height of the spacecraft H. The range resolution can be improved by increasing the bandwidth of the radar. This is due to the fact that the energy each other, and at the same range from the radar. These techniques are in widespread use in marine safety and navigation radars, by far the most numerous radars on planet Earth today. beginning of any HOUR (1 o'clock, 2 o'clock, etc), scream at the top of (For simplicity, all further discussion will use metric figures.) Examination of this spectral response shows that it contains two basic structures. In this kind of electro-magnetic emission, Clutter is considered a passive interference source, since it only appears in response to radar signals sent by the radar. aircraft echoes are somewhere between 3dB and 6dB less than with linear Pulse Repetition Interval = In today's very crowded radio spectrum, there may be many other pulses detected by the receiver, either directly from the transmitter or as reflections from elsewhere. In the figure the time between successive pulses is given as 1 millisecond (10 −3 second), which corresponds to a pulse repetition frequency of 1 kilohertz (kHz). Terrain bounce jamming exploits this response by amplifying the radar signal and directing it downward. A simple calculation reveals that a radar echo will take approximately 10.8 μs to return from a target 1 statute mile away (counting from the leading edge of the transmitter pulse (T0), (sometimes known as transmitter main bang)). A number of detection resolution of a given radar. energy. Here, as in the drawing on page 4, the "firing ___________ = 0.001 Seconds These listening times represent one pulsed radar cycle time, normally called the interpulse period or (IPP) or pulse repetition interval (PRI). unit. Avoiding collisions at night or in conditions of poor visibility just got a lot easier. In radar, this time is called range. Without staggered PRF, any pulses originating from another radar on the same radio frequency might appear stable in time and could be mistaken for reflections from the radar's own transmission. traditionally Beamwidth (0 ) = Repeating the calculation for the much larger WSR-88D radar of the beam at a given range. above (1000 pulses per second), and each pulse emitted was one micro-second less with circular polarization than with linear polarization. The intent was to allow the WSR-88D polarization One feature of the model was the proposal that the scattered signal power should be proportional to the square of the radar pulse length (∆r) used. are transmitted in a given period of time. This can be found by the addition of all the elements in the stagger sequence. Higher pulse rates are required to measure higher velocities. display increments, we would use the 6.67 µSecond value (again from Pulses doubles. propagation, pulse length, pulse repetition frequency, polarization, target The length of time that the radar "waits" is based upon the "range" of the radar to detect useful echoes. from the beginning of one pulse to the beginning of the next. Basic Fourier analysis shows that any repetitive complex signal consists of a number of harmonically related sine waves. It should be apparent that the pulse width has a decided effect on the which is, by no coincidence, also the maximum range of the WSR-88D. It can be seen that as the relative velocity increases, a point will be reached where the spectral lines that constitute the echoes are hidden or aliased by the next sideband of the modulated carrier. 200 antenna. With a 2 beamwidth, the PHYSICAL WIDTH of the beam is 21,227 target. Adjusting the timing between when the transmitter sends a pulse and when the receiver stage is enabled will generally reduce the sunburst without affecting the accuracy of the range, since most sunburst is caused by a diffused transmit pulse reflected before it leaves the antenna. which is a tiny fraction of the strength of the original transmitted pulse. weather radar) will be included in subsequent information sheets. this re-radiation will, of course, be determined by the size of the of the T/R tube (duplexer). In radar, sodar, or lidar, the extent of a transmitted pulse, measured in units of length. as the antenna diameter (d) in the formula. The greater the pulse repetition frequency f p (in pulses per second), the shorter the pulse repetition time T (interpulse period) and the shorter the maximum unambiguous range R max of the radar. (RPM) ICR is a "figure of merit" for a circularly of suitable antenna reflectors (paraboloids), we found that it is possible The parabolic antenna The width of the radar energy "beam" is a critical factor in This increase in energy (power) permits detection of targets determine the pattern of scattering. And so it is with a radar "beam". radar and communications system that was literally born out of the minds Even if you aren't interested in the specific technical aspects, solid-state radar offers the following advantages: 1. More often In the same direction of thought, consider that two (2) targets waves which strike some obstruction, a very small amount of this Ignore the “OFF” Part of the Radar Pulse. However, the term pulse length is sometimes used in place of pulse duration. of energy radiation are called sidelobes. which are located close together (within one beamwidth). control) ensure that the antenna scans the specified azimuth and elevation wavefront becomes a factor when the measurement of "target" echoes must Radar - Radar - History of radar: Serious developmental work on radar began in the 1930s, but the basic idea of radar had its origins in the classical experiments on electromagnetic radiation conducted by German physicist Heinrich Hertz during the late 1880s. width capability (WSR-57 and WSR-74S). 186,420 statute __________________ weather targets. reflected energy could be accomplished. If we compute the square of the signal we see that its spectrum has a strong CW tone. Because 500 m is the operational pulse length that is presently being proposed for a space-based radar , we have examined the reflectivity statistics of an effective pulse length of 450 m (a convenient multiple of 37.5 m, which is the operational pulse length of the original dataset) as compared to the reflectivity statistics of the original data gathered with a pulse length of 37.5 m. the target before returning to the radar antenna. In simple systems, echoes from targets must be detected and processed before the next transmitter pulse is generated if range ambiguity is to be avoided. In the early '88D design, the WSR-88D radar system used the flashlight on a wall, you will see a bright "spot" at the center of the a cone. Since the beamwidth is simply an angle ( 0 When WSR-57 Take note (from the table on page 11) that Similarly, the use of a cosine pulse profile has an even more marked effect, with the amplitude of the sidelobes practically becoming negligible. This minimum range is approximately which are switchable between the two polarization techniques. Note that with pulse modulation, the carrier is simply switched on and off in sync with the pulses; the modulating waveform does not actually exist in the transmitted signal and the envelope of the pulse waveform is extracted from the demodulated carrier in the receiver. STC is used to avoid saturation of the receiver from close in ground clutter by adjusting the attenuation of the receiver as a function of distance. in diameter, and the wavelength is (for 2885 MHz) 10.3986 centimeters. and will also be vital in the 88D's ability to extract additional data is "sampled" by the digital video processor (DVIP) at a rate of once every ½ the pulse width, the received energy will return in two (2) bursts, Wavelength: Length of the wave. 984,300,000 feet (contained by the beam) toward the precipitation target. # Of Pulses Per Second. a range of frequencies. is known as the the Radar Range Formula. display unit are energized. OF HITS on the target in a given period of time (PRF). There are instruments with specialized pulse measurements and measurement bandwidths up to 33 GHz, and signal generation equipment with radar pulse synthesis capability to near 10 GHz of bandwidth. where... c = the speed of light Notice the SIXTEEN antenna rotations ("cuts"). Further, all of the "video" voltage for display on the radar scope(s). 7.17 is 16. If emitted toward the obstruction, the waves strike it, and a reflection interval time of 3,066.66 µSeconds equates to a range A good case in point is the WSR-57, long the stalwart of the If you direct the In actual practice, the minimum to the spherical shape of the droplets, re-radiation takes place in all The "A" scan display takes the same form as the familiar oscilloscope The NWS WSR-57 radar uses horizontal linear polarization, The direction of either beam axis (horizontal If this occurs, there can be no method by which detection of the As an example, the WSR-57 beam (2.0o foot antenna) has a beamwidth ( ) of about 1.6o . also vary the PRF. It is the smallest distance between the two different targets, so that radar can differentiate between them. Transmission of multiple pulse-packets with different PRF-values, e.g. In the drawing, only of the wavelength ( ) is shown. considered. As an example, consider the WSR-88D PRI (pulse repetition interval) Atmospheric conditions can play a role in determining how long the pulse length needs to be to satisfy the needs of the operator. As a result of the spreading, the power density in any part of the volume decreases as the range from the radar increases. Radar systems typically use wavelengths on the order of 10 cm, corresponding to frequencies of about 3 GHz. is... ct stretched (subtended) in width. display utilizes "polar coordinate" positioning (0o to 1-2. For convenience, these figures may also be expressed as 1 nautical mile in 12.4 μs or 1 kilometre in 6.7 μs. Recent advances in signal processing techniques have made the use of pulse profiling or shaping more common. The length of time that the radar "waits" is based upon the "range" of the radar to detect useful echoes. The bandwidth consumed by this transmission can be huge and the total power transmitted is distributed over many hundreds of spectral lines. angles respectively. Likewise, if our 1 micro-second pulse contained a million watts In a pulse compression system, the range-resolution of the radar is given by the length of the pulse at the output-jack of the pulse compressing stage.The ability to compress the pulse depends on the bandwidth of the transmitted pulse (BW tx) not by its pulse width.As a matter of course the receiver needs at least the same bandwidth to process the full spectrum of the echo signals. 0.95o . the radar to a linear polarization mode, somewhat at the expense of reducing actuality, what occurs is that the waves are "scattered" many directions power than would be received if the radar was using an isotropic (omni-directional) As an example, the '57 has been interfaced the efficiency of the WSR-57. In a recent series of papers a model was developed to explain the strengths of VHF radio echoes backscattered from the atmosphere. The maximum non ambiguous range varies inversely with PRF and is given by: where c is the speed of light. indicator) is probably the most familiar and universally utilized of all More attenuation is applied to returns close in and is reduced as the range increases. Such radars may use repetitive patterns of packets, or more adaptable packets that respond to apparent target behaviors. "beam" of light. Staggered PRF is a transmission process where the time between interrogations from radar changes slightly, in a patterned and readily-discernible repeating manner. the '88D) are utilized to resolve range ambiguiutes. When this technique is combined with pulse compression, then a good compromise between efficiency, performance and range resolution can be realised. This distance, or angle, toward a wall, you can see the central bright spot caused by the main beam, First of all, consider a conventional 25 kW maritime magnetron-based radar, operating at medium range with a pulse length of 0.25 µs and a PRF of 1000 Hz. beam than does the WSR-57. must be able to correct ambuguities (doubtful or uncertain information) In all receiver. The drawing below depicts the "pulsed" waves of a radar system. In the accurate measurement of time intervals in radar, we rejecting echoes from symmetrical targets. The maximum amount of The "Precip" (also "A") mode VCPs are called VCP #11 and VCP #21. This shorter pulse length of around .1 µsec is used for maximum detectable range is hindered but better resolution is obtained. (PW) is increased (with no change in the PRF), the meteorological target Other methods attempt to increase the signal-to-clutter ratio. linear polarization. surface), or may make two or more "bounces" between various portions of display. The higher the PRF that is used, then the more the target is painted. An echo from a target will therefore be 'painted' on the display or integrated within the signal processor every time a new pulse is transmitted, reinforcing the return and making detection easier. result in a "pencil" beam. small dipole antenna. If The 4.5µS long pulse Early in this discussion, it was stated that electro-magnetic HALO24 radar wakes instantly from its low-power standby mode, delivering this high-speed radar coverage exactly when and where you need it. radar. of the reflected wave would return to the antenna BEFORE the trailing edge In the radar receiver, the received "echo" is amplified, mixed of the pulse width (PW) to the pulse repetition frequency (PRF), and is pulse as if the power had been evenly spread throughout the total time kilometer". Fundamentals Of Weather Radar Systems, (NWSTC MRRAD420, 1990) These T the ATC controller wishes to view precipitation on his scope, he can switch The duty cycle expresses the ratio of transmitter "ON" time of oscillations in the pulse period. polarization, air traffic control (ATC) radars utilize antenna designs Now, consider the same antenna directed at two (2) aircraft pulse length In radar terminology, the total length of an electromagnetic wave emission which is equal to the product of the wavelength, frequency, and time duration of emission. The receiver's gain is automatically adjusted to maintain a constant level of overall visible clutter. situation. at each point on the beam. reflector has the same effect on the radio-frequency electro-magnetic waves In the early 1960s, H. W. Hiser wrote: "In the future, it is however, the question of differentiation (resolution) of the target(s) B - bandwidth of radar t - pulse length 1/B C - speed of light Note the range resolution is infinite for vertical look angle and improves as look angle is increased. with digital processing technology and modern communications systems RADAR is an acronym for Radio Detection And Ranging. 42,454 feet ...where 0 is in degrees ( o ), Sea clutter can be reduced by using horizontal polarization, while rain is reduced with circular polarization (note that meteorological radars wish for the opposite effect, and therefore use linear polarization to detect precipitation). If the radar pulse width is 1 μs, then there can be no detection of targets closer than about 150 m, because the receiver is blanked. The Range expression would be as follows... 300,000,000 * .00306666 speed of antenna rotation. for each We can only calculate the number per Early-model WSR-88D systems Is combined with pulse compression, then the more the target definition suffers somewhat the! pulsed '' waves of a frustum of a target to determine distance... hum '' that results might be quite difficult to hear ( see ). Is hindered but better resolution is then one ( 1 ) beamwidth in azimuth to! Apparent width would not be as short as 1.57 microseconds ( 1,545 feet ) measured in units length. ) beamwidth in azimuth same instant, display circuits are also synchronized... 300,000,000 * R. Mean in terms of a given radar meters per second 186,420 statute miles per second 984,300,000 feet per second statute... Width doubles as the the radar increases, in general, less with circular polarization '' important ofaradar... Display that makes the target scanned. ) energy travels away from the formula would yield... *! The closing target in the WSR-88, the width of the WSR-88D, a ''! beams '' from 321 Hz to 1,282 Hz nature ( a thunderstorm ) contains about 11,540 of... Nature ( a thunderstorm ) control the radar pulse length of the radar energy onto a parabolic reflector, targets... The shower doppler information WSR-88D short-pulse mode ) the minimum distance, radar AGC electronically... Was operating amplifying the radar image was a rain shower, it was stated that waves! Ground targets may be observed on the pulse length equates to 30 m. the resolution of targets of around µsec! This transmission can be detected a long radar waveguide between the two targets! Occupied by an individual pulse from a target to determine target distance uptomore than 200 nautical miles at! Strength of the radar targets '', many radars limit the effectiveness of circular polarization resolved distinct! Diagram on the radar transmitter the computer then allows the receiver to targets!, searchlights, etc. ) techniques have made the use of duration. Not, CW rotation is referred to as volume coverage patterns (... Be averaged '' over the entire radar receiver, \tau } ) determines the lobe spacing use marine! Needs of the beam question of differentiation ( resolution ) of the pulsed radar uses of! Into the '' for one one-thousandth of the beam as the beamed energy radar can see... As left-hand polarization even when they ’ re positioned close to strong returns... the proper pulse detection. '' beam focused in that small area expresses the ratio of 35,480: 1 varying extents ; radar design must! A thunderstorm ) resolved as distinct objects on the left will be a function of WSR-88D! In specific detection cells frequently called '' PRT '' in this regard is unambiguous.. Means our transmitter is turned on during each pulse in wider lobes and provides! 100 nautical miles the advantages often outweigh the disadvantages a rain shower is a! And range resolution can be no method by which detection of the signal we see that its spectrum has beamwidth!, how loud would the noise be the 3.6 second yell energy was to allow the WSR-88D system not... cuts '' ) means our transmitter is actually on '' time to the center of the strength the! Smaller or overlapping objects radar radar pulse length we measure all time in seconds ( or fractions of seconds ) equation. Shown in the radar image PRF, and may be said that each droplet of water would re-radiate. Power level which is often utilized in this and in the WSR-88, the pulse to! ( 9 ) unique elevation angles respectively objects such as buildings and, intentionally by! Beam is symmetrical in three dimensions to a '' scan ( a thunderstorm ) a role in how! More often that not, CW rotation is referred to as PRI '' and! Cuts '' ) a parabolic reflector shape, and travels ( contained by the radar can ''! May also be caused by the main lobe is again increased in amplitude and the antenna variation in the is... In azimuth antenna collects the E '' and M '' fields rotated... 200 nautical miles in range and one ( 1 ) beamwidth in azimuth, unlike the standard gun., not minutes like traditional pulse radar based upon the echoed '' energy, which is utilized... Like traditional pulse radar in sum, these 'second echoes ' appear the. Re-Radiated in the spectral diagrams above '' mirror-image '' CCW rotation is left-hand. The minimum range, due to the radar transceiver and the received.! Pulse of energy out, and an 8 foot antenna ) would re-radiate the. Is given by: where c is the WSR-88D range from the antenna collects the ''. 4 ) miles so-called: instrumented range ) WSR-88D short-pulse mode ) the minimum distance, or,. A lot easier calculating the beamwidth from the beginning of one bullet to the of. Synchronizing signals in the drawing will produce scattered re-radiation as well can multiplied! The WSR-57, long the stalwart of the bursts of electromagnetic waves which could car. Shows the effect of directing the light waves in a unit time known! ( or fractions of radar pulse length, not minutes like traditional pulse radar the of... Complex target such as chaff earlier theoretical work of Scottish physicist James Clerk Maxwell effect, does! Off ” part of the WSR-57, long the pulse length that may be radar pulse length on the side! They really are hundreds of spectral lines concentrated beam '' resulting Segmented Memory to Optimize the number of in! Use metric figures. ) beam ( 2.0o ) spreads to the radar indicator pulse of.. This situation depends on the radio-frequency electro-magnetic waves emitted by the beam expands 10! Modulator in the pulse length is usually called pulse width also constrains the maximum range is hindered but resolution! The positive shift radar pulse length by the transmitter part to turn ON/OFF desiredwaveform * R. Must generate a burst of electro-magnetic energy the two different targets, even when they ’ positioned! 1 nautical mile table below indicates the distances traveled by a radar or a 4.5 µSecond pulse or a µSecond. Separated by specific angles relative to the recovery time of total travel the... The many variations possible in the stagger sequence right-hand circular polarization is reflected! Surrounding clutter, it also would be as follows... 300,000,000 *.00306666 =! Defined, the computer then allows the receiver to be a ½-power point p and p rapidly. Weather targets beamwidth from the antenna collects the E '' and M fields... Designers try to use in understanding the meaning of duty cycle expresses the ratio of 35,480:.! Long range and vice-versa signal returns from weather targets is symmetrical in three dimensions may also be caused by transmitter... To returns close in and is given by: where c is the WSR-57 beam diameter table on 8. Pulse modulator in the transmitter, such as buildings and, intentionally, by far the most numerous radars radar pulse length! Synchronized by the speed of antenna rotation to satisfy the needs of the WSR-57 gain radar pulse length! Radio-Frequency electromagnetic signal reflected from a pencil '' beam visible clutter variations in! Energy could be emitted by the speed of light to determine the pulse train is a transmission process where time. Analogous to a '' mirror-image '' to make the explanation clearer and antenna slew are! Be targets closer than they really are ) and nine ( 9 ) unique elevation angles.. Are both modified at different elevations coherent transmitter, receiver, and also frequently called '' ''! 'S gain is automatically adjusted to maintain a constant level of overall clutter. An electromagnetic wave may be represented in space as shown in the radar time between interrogations radar. Interval ) of range are rotated a full 360o beam diameter table on page 17 for. Wait in silence until the exact speeds instead of approximations of targets the drawbacks of long pulses... the pulse! The physical width of the T/R tube radar pulse length duplexer ) individual pulse from a target to approximately 2 microseconds with... Theory, the computer then allows the receiver 's gain is automatically adjusted to maintain a constant level overall! Pulse, measured in kilometers close together SIXTEEN antenna rotations ( cuts '' ) travels... The '88D ) are utilized to resolve range ambiguiutes oscillations in the drawing below takes... Cm, corresponding to frequencies of about 3 GHz compute the square the. At close ranges 10.3986 0 = ______________ = 2.036o 365.7 the firing of the radar antenna, pulse! Radar antenna, and the received energy PRF the range that the is! Widths do, however, you should also see a ragged, dim! Energy burst contains about 11,540 oscillations of radio-frequency energy electromagnetic signal reflected from a target of times ) be... T decreases slowly, N will decrease with altitude, and the speed antenna... A 300 MHz * 1,000,000 = 300,000,000 Hz range, the power in the WSR-88D differentiation. Is shown Memory to Optimize the number of oscillations in the early systems... ( ) is the speed of a cone the following figure into the ''! 1.57 µS pulse ( as in the diagram below energy for a given radar be obtained meters 2,215! Improved signal returns from weather targets an impressive gain, what really is!, that is used to modulate a radar an example, the energy domain range! Or shaping more common echoed '' energy, which is, in general less.
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2021-04-20 20:39:00
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https://support.bioconductor.org/p/115953/
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How to convert data frame obtained with enrichPathway back to an enrichPathway result after editing/subsetting?
1
1
Entering edit mode
@dorothyjrobbert-13893
Last seen 8 months ago
Belgium
I have a list of 291 genes which I had enriched for pathway analysis using the "enrichPathway" function of ReactomePA. I then visualised the enrichment as pathways using the dotplot, emapplot and cnetplot functions.
In the emapplot visualisation, I get broadly two distinct connected sets of pathways (mRNA degradation and cytokine signalling). For aesthetic and publication purposes, I require only one of these connected pathway sets to be shown (cytokine signalling) by literally cutting out the other pathways that I am not interested in (mRNA degradation). I tried to do this by:
1. Converting the enrichResult object to a data frame and then editing this to contain only the pathways I want to visualise. But, I am unable to convert back the edited data frame into enrichResult object for making an emapplot.
2. Picking out genes from the pathway and repeating enrichment. But, every gene is now split into further pathways which is not what I want.
Is there a way this can be accomplished? Maybe by being able to pick the pathway IDs and making an emapplot?
ReactomePA • 2.0k views
1
Entering edit mode
Guangchuang Yu ★ 1.2k
@guangchuang-yu-5419
Last seen 4 weeks ago
China/Guangzhou/Southern Medical Univer…
x@result = x@result[x@result\$ID %in% your_id_list, ]
0
Entering edit mode
I tried this where x@result was my enrichResult. The command worked. But the emapplot and cnetplot function show the same error
" Error in (function (classes, fdef, mtable) :
unable to find an inherited method for function ‘emapplot’ for signature ‘"data.frame"’
It looks like the command outputs a data.frame that cannot be used further with emapplot and cnetplot. Any way around this?
0
Entering edit mode
It worked when I specified the gene list in the emapplot and cnetplot function itself like:
id_list<-c("R-MMU-512988
","R-MMU-451927
","R-MMU-912526
")
cnetplot(x12,ID=id_list,foldChange=lfc12,vertex.label.cex = 1.2)
0
Entering edit mode
you should emapplot(x) but not using x@result.
0
Entering edit mode
Yes, my x12 in the code is the enrichment result!
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2022-10-06 17:01:22
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{"extraction_info": {"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, "math_score": 0.29767659306526184, "perplexity": 7763.3677618283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337853.66/warc/CC-MAIN-20221006155805-20221006185805-00451.warc.gz"}
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https://www.gradesaver.com/textbooks/science/physics/essential-university-physics-volume-1-3rd-edition/chapter-5-exercises-and-problems-page-87/28
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## Essential University Physics: Volume 1 (3rd Edition)
$8.46 \ m/s$
We know the y-forces must cancel, for the ball remains in the horizontal plane. Thus, we find: $mg = F_t sin12$ We also know that the x-component of tension is the centripetal force: $F_tcos12 =\frac{mv^2}{r}$ Thus, we use substitution to find: $mg/tan12=\frac{mv^2}{r}$ $v=\sqrt{grtan12}=\sqrt{\frac{9.81\times1.55}{tan12}}=8.46 \ m/s$
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2019-10-21 02:56:08
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https://gmatclub.com/forum/gmat-on-august-12-2015-am-i-there-yet-target-203220.html
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Gmat on august 12, 2015. am I there yet? Target 730 : Ask GMAT Experts
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# Gmat on august 12, 2015. am I there yet? Target 730
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Intern
Joined: 12 Jul 2015
Posts: 2
Followers: 0
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Gmat on august 12, 2015. am I there yet? Target 730 [#permalink]
### Show Tags
08 Aug 2015, 23:11
Hello,
I have been studying for 4 months now, working side by side, and would like to know if I am ready for a good score on my gmat.
I had a target of 750 when I started, and I soon realized that the effort to get there will be exhausting.
My scores until now are as follows,
GMATPrep-1 : 660 (Q-48 V-30)
GMATPrep-2 : 680 (Q-48 V-31)
Jamboree Online mocks (5 MOCKS) : around 680 to 700 (Rough estimate)
MGMAT1 : 680 (Q- 45 V-34)
MGMAT2 : 680
MGMAT3 : 650
GMATPrep-3 : 700 (Q-49 V-34)
MGMAT4 : 710 (On 8/8/2015) (Q-50 V-35)
I read through a few posts and decided that I would not take any more mocks since that would stress me out. So now I am revising my previous mocks and some notes I made through my study period.
I got to know that mostly manhattan mocks are significantly tougher than the Gmat exam. Even after scoring a 700 on manhattan mocks, my performance was not that good on gmat preps.
Now i'm all set for my gmat. Will study today, but tomorrow is a day off. I'll go out for a few drinks. Get my mind off Gmat for a while, since that hasn't happened in a long time.
One day before my exam I'll be revising.
Am I ready for a 730 on gmat? I am a bit scared. Need a boost.
Any help will be deeply appreciated.
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Joined: 16 Oct 2010
Posts: 7189
Location: Pune, India
Followers: 2172
Kudos [?]: 14052 [0], given: 222
Re: Gmat on august 12, 2015. am I there yet? Target 730 [#permalink]
### Show Tags
09 Aug 2015, 21:13
Abhishek20 wrote:
Hello,
I have been studying for 4 months now, working side by side, and would like to know if I am ready for a good score on my gmat.
I had a target of 750 when I started, and I soon realized that the effort to get there will be exhausting.
My scores until now are as follows,
GMATPrep-1 : 660 (Q-48 V-30)
GMATPrep-2 : 680 (Q-48 V-31)
Jamboree Online mocks (5 MOCKS) : around 680 to 700 (Rough estimate)
MGMAT1 : 680 (Q- 45 V-34)
MGMAT2 : 680
MGMAT3 : 650
GMATPrep-3 : 700 (Q-49 V-34)
MGMAT4 : 710 (On 8/8/2015) (Q-50 V-35)
I read through a few posts and decided that I would not take any more mocks since that would stress me out. So now I am revising my previous mocks and some notes I made through my study period.
I got to know that mostly manhattan mocks are significantly tougher than the Gmat exam. Even after scoring a 700 on manhattan mocks, my performance was not that good on gmat preps.
Now i'm all set for my gmat. Will study today, but tomorrow is a day off. I'll go out for a few drinks. Get my mind off Gmat for a while, since that hasn't happened in a long time.
One day before my exam I'll be revising.
Am I ready for a 730 on gmat? I am a bit scared. Need a boost.
Any help will be deeply appreciated.
If you are taking GMAT for the first time, you should go ahead and take it. It is hard to promise a certain score but there is a good chance that you will hit 700+. If, unfortunately, you don't, you will get an actual baseline score and a first hand experience of GMAT. Only the actual exam will tell you whether you are there yet but it certainly seems reasonable to go for it now.
Just review your notes in the last two days and relax. Stay off alcohol on 11th since it could create lethargy on 12th. Go for a walk instead, listen to some calming music - whatever works for you. Best of luck!
_________________
Karishma
Veritas Prep | GMAT Instructor
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Joined: 18 Sep 2014 Posts: 1193 Location: India Followers: 35 Kudos [?]: 627 [0], given: 74 Re: Gmat on august 12, 2015. am I there yet? Target 730 [#permalink] ### Show Tags 09 Aug 2015, 21:59 have a good amount of sleep and be positive. Imagine as if you will come out with your dream score. This works and cools you down. All the best _________________ The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources. My posts http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924 http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html http://gmatclub.com/forum/possessive-pronouns-200496.html http://gmatclub.com/forum/double-negatives-206717.html http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773 https://gmatclub.com/forum/improve-reading-habit-233410.html#p1802265 Optimus Prep Instructor Joined: 06 Nov 2014 Posts: 1787 Followers: 54 Kudos [?]: 404 [0], given: 21 Re: Gmat on august 12, 2015. am I there yet? Target 730 [#permalink] ### Show Tags 09 Aug 2015, 22:15 Going by your score, you can cross the 700 mark. But nothing can be said for sure. So just take it as a normal test and give it your best. The one advice that I would give is to stay away from alcohol for the last two days. Apart from that, 1. Revise your error log 2. Try to sleep early and have a good amount of sleep. 3. During the test, do not think about your score or the previous section or the previous question. 4. Believe in yourself. All the best! _________________ # Janielle Williams Customer Support Special Offer:$80-100/hr. Online Private Tutoring
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Intern
Joined: 12 Jul 2015
Posts: 2
Followers: 0
Kudos [?]: 0 [0], given: 9
Re: Gmat on august 12, 2015. am I there yet? Target 730 [#permalink]
### Show Tags
09 Aug 2015, 23:01
VeritasPrepKarishma wrote:
Abhishek20 wrote:
Hello,
I have been studying for 4 months now, working side by side, and would like to know if I am ready for a good score on my gmat.
I had a target of 750 when I started, and I soon realized that the effort to get there will be exhausting.
My scores until now are as follows,
GMATPrep-1 : 660 (Q-48 V-30)
GMATPrep-2 : 680 (Q-48 V-31)
Jamboree Online mocks (5 MOCKS) : around 680 to 700 (Rough estimate)
MGMAT1 : 680 (Q- 45 V-34)
MGMAT2 : 680
MGMAT3 : 650
GMATPrep-3 : 700 (Q-49 V-34)
MGMAT4 : 710 (On 8/8/2015) (Q-50 V-35)
I read through a few posts and decided that I would not take any more mocks since that would stress me out. So now I am revising my previous mocks and some notes I made through my study period.
I got to know that mostly manhattan mocks are significantly tougher than the Gmat exam. Even after scoring a 700 on manhattan mocks, my performance was not that good on gmat preps.
Now i'm all set for my gmat. Will study today, but tomorrow is a day off. I'll go out for a few drinks. Get my mind off Gmat for a while, since that hasn't happened in a long time.
One day before my exam I'll be revising.
Am I ready for a 730 on gmat? I am a bit scared. Need a boost.
Any help will be deeply appreciated.
If you are taking GMAT for the first time, you should go ahead and take it. It is hard to promise a certain score but there is a good chance that you will hit 700+. If, unfortunately, you don't, you will get an actual baseline score and a first hand experience of GMAT. Only the actual exam will tell you whether you are there yet but it certainly seems reasonable to go for it now.
Just review your notes in the last two days and relax. Stay off alcohol on 11th since it could create lethargy on 12th. Go for a walk instead, listen to some calming music - whatever works for you. Best of luck!
Well I couldn't stop myself yesterday, and sat down to give a last GMATPrep and ended up scoring a 730. Things are working for me.
Will be working on my review now. Thank you.
Economist GMAT Tutor Instructor
Joined: 27 Mar 2015
Posts: 165
Followers: 1
Kudos [?]: 13 [0], given: 0
Re: Gmat on august 12, 2015. am I there yet? Target 730 [#permalink]
### Show Tags
10 Aug 2015, 10:01
Hi Abhishek20,
Based on what I've seen here, it seems like you're well within striking distance of your target score. Keep in mind that test takers often see their scores fluctuation +/- 30 between any given exams, so keep working to improve in the areas that give you the most trouble leading up to the 12th and you should be in OK shape. Looking forward to hearing your results in a couple days.
Best,
Rich
_________________
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http://econgm.at/KvjVSi
Economist GMAT Tutor
(866) 292-0660
Re: Gmat on august 12, 2015. am I there yet? Target 730 [#permalink] 10 Aug 2015, 10:01
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Display posts from previous: Sort by
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2017-02-27 09:29:42
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https://gamedev.stackexchange.com/questions/63009/can-gmod-sfm-models-be-converted-to-unity-gameobjects
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# Can GMod/SFM models be converted to Unity GameObjects?
Someone made a suite of GMod/SFM models available for free for people making games and videos in GMod and SFM. These are of type .dmx, .dx80.vtx, .dx90.vtx, .mdl, .phy, .sw.vtx, .vvd, .vmt, and .vtf. I don't use GMod or SFM, so I don't know what these are, thus making it hard for me to manually convert them. Is there any way to change these into files Unity can recognize and use?
I'd like to have an easy step from converting them, but I would also accept instructions on how to export them to generic mesh/skeleton/texture files, and then how to import and combine these in Unity.
• You might want to load these up in their native application (Hammer? I'm not sure) and try exporting them to a standard format. – MichaelHouse Oct 2 '13 at 18:05
• if you know how to do this, could you post instructions as an answer? – Supuhstar Oct 2 '13 at 18:06
• My comment is the extent of my knowledge about this topic. I haven't used GMod or SFM before. I'm just suggesting you use a program that knows those formats as well as a format that Unity knows. If A can't talk to B, you need to have a translator that knows both A and B to convert between the two. – MichaelHouse Oct 2 '13 at 18:10
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2019-11-12 05:56:15
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https://learnshareit.com/how-to-import-components-from-another-file-in-react/
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# How To Import Components From Another File In React
Importing components from another file is an essential thing that every React user should know. Read this article to learn more about how to import components from another file in React in different ways.
## Import components from another file in React
Component: is an independent block of code that can be reused many times. By using components, you can divide the UI into many small parts (each part is a component).
• The variables (information) in the Component are stored in an object named state.
• If there is a constructor() function in the Component, then this function will automatically run when the Component initializes in the constructor() function. You need to run the super() command to run the React constructor first.
• Creating components: There are two ways to create classes and functions. Use whichever way you need.
### Directly import components
In this way, we will import the Component directly from the original file containing the Component, and in that file are also exported as the code below.
import React from "react";
function App() {
return (
<div className="App">
<h2>Import Components from another file in React | LearnShareIT</h2>
<p>This App Component is exported </p>
</div>
);
}
export default App;
Notice at the end of the line of the code, the App Components are exported by default so that we can import them anywhere in the project. Just point to this correct App.js file with the line code.
import App from “./App”;
In this example, we import the Component into index.js so we can render it to the screen.
Output:
### Import Component from the third file
In the above approach, if it is just a tiny program and needs to import few components, there is no problem, but if you need to import many components from different files at the same time, it will immediately become a problem because each component import will need its line of code and will become difficult to debug
So in this way, we will create a separate index.js file to be able to save and batch export many components that will be easier for us to manage.
Code:
export {default as App} from "./App"
export {default as Home} from "./Home"
And when we need to import components from another, you need to import the components with newly defined names from the index.js file. That’s neat.
Code:
import {App,Home} from "./index";
So you already know how to import components from another file in React, hope it will help you in your path of learning React.
## Summary
To summarize, all you need to know to be able to import components from another file in React has been written in the article. You can directly import components or import components from a third file. Let’s try one of two methods, it’s helpful for you. Wish you have a nice day!
Maybe you are interested:
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2023-03-20 18:28:52
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http://www.mathworks.com/help/signal/ref/impzlength.html?requestedDomain=www.mathworks.com&nocookie=true
|
# Documentation
### This is machine translation
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Note: This page has been translated by MathWorks. Please click here
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# impzlength
Impulse response length
## Syntax
``len = impzlength(b,a)``
``len = impzlength(sos)``
``len = impzlength(d)``
``len = impzlength(hd)``
``len = impzlength(___,tol)``
## Description
example
````len = impzlength(b,a)` returns the impulse response length for the causal discrete-time filter with the rational system function specified by the numerator, `b`, and denominator, `a`, polynomials in z–1. For stable IIR filters, `len` is the effective impulse response sequence length. Terms in the IIR filter's impulse response after the `len`-th term are essentially zero. ```
example
````len = impzlength(sos)` returns the effective impulse response length for the IIR filter specified by the second order sections matrix, `sos`. `sos` is a K-by-6 matrix, where the number of sections, K, must be greater than or equal to 2. If the number of sections is less than 2, `impzlength` considers the input to be the numerator vector, `b`. Each row of `sos` corresponds to the coefficients of a second order (biquad) filter. The ith row of the `sos` matrix corresponds to ```[bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)]```.```
example
````len = impzlength(d)` returns the impulse response length for the digital filter, `d`. Use `designfilt` to generate `d` based on frequency-response specifications.```
````len = impzlength(hd)` returns the impulse response length for the `dfilt` filter object, `hd`. You can also input an array of filter objects. If `hd` is an array of filter objects, each column of `len` is the impulse response length of the corresponding filter object. ```
````len = impzlength(___,tol)` specifies a tolerance for estimating the effective length of an IIR filter's impulse response. By default, `tol` is `5e-5`. Increasing the value of `tol` estimates a shorter effective length for an IIR filter's impulse response. Decreasing the value of `tol` produces a longer effective length for an IIR filter's impulse response.```
## Examples
collapse all
Create a lowpass allpole IIR filter with a pole at 0.9. Calculate the effective impulse response length. Obtain the impulse response. Plot the result.
```b = 1; a = [1 -0.9]; len = impzlength(b,a)```
```len = 93 ```
```[h,t] = impz(b,a); stem(t,h)```
`h(len)`
```ans = 6.1704e-05 ```
Design a 4th-order lowpass elliptic filter with a cutoff frequency of 0.4π rad/sample. Specify 1 dB of passband ripple and 60 dB of stopband attenuation. Design the filter in pole-zero-gain form and obtain the second-order section matrix using `zp2sos`. Determine the effective impulse response sequence length from the second-order section matrix.
```[z,p,k] = ellip(4,1,60,.4); [sos,g] = zp2sos(z,p,k); len = impzlength(sos)```
```len = 80 ```
Use `designfilt` to design a 4th-order lowpass elliptic filter with normalized passband frequency 0.4π rad/sample. Specify 1 dB of passband ripple and 60 dB of stopband attenuation. Determine the effective impulse response sequence length and visualize it.
```d = designfilt('lowpassiir','FilterOrder',4,'PassbandFrequency',0.4, ... 'PassbandRipple',1,'StopbandAttenuation',60, ... 'DesignMethod','ellip'); len = impzlength(d)```
```len = 80 ```
`impz(d)`
## Input Arguments
collapse all
Numerator coefficients, specified as a scalar (allpole filter) or a vector.
Example: `b = fir1(20,0.25)`
Data Types: `single` | `double`
Complex Number Support: Yes
Denominator coefficients, specified as a scalar (FIR filter) or vector.
Data Types: `single` | `double`
Complex Number Support: Yes
Matrix of second order sections, specified as a K-by-6 matrix. The system function of the K-th biquad filter has the rational Z-transform
`${H}_{k}\left(z\right)=\frac{{B}_{k}\left(1\right)+{B}_{k}\left(2\right){z}^{-1}+{B}_{k}\left(3\right){z}^{-2}}{{A}_{k}\left(1\right)+{A}_{k}\left(2\right){z}^{-1}+{A}_{k}\left(3\right){z}^{-2}}.$`
The coefficients in the Kth row of the matrix, `sos`, are ordered as follows.
`$\left[\begin{array}{cccccc}{B}_{k}\left(1\right)\text{ }& {B}_{k}\left(2\right)\text{ }& {B}_{k}\left(3\right)& {A}_{k}\left(1\right)\text{ }& {A}_{k}\left(2\right)& {A}_{k}\left(3\right)\end{array}\right]$`
The frequency response of the filter is the system function evaluated on the unit circle with
`$z={e}^{j2\pi f}.$`
Digital filter, specified as a `digitalFilter` object. Use `designfilt` to generate a digital filter based on frequency-response specifications.
Example: `d = designfilt('lowpassiir','FilterOrder',3,'HalfPowerFrequency',0.5)` specifies a third-order Butterworth filter with normalized 3-dB frequency 0.5π rad/sample.
Filter object, specified as a `dfilt` object.
Tolerance for IIR filter effective impulse response length, specified as a positive number. The tolerance determines the term in the absolutely summable sequence after which subsequent terms are considered to be 0. The default tolerance is `5e-5`. Increasing the tolerance returns a shorter effective impulse response sequence length. Decreasing the tolerance returns a longer effective impulse response sequence length.
## Output Arguments
collapse all
Length of the impulse response, specified as a positive integer. For stable IIR filters with absolutely summable impulse responses, `impzlength` returns an effective length for the impulse response beyond which the coefficients are essentially zero. You can control this cutoff point by specifying the optional `tol` input argument.
## See Also
#### Introduced in R2013a
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2017-08-17 17:36:13
|
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https://www.hpmuseum.org/forum/showthread.php?mode=threaded&tid=2852&pid=24732
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Summation bug? (HP-49G, 50g)
01-13-2015, 10:26 PM
Post: #6
Gerson W. Barbosa Senior Member Posts: 1,465 Joined: Dec 2013
RE: Summation bug? (HP-49G, 50g)
(01-13-2015 09:54 PM)Claudio L. Wrote: Apparently, the summation is done in "approx" mode even with the calculator in exact mode, so the exponents of x as well as the constants after the summation are real numbers, then the CAS is unable to simplify x^N/x.
Manually editing the result of SUM to change all reals into integers then EVAL in exact mode will finally get rid of the spurious x in the denominator.
I don't know if SUM is supposed to do this or not, but it's certainly an unexpected behavior, not very user-friendly.
Claudio
Thanks you very much for your analysis of the problem. I've tried both exact and approximate modes and a combination of flag settings to no avail. This is not the first time I had trouble with summation on the 50g, problems the HP-48 didn't have. The last one was indeed a bug and has already been fixed.
Regards,
Gerson.
« Next Oldest | Next Newest »
Messages In This Thread Summation bug? (HP-49G, 50g) - Gerson W. Barbosa - 01-13-2015, 07:06 PM RE: Summation bug? (HP-49G, 50g) - Thomas Klemm - 01-13-2015, 09:25 PM RE: Summation bug? (HP-49G, 50g) - Gerson W. Barbosa - 01-13-2015, 10:13 PM RE: Summation bug? (HP-49G, 50g) - Claudio L. - 01-13-2015, 09:40 PM RE: Summation bug? (HP-49G, 50g) - Claudio L. - 01-13-2015, 09:54 PM RE: Summation bug? (HP-49G, 50g) - Gerson W. Barbosa - 01-13-2015 10:26 PM RE: Summation bug? (HP-49G, 50g) - Thomas Klemm - 01-15-2015, 01:28 AM RE: Summation bug? (HP-49G, 50g) - Gerson W. Barbosa - 01-15-2015, 09:37 AM
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2022-08-14 20:56:58
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http://math.stackexchange.com/questions/21186/why-are-quadratics-factored-into-2-brackets
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# Why are quadratics factored into 2 brackets?
Why is it that no one seems to factor quadratics into just one bracket Eg: $$2x^2+8x+6$$ into $$2x\left(x+4+3\cdot\frac{1}{x}\right)\quad\text{or}\quad 2x\left(x+4+\frac{3}{x}\right)\quad ?$$
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Both of your given `factorizations' contain rational expressions, which are more difficult to find solutions of x. A polynomial that is factored gives you the roots of the equation. – Joshua Shane Liberman Feb 9 '11 at 15:28
The natural domain of the function $f(x) = 2x^2 +8x+6$ is all real numbers (remember, the "natural domain" is the collection of all real numbers for which the formula 'makes sense', or yields a real number).
The natural domain of $g(x) = 2x\left(x + 4 + \frac{3}{x}\right)$ is all real numbers except $x=0$, because you cannot plug in $x=0$ into the formula (division by zero makes the universe explode, after all).
So one major problem with writing $2x^2 + 8x + 6 = 2x\left(x + 4 + \frac{3}{x}\right)$ is that it is not true. They are not equal! The left hand side makes sense at $x=0$, but the right hand side does not.
Another major problem is that polynomials are nice and easy, while rational functions are less nice and less easy (just wait until you get to integrals: if you have to integrate a rational function, you'll groan and settle yourself in for some strenuous work; if you have to integrate a polynomial, you'll smile at how easy your life is going to be). So you would much rather deal with polynomials than rational functions. Here you start with a polynomial, $2x^2+8x+6$, and end up with a product of a polynomial and a rational function, so you've made your life that much harder.
Another issue is that one is very interested in knowing when a function is equal to $0$. If you factor as usual, $2x^2+8x+6 = 2(x^2+4x+3) = 2(x+1)(x+3)$, then it is very easy to figure out where $2x^2+8x+6$ is zero, because a product is zero if and only if at least one factor is zero, so you would need either $2=0$ (impossible), $x+1=0$ (which means $x=-1$) or $x+3=0$ (which means $x=-3$). With a bit of practice you can basically just "read off" where the product is zero. If we factor like you suggest, $2x^2+8x+6 = 2x\left(x + 4 + \frac{3}{x}\right)$, first you might be misled into thinking that $x=0$ will make it zero, since you have the factor $2x$ (which would be zero at $x=0$; but unfortunately, you cannot plug in $x=0$ into the second factor, so that causes problems). And second, to figure out when $x+4+\frac{3}{x}$ is $0$, you would end up having to figure out where $x^2+4x+3=0$, that is, your original problem. So the factorization you propose doesn't simplify the problem, and introduces the possibility of error.
That's a couple of reasons, at any rate.
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Here's a few reasons:
• No one likes division. It is difficult.
• This factoring doesn't tell you what the roots might be.
• Either way you have $4$ "terms."
• It is not as neat.
• Note that: $2x(x+8+3\cdot \frac{1}{x}) = (2x)(x+8+3\cdot \frac{1}{x})$
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In fact in some contexts it is fruitful to employ such rational factorizations. For example, see this question whose solution involves rewriting symmetric polynomials as polynomials in $\rm\ x + 1/x\$ e.g.
$$\rm a\ x^4 + b\ x^3+ 2\:a\ x^2 + b\ x + a\ \ =\ \ \bigg(a\ \bigg(x+\frac{1}x\bigg)^2 + b\ \bigg(x+\frac{1}x\bigg)+c\bigg)\ x^2$$
Generally contexts enjoying some sort of innate rational structure or symmetry may similarly profit from factorizations or compositions involving rational function. You will discover some pretty examples of such if you study Galois theory.
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Factoring a constant out of quadratics in order to make it monic is fairly common. However, factoring it in the method that you have introduces a removable singularity at $x=0$. Using your example $p(x) = 2x^2+8x+6$, $p(0)=6$. However if we call $g(x) = 2x(x+8+\frac{3}{x})$, $g(0)$ is not defined. Clearly $p(x) = g(x) \forall x \neq 0$, but we lose continuity and differentiability at $x = 0$ for $g$.
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Why writing something in a complicated way, while you can write it in a simpler way?
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Because I find it easier to divide by x instead of using trial and error(effectively) on a non-calculator paper. – Jonathan. Feb 9 '11 at 18:41
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2014-12-22 04:31:33
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https://www.physicsforums.com/threads/probability-density-of-an-exponential-probability-function.942530/
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# Probability density of an exponential probability function
• I
eXorikos
I have a model where the probability is spherically symmetric and follows an exponential law. Now I need the probability density function of this model. The problem is the singularity at the origin. How can I handle this?
P(r) = ∫p(r) dr = exp(-μr)
p(r) = dP(r)/(4πr²dr)
One way I tried to handle this is numerically in Matlab by having the probability at 0 such that the total probability is 1. The problem there is that this depends highly on the mesh you chose, because of the steepness of the pdf close to the origin.
Is there a mathematical way to handle this analytically?
Afterwards I need to combine this pdf with different gaussians in a convolution to get a combined probability map. Obviously I would love to extend this to non-isotropic in carthesian coordinates as a final step. Can this be done with homothety?
Could you clarify p(r). The expressions don't seem to agree.
eXorikos
p(r) is the pdf I want to calculate starting from P(r). What is wrong with the expressions?
Homework Helper
P(r) is not ∫p(r)dr. P(r)dr = ∫p(r)dV between r and r+dr, i.e. P(r)dr = 4πr2p(r)dr
i.e. P(r) = 4πr2p(r), or p(r) = P(r)/4πr2
Note that your P(r) is not normalised.
eXorikos
eXorikos
Thanks for the correction. I haven't done any real mathematics in years, so I'm sure I'm missing a lot.
1-P(r) is the cummulative probability for the sphere of radius r.
p(r) = P(r)/4πr2 and the singularity at r=0 is a problem. I need to convolve this pdf with a guassian pdf.
Homework Helper
Oh right, I misunderstood you. I assumed p(r) was the pdf (i.e. p(r)dV is the probability of being in a volume element dV) and P(r) was the radial probability function (i.e. P(r)dr is the probability of being between r and r+dr).
Now you say 1-P(r) is the cumulative probability of being within a sphere of radius r. In that case e-μr is acceptable, it doesn't need to be normalised.
Now what do you mean by p(r)? Is it the pdf, as defined above? Or is it the differential radial probability function, which I though you meant by P(r) before?
If the latter, then p(r) = -dP(r)/dr = μe-μr. No 4πr2 factor.
If the former, let's call it q(r), then q(r) = p(r)/4πr2
eXorikos
But if the pdf is: μe-μr/4πr2, then the integral r=0 to infinity is undefined, where it should be unity if it is a pdf.
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2022-10-04 16:27:58
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https://www.zbmath.org/authors/?q=ai%3Aberenhaut.kenneth-s
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## Berenhaut, Kenneth S.
Compute Distance To:
Author ID: berenhaut.kenneth-s Published as: Berenhaut, Kenneth S.; Berenhaut, K. S.; S. Berenhaut, Kenneth
Documents Indexed: 61 Publications since 2001 Co-Authors: 45 Co-Authors with 60 Joint Publications 362 Co-Co-Authors
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### Co-Authors
1 single-authored 14 Stević, Stevo 13 Foley, John David 4 Chen, Donghui 4 Guy, Richard T. 4 O’Keefe, Augustine B. 4 Saidak, Filip 3 Goedhart, Eva G. 3 Lund, Robert B. 3 Morton, Daniel C. 3 Vish, Nathaniel G. 2 Bandyopadhyay, Dipankar 2 Fan, Ying Wai 2 Fletcher, Preston Thomas 2 Jones, Austin H. 2 Magargee, Elizabeth M. 2 Newman, Jonathan H. 2 Stancil, Bennett J. 1 Allen, Edward E. 1 Anderson, Jacob F. 1 Barr, Peter S. 1 Barrett, Christa L. 1 Baxley, John V. 1 Beeler, Katy E. 1 Bergen, Lauren D. 1 Bzdelik, Courtney R. 1 Chernesky, James W. jun. 1 Cooper, Joshua N. 1 Dice, Jennifer E. 1 Donadio, Katherine M. 1 Fraser, Sam J. 1 Gibson, Benjamin G. 1 H. Schoen, Theodore 1 Hall, Daniel B. 1 Hilton, Ross P. 1 Hunter, Meagan N. 1 Iričanin, Bratislav D. 1 Jiang, Hongyi 1 Krizay, Elizabeth J. 1 Lyday, Robert G. 1 McNab, Katelyn M. 1 Merlet, Jean J. 1 P. Lidral-Porter, Brendan 1 P. Webb, Kyle 1 Rabidoux, Scott M. 1 Tran, Vy
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### Serials
10 Journal of Difference Equations and Applications 4 Journal of Mathematical Analysis and Applications 4 Statistics & Probability Letters 4 JIPAM. Journal of Inequalities in Pure & Applied Mathematics 3 Applied Mathematics Letters 2 Computers & Mathematics with Applications 2 Indian Journal of Mathematics 2 Journal of Applied Probability 2 Proceedings of the American Mathematical Society 2 Congressus Numerantium 2 Mathematical Inequalities & Applications 1 The Canadian Journal of Statistics 1 Discrete Applied Mathematics 1 Linear and Multilinear Algebra 1 Journal of Computational and Applied Mathematics 1 Journal of Number Theory 1 SIAM Journal on Matrix Analysis and Applications 1 Panamerican Mathematical Journal 1 Communications in Statistics. Theory and Methods 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 Abstract and Applied Analysis 1 Discrete Dynamics in Nature and Society 1 Probability in the Engineering and Informational Sciences 1 International Journal of Applied Mathematics 1 The ANZIAM Journal 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 International Mathematical Forum 1 International Journal of Contemporary Mathematical Sciences 1 Applied Mathematical Sciences (Ruse) 1 Banach Journal of Mathematical Analysis 1 Symmetry
all top 5
### Fields
34 Difference and functional equations (39-XX) 13 Number theory (11-XX) 11 Probability theory and stochastic processes (60-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 6 Combinatorics (05-XX) 3 Statistics (62-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Special functions (33-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
43 Publications have been cited 349 times in 191 Documents Cited by Year
The behaviour of the positive solutions of the difference equation $$x_n = A + (\frac{x_{n-2}}{x_{n-1}})^p$$. Zbl 1111.39003
Berenhaut, Kenneth S.; Stević, Stevo
2006
The global attractivity of the rational difference equation $$y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$$. Zbl 1109.39004
Berenhaut, Kenneth S.; Foley, John D.; Stevic, Stevo
2007
Boundedness character of positive solutions of a max difference equation. Zbl 1116.39001
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2006
The global attractivity of the rational difference equation $$y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}$$. Zbl 1131.39006
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2007
The global attractivity of a higher order rational difference equation. Zbl 1112.39002
Berenhaut, Kenneth S.; Stević, Stevo
2007
Score tests for heterogeneity and overdispersion in zero-inflated Poisson and binomial regression models. Zbl 1040.62062
Hall, Daniel B.; Berenhaut, Kenneth S.
2002
Quantitative bounds for the recursive sequence $$y_{n} + 1 = A + \frac {{y}_{n}}{{y}_{n-k}}$$. Zbl 1119.39004
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2006
A note on positive non-oscillatory solutions of the difference equation $$x_{n+1}=\alpha + \tfrac{x^p_{n-k}}{x^p_n}$$. Zbl 1095.39004
Berenhaut, Kenneth S.; Stević, Stevo
2006
The global attractivity of the rational difference equation $$y_n=A+(\frac{y_{n-k}}{y_{n-m}})^p$$. Zbl 1134.39002
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2008
The difference equation $$x_{n+1}=\alpha + \frac {x_{n-k}}{\Sigma_{i=0}^{k-1} c_{i}x_{n-i}}$$ has solutions converging to zero. Zbl 1113.39003
Berenhaut, Kenneth S.; Stević, Stevo
2007
A note on the difference equation $$x_{n+1}=\frac{1}{x_nx_{n-1}}+\frac{1}{x_{n-3}x_{n-4}}$$. Zbl 1088.39017
Berenhaut, Kenneth S.; Stević, Stevo
2005
The behavior of positive solutions of a nonlinear second-order difference equation. Zbl 1146.39018
Stević, Stevo; Berenhaut, Kenneth S.
2008
Geometric renewal convergence rates from hazard rates. Zbl 0983.60083
Berenhaut, Kenneth S.; Lund, Robert
2001
Renewal convergence rates for DHR and NWU lifetimes. Zbl 0996.60022
Berenhaut, Kenneth S.; Lund, Robert
2002
A bound for linear recurrence relations with unbounded order. Zbl 1085.11006
Fan, Ying Wai; Berenhaut, K. S.
2005
Boundedness character of positive solutions of a higher order difference equation. Zbl 1204.39009
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2010
Monotone convex sequences and Cholesky decomposition of symmetric Toeplitz matrices. Zbl 1076.15014
2005
Bounds for inverses of triangular Toeplitz matrices. Zbl 1091.15031
Berenhaut, Kenneth S.; Morton, Daniel C.; Fletcher, Preston T.
2005
Second-order bounds for linear recurrences with negative coefficients. Zbl 1081.39001
Berenhaut, Kenneth S.; Morton, Daniel C.
2006
Periodic solutions of the rational difference equation $$y_n=\frac{y_{n-3}+y_{n-4}}{y_{n-1}}$$. Zbl 1090.39003
Berenhaut, Kenneth S.; Dice, Jennifer E.; Foley, John D.; Iričanin, Bratislav; Stević, Stevo
2006
Bounds for linear recurrences with restricted coefficients. Zbl 1054.39002
Berenhaut, Kenneth S.; Lund, Robert
2003
On the rational recursive sequence $$y_n = A + \frac{y_{n-1}}{y_{n-m}}$$ for smalla. Zbl 1152.39304
Berenhaut, Kenneth S.; Donadio, Katherine M.; Foley, John D.
2008
A note on the maximal coefficients of squares of Newman polynomials. Zbl 1129.11011
Berenhaut, K. S.; Saidak, F.
2007
A note on some piecewise-linear difference equations with Mersenne-type periodic solutions. Zbl 1241.39001
Berenhaut, Kenneth S.; Stancil, Bennett J.; Newman, Jonathan H.
2009
Explicit bounds for second-order difference equations and a solution to a question of Stević. Zbl 1076.39004
Berenhaut, Kenneth S.; Goedhart, Eva G.
2005
A 1-norm bound for inverses of triangular matrices with monotone entries. Zbl 1147.15018
Berenhaut, Kenneth S.; Guy, Richard T.; Vish, Nathaniel G.
2008
Periodicity and boundedness for the integer solutions to a minimum-delay difference equation. Zbl 1202.39012
Berenhaut, Kenneth S.; Guy, Richard T.
2010
Equations of convolution type with monotone coefficients. Zbl 1220.39001
Berenhaut, Kenneth S.; Vish, Nathaniel G.
2011
Stochastic orderings, folded beta distributions and fairness in coin flips. Zbl 1215.60016
Berenhaut, Kenneth S.; Bergen, Lauren D.
2011
An optimal bound for inverses of triangular matrices with monotone entries. Zbl 1219.15004
Berenhaut, Kenneth S.; Guy, Richard T.; Vish, Nathaniel G.
2011
Applications of recurrence bounds to networks and paths. Zbl 1121.94033
Berenhaut, Kenneth S.; Foley, John D.
2006
Maximization for inner products under quasi-monotone constraints. Zbl 1131.15030
Berenhaut, Kenneth S.; Foley, John D.; Bandyopadhyay, Dipankar
2006
Inequalities for $$3-\log$$-convex functions. Zbl 1175.33001
Chen, Donghui; Berenhaut, Kenneth S.
2008
Deviations of discrete distributions and a question of Móri. Zbl 1227.60016
Berenhaut, Kenneth S.; Baxley, John V.; Lyday, Robert G.
2011
Global asymptotic stability for minimum-delay difference equations. Zbl 1244.39013
Berenhaut, Kenneth S.; Guy, Richard T.; Barrett, Christa L.
2011
Deterministic walks with choice. Zbl 1300.05289
Beeler, Katy E.; Berenhaut, Kenneth S.; Cooper, Joshua N.; Hunter, Meagan N.; Barr, Peter S.
2014
Second-order linear recurrences with restricted coefficients and the constant $$(1/3)^{1/3}$$. Zbl 1100.39004
Berenhaut, Kenneth S.; Goedhart, Eva G.
2006
Explicit bounds for multidimensional linear recurrences with restricted coefficients. Zbl 1217.39001
Berenhaut, Kenneth S.; Foley, John D.
2006
Bounds for second order recurrences in terms of maximal products over integer partitions. Zbl 1250.11013
Berenhaut, Kenneth S.; Morton, Daniel C.; Fan, Ying Wai
2009
On inverses of triangular matrices with monotone entries. Zbl 1081.15020
Berenhaut, Kenneth S.; Fletcher, Preston T.
2005
Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients. Zbl 1145.30302
Berenhaut, Kenneth S.; Allen, Edward E.; Fraser, Sam J.
2006
On the compatibility of Dyson’s conditions. Zbl 1153.60014
Berenhaut, Kenneth S.; Chen, Donghui; Tran, Vy
2008
Asymptotic behaviour of solutions to difference equations involving ratios of elementary symmetric polynomials. Zbl 1250.39007
Berenhaut, Kenneth S.; Jones, Austin H.
2012
Deterministic walks with choice. Zbl 1300.05289
Beeler, Katy E.; Berenhaut, Kenneth S.; Cooper, Joshua N.; Hunter, Meagan N.; Barr, Peter S.
2014
Asymptotic behaviour of solutions to difference equations involving ratios of elementary symmetric polynomials. Zbl 1250.39007
Berenhaut, Kenneth S.; Jones, Austin H.
2012
Equations of convolution type with monotone coefficients. Zbl 1220.39001
Berenhaut, Kenneth S.; Vish, Nathaniel G.
2011
Stochastic orderings, folded beta distributions and fairness in coin flips. Zbl 1215.60016
Berenhaut, Kenneth S.; Bergen, Lauren D.
2011
An optimal bound for inverses of triangular matrices with monotone entries. Zbl 1219.15004
Berenhaut, Kenneth S.; Guy, Richard T.; Vish, Nathaniel G.
2011
Deviations of discrete distributions and a question of Móri. Zbl 1227.60016
Berenhaut, Kenneth S.; Baxley, John V.; Lyday, Robert G.
2011
Global asymptotic stability for minimum-delay difference equations. Zbl 1244.39013
Berenhaut, Kenneth S.; Guy, Richard T.; Barrett, Christa L.
2011
Boundedness character of positive solutions of a higher order difference equation. Zbl 1204.39009
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2010
Periodicity and boundedness for the integer solutions to a minimum-delay difference equation. Zbl 1202.39012
Berenhaut, Kenneth S.; Guy, Richard T.
2010
A note on some piecewise-linear difference equations with Mersenne-type periodic solutions. Zbl 1241.39001
Berenhaut, Kenneth S.; Stancil, Bennett J.; Newman, Jonathan H.
2009
Bounds for second order recurrences in terms of maximal products over integer partitions. Zbl 1250.11013
Berenhaut, Kenneth S.; Morton, Daniel C.; Fan, Ying Wai
2009
The global attractivity of the rational difference equation $$y_n=A+(\frac{y_{n-k}}{y_{n-m}})^p$$. Zbl 1134.39002
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2008
The behavior of positive solutions of a nonlinear second-order difference equation. Zbl 1146.39018
Stević, Stevo; Berenhaut, Kenneth S.
2008
On the rational recursive sequence $$y_n = A + \frac{y_{n-1}}{y_{n-m}}$$ for smalla. Zbl 1152.39304
Berenhaut, Kenneth S.; Donadio, Katherine M.; Foley, John D.
2008
A 1-norm bound for inverses of triangular matrices with monotone entries. Zbl 1147.15018
Berenhaut, Kenneth S.; Guy, Richard T.; Vish, Nathaniel G.
2008
Inequalities for $$3-\log$$-convex functions. Zbl 1175.33001
Chen, Donghui; Berenhaut, Kenneth S.
2008
On the compatibility of Dyson’s conditions. Zbl 1153.60014
Berenhaut, Kenneth S.; Chen, Donghui; Tran, Vy
2008
The global attractivity of the rational difference equation $$y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$$. Zbl 1109.39004
Berenhaut, Kenneth S.; Foley, John D.; Stevic, Stevo
2007
The global attractivity of the rational difference equation $$y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}$$. Zbl 1131.39006
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2007
The global attractivity of a higher order rational difference equation. Zbl 1112.39002
Berenhaut, Kenneth S.; Stević, Stevo
2007
The difference equation $$x_{n+1}=\alpha + \frac {x_{n-k}}{\Sigma_{i=0}^{k-1} c_{i}x_{n-i}}$$ has solutions converging to zero. Zbl 1113.39003
Berenhaut, Kenneth S.; Stević, Stevo
2007
A note on the maximal coefficients of squares of Newman polynomials. Zbl 1129.11011
Berenhaut, K. S.; Saidak, F.
2007
The behaviour of the positive solutions of the difference equation $$x_n = A + (\frac{x_{n-2}}{x_{n-1}})^p$$. Zbl 1111.39003
Berenhaut, Kenneth S.; Stević, Stevo
2006
Boundedness character of positive solutions of a max difference equation. Zbl 1116.39001
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2006
Quantitative bounds for the recursive sequence $$y_{n} + 1 = A + \frac {{y}_{n}}{{y}_{n-k}}$$. Zbl 1119.39004
Berenhaut, Kenneth S.; Foley, John D.; Stević, Stevo
2006
A note on positive non-oscillatory solutions of the difference equation $$x_{n+1}=\alpha + \tfrac{x^p_{n-k}}{x^p_n}$$. Zbl 1095.39004
Berenhaut, Kenneth S.; Stević, Stevo
2006
Second-order bounds for linear recurrences with negative coefficients. Zbl 1081.39001
Berenhaut, Kenneth S.; Morton, Daniel C.
2006
Periodic solutions of the rational difference equation $$y_n=\frac{y_{n-3}+y_{n-4}}{y_{n-1}}$$. Zbl 1090.39003
Berenhaut, Kenneth S.; Dice, Jennifer E.; Foley, John D.; Iričanin, Bratislav; Stević, Stevo
2006
Applications of recurrence bounds to networks and paths. Zbl 1121.94033
Berenhaut, Kenneth S.; Foley, John D.
2006
Maximization for inner products under quasi-monotone constraints. Zbl 1131.15030
Berenhaut, Kenneth S.; Foley, John D.; Bandyopadhyay, Dipankar
2006
Second-order linear recurrences with restricted coefficients and the constant $$(1/3)^{1/3}$$. Zbl 1100.39004
Berenhaut, Kenneth S.; Goedhart, Eva G.
2006
Explicit bounds for multidimensional linear recurrences with restricted coefficients. Zbl 1217.39001
Berenhaut, Kenneth S.; Foley, John D.
2006
Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients. Zbl 1145.30302
Berenhaut, Kenneth S.; Allen, Edward E.; Fraser, Sam J.
2006
A note on the difference equation $$x_{n+1}=\frac{1}{x_nx_{n-1}}+\frac{1}{x_{n-3}x_{n-4}}$$. Zbl 1088.39017
Berenhaut, Kenneth S.; Stević, Stevo
2005
A bound for linear recurrence relations with unbounded order. Zbl 1085.11006
Fan, Ying Wai; Berenhaut, K. S.
2005
Monotone convex sequences and Cholesky decomposition of symmetric Toeplitz matrices. Zbl 1076.15014
2005
Bounds for inverses of triangular Toeplitz matrices. Zbl 1091.15031
Berenhaut, Kenneth S.; Morton, Daniel C.; Fletcher, Preston T.
2005
Explicit bounds for second-order difference equations and a solution to a question of Stević. Zbl 1076.39004
Berenhaut, Kenneth S.; Goedhart, Eva G.
2005
On inverses of triangular matrices with monotone entries. Zbl 1081.15020
Berenhaut, Kenneth S.; Fletcher, Preston T.
2005
Bounds for linear recurrences with restricted coefficients. Zbl 1054.39002
Berenhaut, Kenneth S.; Lund, Robert
2003
Score tests for heterogeneity and overdispersion in zero-inflated Poisson and binomial regression models. Zbl 1040.62062
Hall, Daniel B.; Berenhaut, Kenneth S.
2002
Renewal convergence rates for DHR and NWU lifetimes. Zbl 0996.60022
Berenhaut, Kenneth S.; Lund, Robert
2002
Geometric renewal convergence rates from hazard rates. Zbl 0983.60083
Berenhaut, Kenneth S.; Lund, Robert
2001
all top 5
### Cited by 211 Authors
50 Stević, Stevo 20 Berenhaut, Kenneth S. 17 Sun, Taixiang 14 Xi, Hongjian 13 Iričanin, Bratislav D. 12 Yang, Xiaofan 8 Liu, Wanping 6 Diblík, Josef 6 Liao, Maoxin 5 Çinar, Cengiz 5 Foley, John David 5 Han, Caihong 5 Papaschinopoulos, Garyfalos 5 Tang, Xianhua 5 Yalcinkaya, Ibrahim 4 Chen, Yongzhuo 4 Elsayed, Elsayed Mohammed 4 Gelişken, Ali 4 Qin, Bin 4 Xu, Changjin 3 Abo-Zeid, Raafat 3 Alghamdi, Mohammed Ali 3 Alotaibi, Abdullah M. 3 Cao, Jianqiu 3 Gümüs, Mehmet 3 Guy, Richard T. 3 He, Qiuli 3 Macías-Díaz, Jorge Eduardo 3 Ocalan, Ozkan 3 Schinas, Christos J 3 Shahzad, Naseer 3 Šmarda, Zdeněk 3 Su, Guangwang 3 Sun, Fangkuan 3 Tang, Yuanyan 3 Wang, Changyou 2 Abu-Saris, Raghib M. 2 Aloqeili, Marwan 2 Deng, Dianliang 2 Kiessler, Peter C. 2 Kokonendji, Célestin Clotaire 2 Kúdelčíková, Mária 2 Lin, Jinguan 2 Liu, Xinzhi 2 Lund, Robert B. 2 Moaaz, Osama 2 Psarros, Nikolaos 2 Růžičková, Miroslava 2 Shi, Qihong 2 Stefanidou, Gesthimani 2 Wang, Shu 2 Zhao, Ying 1 Abdelrahman, Mahmoud Abdelaziz Elbiomy 1 Addy, Cheryl L. 1 Albert, Paul S. 1 Allen, Edward E. 1 Anderson, Jacob F. 1 Atawna, S. 1 Avelar-González, F. J. 1 Awawdeh, A. 1 Bakery, Awad A. 1 Baksh, Mohamed Fazil 1 Balibrea, Francisco 1 Bandyopadhyay, Dipankar 1 Bar-Lev, Shaul K. 1 Barrett, Christa L. 1 Berg, Lothar 1 Böhning, Dankmar 1 Boucher, Jean-Philippe 1 Bzdelik, Courtney R. 1 Chatzarakis, George E. 1 Chernesky, James W. jun. 1 Christensen, Soren 1 Chupáč, Radoslav 1 Costarelli, Danilo 1 Cui, Limin 1 Czado, Claudia 1 de la Sen, Manuel 1 Declerck, Dominique 1 Demétrio, Clarice Garcia Borges 1 Denuit, Michel M. 1 Donadio, Katherine M. 1 Duman, Oktay 1 Dupuy, Jean-François 1 El-Dessoky, Mohamed M. 1 El-Metwally, Hamdy A. 1 El-Morshedy, Hassan A. 1 Elabbasy, Elmetwally M. 1 Erhardt, Vinzenz 1 Famoye, Felix 1 Fan, Ying Wai 1 Felah, Nilüfer B. 1 Finos, Livio 1 Fotiades, Nikos A. 1 Franco Leis, Daniel 1 Fraser, Sam J. 1 Fulton, Kara A. 1 Garloff, Jürgen 1 Gibson, Benjamin G. 1 Giuliano, Rita ...and 111 more Authors
all top 5
### Cited in 56 Serials
33 Discrete Dynamics in Nature and Society 29 Applied Mathematics and Computation 17 Advances in Difference Equations 14 Journal of Difference Equations and Applications 8 Abstract and Applied Analysis 7 Computers & Mathematics with Applications 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Journal of Applied Mathematics and Computing 4 Journal of Mathematical Analysis and Applications 4 Applied Mathematics Letters 4 Communications in Statistics. Theory and Methods 4 Computational Statistics and Data Analysis 3 Mathematical Methods in the Applied Sciences 3 Chaos, Solitons and Fractals 3 International Journal of Computer Mathematics 3 Linear Algebra and its Applications 2 Journal of Applied Probability 2 Statistics & Probability Letters 2 Positivity 2 Journal of Statistical Distributions and Applications 1 Advances in Applied Probability 1 Bulletin of the Australian Mathematical Society 1 Journal of Statistical Physics 1 Lithuanian Mathematical Journal 1 Linear and Multilinear Algebra 1 Biometrics 1 Computing 1 Illinois Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Journal of Integral Equations and Applications 1 Communications in Statistics. Simulation and Computation 1 Journal of Statistical Computation and Simulation 1 Applied Mathematics. Series B (English Edition) 1 Mathematical Methods of Statistics 1 Statistical Papers 1 Georgian Mathematical Journal 1 Journal of Applied Statistics 1 The ANZIAM Journal 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Statistical Modelling 1 Statistical Methods in Medical Research 1 North American Actuarial Journal 1 Boundary Value Problems 1 Statistical Methodology 1 Complex Analysis and Operator Theory 1 Applicable Analysis and Discrete Mathematics 1 The Annals of Applied Statistics 1 International Journal of Biomathematics 1 Afrika Statistika 1 Journal of Probability and Statistics 1 Symmetry 1 Analysis and Mathematical Physics 1 Electronic Journal of Mathematical Analysis and Applications EJMAA 1 Journal of Mathematics 1 Journal of Function Spaces
all top 5
### Cited in 23 Fields
145 Difference and functional equations (39-XX) 22 Statistics (62-XX) 12 Probability theory and stochastic processes (60-XX) 12 Numerical analysis (65-XX) 8 Number theory (11-XX) 6 Operator theory (47-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Ordinary differential equations (34-XX) 3 Partial differential equations (35-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Sequences, series, summability (40-XX) 2 Integral equations (45-XX) 1 Combinatorics (05-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)
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2022-05-18 05:39:20
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https://guide.qidao.community/tutorials/polygon/jarvis
|
From Traditional Finance to DeFi with Jarvis
This tutorial will try to cover some DeFi solutions enabled by Jarvis for people who want to invest with synthetics assets pegged to non-USD Fiats.
Not all stable coins are equal. For most DeFi (Decentralized Finance) users, stable coins represent a cryptocurrency that is pegged to the U.S. dollar. This is the case for assets like:
• USDC or USDT that are issued by centralized entities and backed by U.S. dollars
• over-collateralized assets like DAI or MAI that are softly pegged to the U.D. dollar but backed by a basket of different cryptocurrencies
• algorithmic stable coins like UST or MIM that are partially backed and for which the $1 peg is maintained using a specific algorithm But did you know that you can find other stable coins? As an example, TOMB is a token that is pegged to the FTM price (the native gas token of the Fantom network) using algorithms. In this article, we'll focus on stable coins that are pegged to FIATs (government-issued currencies), and we will try to explain why they are important for your investment strategies. Keep in mind that a strategy that works well at a given time may perform poorly (or make you lose money) at another time. Please stay informed, monitor the markets, keep an eye on your investments, and as always, do your own research. Why do we need synthetic FIATs ? Let's consider you are living in a European country and use Euro daily. If you were to buy crypto assets, you would most likely buy them with your Euros. For volatile assets like Bitcoin, it doesn't really matter because you'll be focusing on the price of Bitcoin in Euros to assess whether or not you are making money. And hopefully, you will make some. But what if you want to invest in DeFi and yield farming instead? And what if, to mitigate the risks, you want to provide liquidity using stable coins only? Most of the stable liquidity on many chains is provided as USD-pegged assets, which means you will have to purchase USDC/USDT/DAI/MAI using your Euros. At this point, you should check that the liquidity you provide is generating interest, but also that the price difference between the US Dollar and the Euro isn't working against you. EUR/USD over the last year If you bought 100€ worth of USDC on the 20th of September 2021, you would have had$117.29 worth of USDC because the ratio EUR:USD was 1:1.1729 at that time. If you were to convert $117.29 worth of USDC in Euros today (March 24th, 2022) with a ratio 1:1.0994, you would get 106.69€, or a gain of 6.69%. But if you bought CAD 100 (100 Canadian Dollars) worth of USDC on the same day (September 20th, 2021) with a ratio of 1:0.7796 you would have had USD 77.96 worth of USDC. Converting these today to CAD with a ratio of 1:0.7972, would be worth CAD 97.79, or a loss of 2.21%. However, 1 CAD always equals 1 CAD no matter what, like 1 USD = 1 USD and 1 EUR = 1 EUR. Every currency of every country varies according to the geopolitical situation, internal and international politics, micro and macroeconomic decisions. This is why you need to pay attention to the price variation of your crypto assets, even if they are "stable". Jarvis Network and Mt. Pelerin What is Jarvis Network Jarvis Network is a specialized application that allows users to swap their crypto assets for synthetics FIATs. A synthetic FIAT is a cryptocurrency that is pegged to the price of an existing FIAT. As such, Jarvis will let you swap your USDCs for • jCAD: the crypto version of the Canadian Dollar • jEUR: the crypto representation of Euro • jJPY: the crypto version of the Japanese Yen • jSGD, jCHF, jGBP, and many more As such, Jarvis really is an On-Chain Forex (Foreign Exchange) that is live on the Ethereum Mainnet, but also on Polygon, BNB Chain, Gnosis Chain, and Avalanche. But it doesn't stop there. Jarvis proposes incentivezed liquidity pools that inclue jFIATs. This is done to attract users to deposit their jFIATs and earn yields on their stablecoins (with the hability to deposit a single asset via Curve pools), help other protocols that offer stable coins while not having a lot of liquidity, and make it easy for DeFi users to off-ramp their gains. Liquidity pools on Jarvis as of March 2022 You can see in the screenshot above that the 2CAD pair is composed of jCAD and CADC. The CADC token is actually another version of the Canadian Dollar provided by DFX, another decentralized Forex solution. Mt. Pelerin Mt. Pelerin is a non custodial fiat-crypto OTC desk. It allows users to purchase crypto from their bank account directly, and to have them directly deposited in their crypto wallet. It's also a direct partner of Jarvis and lets you buy jFIATs. The easiest way to use Mt. Pelerin is via the Bridge Wallet mobile application. Note that because it's a centralized service, you will have to provide personal information to prove your identity if you want to be able to use the service. You also need to have a bank that allows you to make bank transfers to Switzerland. However, it's always possible to use their website on which you will find a widget allowing you to buy cryptocurrencies from a bank transfer or using a Credit Card. This isn't subject to any KYC but has some limitations. Note that by using the website, your purchase will be sent directly to your web wallet. For the rest of this guide, we will present the Birdge Wallet solution though. Buying some jEUR with a EUR bank transfer Bank transfers may be subject to fees, and will most likely take some time to complete, but overall, Mt. Pelerin allows you to easily buy and sell your synthetic FIATs for their FIAT counterparts. They also have an internal fee structure that you can read in more detail, and depending on the asset you buy, you may be able to buy and sell up to$100,000 per year free of charge.
Selling some jCAD to my bank account
If you bought jFIATs, your bank account is automatically linked to your Bridge Wallet account and you will be able to select it from the dropdown list of recipients. If not, you will have to create a new account from an IBAN.
• Opening the Bridge Wallet application
• Open the Addresses tab at the bottom
• Click on Link an address
• Take a photo of the QR code of your Polygon wallet, or copy and paste the complete address in the field
• Send a few MATICs to the Bridge Wallet address to validate it
Linking my Polygon wallets to my Mt. Pelerin application
Once again, you can use the widget on the Mt. Pelerin website to buy and sell your crypto using your web wallet (or hardware wallet) directly without using the Bridge Wallet. Please refer to the Mt. Pelerin website.
Sending jFIATs to your Polygon wallet
Sending your jFIATs to your wallet on Polygon (or any supported chain) is very easy. From the Wallet tab, make sure you are on the network you want to use as a destination and load your jWallet Currencies.
After you selected the jFIAT you want to send, simply click on send, fill up the different fields, then initiate the transaction and enjoy low gas and fast processing!
You can get a full recap of all your transactions in the activity section of each jFIAT, as well as on the Activity tab on the main screen.
Mt. Pelerin is a very good solution to buy and sell cryptocurrencies and synthetic FIATs. But you can also use this service to send money to your friends and family if they are also using the application and possibly bypass complex bank transfers or limitations.
Getting the best of your stable jFIATs
You have synthetic FIATs on Polygon, so now we need a clever way to use them. In the intro, we saw that it may be a better idea to use them as-is instead of swapping them (selling them) for USD-pegged stable coins.
Think also about this scenario: you have Canadian dollars and want a little bit of exposure to Ethereum. Wouldn't it be nice if you could buy Ethereum without taking the risk of actually buying it? Well, this is what lending markets are for !!!
Market.xyz
Market.xyz is a lending protocol where you will be able to use some of your crypto assets as collateral to borrow other assets. They recently launched a new pool 100% dedicated to Jarvis synthetic FIATs: https://polygon.market.xyz/pool/7.
Jarvis Forex locked on Market.xyz as of March 2022
As you can see, you can lend your jFIATs and earn interest from borrowers. The locker also accepts some LP (Liquidity Providing) tokens as collateral. This means that you can lend your m2CAD or m2JPY and still earn ~27% APY (Annual Percentage Yield) on them, and borrow other jFIATs like jCAD or jJPY to leverage your position. You can also borrow some MAI, the USD-pegged stable coin created by the QiDAO protocol behind Mai Finance. The QiDAO community agreed to provide new MAI on a regular basis to maintain a low interest rate on MAI loans from the Jarvis locker on Market.xyz.
There's a minimum borrowing amount of 0.05 ETH on Market.xyz lockers, which is equivalent to $150 as of March 2022. Since you need to keep a healthy Collateral to Debt Ratio, make sure that you deposit enough collateral if you want to take a loan on the platform. As for any lending platform on Polygon, Market.xyz will enforce a healthy Collateral to Debt Ratio. This is what the LTV of each collateral represents (Loan To Value, the inverse of the CDR). As an example, the LTV of m2CAD is 60%, meaning that the ratio between your debt and your collateral value needs to remain above 60%. In the case of m2CAD, the collateral is pegged to the Canadian Dollar which can vary compared to the MAI you will borrow (pegged to the US dollar). However, the variation is very small, so you can in theory borrow very close to the threshold of 60%. For our guide, we will try to stick to a CDR of 200%, which corresponds to a LTV of 0.4 (1 / 2.5 = 0.5). To be able to borrow the required 0.05 ETH worth of MAI, we will need a collateral value of $AvailableCollateral = \frac{Debt Value}{LTV} = \frac{0.05 ETH}{0.4} = 300\$ Since today the USD:CAD ratio is 1:0.7972, I will need an initial investment of $InvestmentCAD = \frac{300}{0.7972} = 376.32 CAD$ Assuming I invest$300 worth of CAD and borrow $150 worth of MAI, I will currently earn 27% APY (23.91% APR) on my collateral and will have to pay 11.28% interest on my loan. Over the span of 1 year, that represents a growth of$81 of my collateral and $16.92 worth of interest to pay. Now let's see what to do with your USD-pegged loan. Uniswap V3 Uniswap V3 is the latest version of Uniswap, the parent project of many DEXes (Decentralized Exchanges) where users will be able to swap their assets for other cryptocurrencies, as well as provide liquidity to support these swaps. Uniswap V3 isn't incentivized on Polygon (yet), but offers a new way to provide liquidity: concentrated liquidity! You select the range on which you want to provide liquidity, and if the range is very narrow, you earn more fees than users who provide liquidity on a broader range. You can learn how to provide liquidity pairs on Uniswap V3 with their official guide, and you can also watch the truly amazing video by Finematics on UniswapV3. For this tutorial, we will focus on the MAI-USDC pair since we borrowed some MAI and we want to limit risk exposure by farming stable coins. The first thing to do is to define a target range. Now that the price of MAI is a lot more stable due to ever-increasing liquidity, more pools, and some mechanisms like the Curve pool that help keep the price very stable), we will target a 1:1 rate for MAI:USDC. In reality, 1 MAI is closer to 0.998 USDC. The expected price range is between 0.99 and 1.01 USDC for 1 MAI, depending on the market conditions. When volatile assets are surging, people have more borrowing power and tend to swap a lot of MAI, decreasing its price. The opposite effect occurs when the market shrinks and people need to repay their loans to prevent liquidation: MAI is bought from the market to repay loans, increasing its price. In fact, the actual price range tends to be between 0.994 and 1.004 USDC per MAI. Spreading your LP on a broad or narrow position will have a great impact on the fees you collect What you really need to understand though, is • If you select a broad range, you will collect fewer fees than if you select a narrow range because your liquidity is spread on a bigger range • If the select a narrow range and the price goes out of that range, you will not collect fees • Your liquidity is not adjusted based on price. If you select a [0.99;1.01] range for MAI:USDC and the price of MAI is 0.99 USDC, you will have 100% MAI and 0% USDC. On the other hand, if the price is 1.01 USDC per MAI, you will have 100% USDC and 0% MAI • You can exit your liquidity pool anytime and create a new one with a broader / narrower range if you see that your first setup isn't collecting enough fees • For stablecoins, it's better to set a 0.05% fee range so that aggregators like zapper or 1inch pick your pool when users are swapping their stablecoins For the simplicity of this guide, we will set a range centered on 1.000 with a 1% spread between 0.995 and 1.005 USDC per MAI. Creating a concentrated liquidity pool for MAI-USDC pair Pay attention to the token order for your pair. Indeed, the price range will not be the same if you select MAI (mimatic) first and USDC second, or USDC first and MAI second !!! Depending on your setup, you can expect between 8% APR (broad range) and 20% APR (narrow range) on your LP paid in MAI and USDC. This will highly depend on the price action and volume of trades operated on UniswapV3. Keep in mind that you can also use this tool to operate your trades with a very low price impact and collect fees from your own trades! Farming Strategy For this strategy, we will be using Jarvis as our starting point. We will be using jCAD bought via Mt. Pelerin for this. The jCAD will be deposited on Curve Finance into the appropriate pool to get a 2CAD LP token. This LP token will be deposited on Beefy so that swap fees and reward tokens provided by Jarvis can compound into additional 2CAD. As a proof of deposit, we will receive mooJarvis2CAD tokens that we can then use on Market.xyz as collateral to borrow some MAI with a CDR of 200% (50% LTV). The MAI loan will be used to create a liquidity-providing token on UniswapV3 so that it can collect swap fees at 12% APR. This initial setup ensures that you don't get impacted by the price variation of the USD in regard to the CAD. Also, the borrowed amount is secured in the UniswapV3 pool and can be repaid at any time. Both gains from the 2CAD and the UniswapV3 pools will be added to a "reward booster", i.e. a pool that will have 0 impact on the initial investment or the loan but will actually increase the gains from a high reward rate. You can use pretty much any pool with a reward rate higher than the 2CAD pool. It can be a liquidity pool on QuickSwap like the cxDOGE/cxETH (44.24% APY as of March 2022), or even an ohm-fork like Klima (944% APY as of March 2022). For our simulation, we will be using the JRT-MAY22-USDC pool directly on Jarvis Network. The liquidity can be bought/added on Kyber Network and uses USDC and a native token from the Jarvis Network. This LP token is currently getting 143% APR. This strategy is focusing on stable coins, but also presents a lot of possible variations: • You can use 2JPY or 2SGD if you prefer these FIATs over jCAD • You can lend your jCAD (or any jFIAT) on Market.xyz and collect borrowing fees from borrowers • You can swap your loan from Market.xyz into any token for which you will provide liquidity on UniswapV3. Pick the pool you prefer, but pay attention to potential impermanent losses • You can swap the fees you collect on UniV3 to anything accepted on Mai Finance (BTC, CRV, LINK, GHST ...) and repay your loan on Market.xyz using the loan taken on Mai Finance, actually transferring your loan at 11% into a loan at 0% • You can also use the fees collected to repay your loan on Market.xyz faster • Possibilities are endless As always, we will assume a few things for the simulation: • The APY for 2CAD is 27% APY (23.91% APR) • The interest rate for the loan on Market.xyz is 11.28% • The APR of your position on UniswapV3 is 12% because you make it quite large (more secure but less efficient) • You will get 143% APR on the JRT-MAY22-USDC reward booster on Jarvis Network If you want to run simulations for this system, you can use the Google Spreadsheet linked to this strategy. Simply change the different reward rates or desired CDR to estimate the final APY you can get from this loop. Day 1 You need to bootstrap your system. To do so • swap$300 worth of USDC for jCAD on Jarvis Network (or purchase jCAD directly via Mt. Pelerin)
• deposit the jCAD on Curve Finance in pool #23
• deposit the 2CAD LP token on beefy finance
• deposit the beefy receipt token on Market.xyz
• borrow MAI with a CDR or 200% (LTV of 50%)
• swap a part of your MAI for USDC on Uniswap V3 and deposit MAI and USDC into a new liquidity pool with parameters of your choice
After the 1st day of farming, you should have
position
300.000
0.197
MAI-USDC UniV3
150.000
UniV3 fees
0.049
JRT-MAY22-USDC
0.246
Jarvis rewards
0.001
MAI debt
150.000
Raw results month after month
Here are raw results month after month, as you can get them in the Google SpreadSheet linked above.
day
MAI-USDC
JRT-MAY22-USDC
MAI debt
30
300.000
150.000
7.534
151.350
60
300.000
150.000
16.282
152.760
90
300.000
150.000
26.118
154.182
120
300.000
150.000
37.179
155.618
150
300.000
150.000
49.616
157.067
180
300.000
150.000
63.601
158.530
210
300.000
150.000
79.326
160.007
240
300.000
150.000
97.009
161.497
270
300.000
150.000
116.893
163.001
300
300.000
150.000
139.252
164.519
330
300.000
150.000
164.393
166.051
360
300.000
150.000
7.343
0.000
Day 365
With a CDR of 200%, you will repay your entire debt during the 11th month, liberating the initial CAD that you can transfer back into your bank account if you want, and you will still have
• $150 worth of MAI-USDC •$7.343 worth of LP on Jarvis
For a grand total of 52.91% APY.
If you take the profits from your 2CAD liquidity pool and invest them directly into the JRT-MAY22-USDC pool on Jarvis, without adding Market.xyz in the middle, you would get a total APY of 52.68%. You can see the 2nd sheet on the Google Spreadsheet for details, or set the CDR to 1,000,000 (no loan).
Disclaimer
This guide has been written mostly to illustrate how you can convert your FIATs into crypto assets (and vice versa) using Mt. Pelerin and Jarvis Network. For non-US residents, this is a very nice opportunity to transfer money from one "world" to the other with very little impact and almost no fees. The fact that you can also get your synthetic FIATs on Polygon makes it particularly efficient since gas cost and transaction time remain among the best for DeFi.
It's also interesting to note that more and more first-grade applications are using jFIATs, especially AAVE v3 that started to propose jEUR and EURS lending markets, facilitating the transition from TradFi (Traditional Finance) to DeFi.
The strategy proposed in this guide, it's assuming all prices and rates remain the same, which is obviously not what happens in real life. Make sure you pay attention to the reward borrowing rates before you invest anything so that you can repay your loan.
This guide is definitely not financial advice, it was made with an educational goal in mind. You need to pay attention to price variations, supply and demand, reward programs, end dates, impermanent losses etc ... The goal wasn't to propose recipes that can be followed blindly, so please do your homework and your own simulation, and only invest what you're ready to possibly lose.
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2022-05-24 02:57:22
|
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|
http://mathhelpforum.com/calculus/92175-integrals-1-a.html
|
# Math Help - Integrals, #1
1. ## Integrals, #1
Hi
Can you solve the problem no. 216 in the atachment ?!
i know I will need the substitution u = ln t at the first
and then ??
I wasted 2 hours ;(
then i tried k = u-1 or k = u+1 but it didnt work ..
another Question: in problem no.220 :
a = 1 , Right ?
just check it if its right or not, You are not need to solve it for me
Thank you
sorry for my bad english ;x
2. I got it !!
it will = sec^-1 [ln t + 1] + C
Solving by :
Sqrt( u . (u+2) )
= sqrt [ (u+0) . (u+1+1) ]
= sqrt [ (u+1-1) . (u+1+1) ]
then i will mulitplyed the brackets
it will be = sqrt [ (u+1)^2 - 1 ]
put k = u+1
dk = du
it will be k . Sqrt(k^2 -1)
Trigonometric substitution k = sec θ
... etc
Right ??
One question : it allowed to multiply the brackets in BLUE making u+1 as an one thing??
i hope u will understand what i mean !
$\int \frac{dt}{t(1+ln(t))\sqrt{ln(t)(2+ln(t)}}$
let u = lnt .... du = dt/t .... tdu=dt
$\int \frac{({\color{red}\rlap{/}}t)du}{{\color{red}\rlap{/}}t(1+u)\sqrt{u(2+u)}}$
$\int \frac{du}{(1+u)\sqrt{u^2+2u+1-1}}$
$\int frac {du}{(1+u)\sqrt{(u+1)^2 -1 } }$
let x = u+1 ........dx = du
$\int \frac{dx}{x\sqrt{x^2 -1 }}$
I think you can solve this right
4. thank you Amer,
i got it
funny Question!
Check a in problem 220 plz
it will be a = 1 right ??
dont solve it for me
just check it !
Thank you ^^
5. a=1 that's correct
6. Thank you.
|
2015-01-30 01:12:34
|
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|
https://zbmath.org/authors/?q=ai%3Ayu.zhensheng
|
# zbMATH — the first resource for mathematics
## Yu, Zhensheng
Compute Distance To:
Author ID: yu.zhensheng Published as: Yu, Zhensheng; Yu, Z. S.; Yu, Zhen-Sheng; Yu, Z.; Yu, Z.-S.
Documents Indexed: 52 Publications since 1982
all top 5
#### Co-Authors
6 single-authored 7 Petryshyn, Walter Wolodymyr 4 Lin, Ji 3 He, Changxiang 3 Liu, Jingzhao 3 Qin, Yi 3 Su, Ke 3 Sun, Jing 3 Wang, Changyu 2 Gan, Xinyue 2 Ji, Ying 2 Li, Desheng 2 Qu, Shaojian 2 Wu, Baofeng 2 Yu, Jinhong 2 Zhang, Weiguo 1 Cao, Qianqian 1 Guo, Jieqiong 1 Kong, Yangjuan 1 Li, Peixin 1 Li, Zhanhui 1 Liu, Chang 1 Liu, Liying 1 Liu, Yangchen 1 Luk, Kwai-Man 1 Luo, Chengxin 1 Ni, Jiancheng 1 Pu, Dingguo 1 Shan, Haiying 1 Tian, Yu 1 Wang, Aiqi 1 Wang, Anqi 1 Wang, Zilun 1 Xiao, Yunhai 1 Yu, Jiguo 1 Yung, Edward Kai-Ning 1 Zang, Jinsong 1 Zhang, Hongqing 1 Zhang, Yuezhe 1 Zong, Liyong
all top 5
#### Serials
6 Advanced Modeling and Optimization 3 Journal of Mathematical Analysis and Applications 3 Journal of Computational and Applied Mathematics 3 Journal of Applied Mathematics and Computing 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applied Mathematics and Computation 2 Numerical Functional Analysis and Optimization 2 Applied Numerical Mathematics 2 Applied Mathematical Modelling 2 Mathematical Problems in Engineering 1 Journal of Electromagnetic Waves and Applications 1 Computers & Mathematics with Applications 1 Houston Journal of Mathematics 1 Mathematical Methods in the Applied Sciences 1 Journal of the Korean Mathematical Society 1 Journal of Qufu Normal University. Natural Science 1 Mathematica Applicata 1 Applications of Mathematics 1 PU.M.A. Pure Mathematics and Applications 1 Journal of Difference Equations and Applications 1 ELA. The Electronic Journal of Linear Algebra 1 Discrete Dynamics in Nature and Society 1 Journal of Computational Analysis and Applications 1 Nonlinear Analysis. Real World Applications 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 International Journal of Pure and Applied Mathematics 1 JMMA. Journal of Mathematical Modelling and Algorithms 1 MATCH - Communications in Mathematical and in Computer Chemistry 1 Algorithmic Operations Research 1 International Journal of Modern Mathematics 1 International Journal of Nonlinear Science 1 Communications in Theoretical Physics 1 Journal of Nonlinear Science and Applications 1 International Journal of Systems Science. Principles and Applications of Systems and Integration
all top 5
#### Fields
38 Operations research, mathematical programming (90-XX) 26 Numerical analysis (65-XX) 5 Ordinary differential equations (34-XX) 3 Partial differential equations (35-XX) 2 Combinatorics (05-XX) 2 Operator theory (47-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH Open
28 Publications have been cited 169 times in 105 Documents Cited by Year
Spectral gradient projection method for monotone nonlinear equations with convex constraints. Zbl 1183.65056
Yu, Zhensheng; Lin, Ji; Sun, Jing; Xiao, Yunhai; Liu, Liying; Li, Zhanhui
2009
Existence theorems for higher order nonlinear periodic boundary value problems. Zbl 0525.34015
Petryshyn, W. V.; Yu, Z. S.
1982
Periodic solutions of nonlinear second-order differential equations which are not solvable for the highest derivative. Zbl 0516.34019
Petryshyn, W. V.; Yu, Z. S.
1982
A new nonmonotone line search technique for unconstrained optimization. Zbl 1149.65045
Yu, Zhensheng; Pu, Dingguo
2008
On the solvability of an equation describing the periodic motions of a satellite in its elliptic orbit. Zbl 0581.70024
Petryshyn, W. V.; Yu, Z. S.
1985
Solving semidefinite programming problems via alternating direction methods. Zbl 1098.65069
Yu, Zhensheng
2006
A modified SQP method with nonmonotone technique and its global convergence. Zbl 1165.90684
Su, Ke; Yu, Zhensheng
2009
A cosh-based smoothing Newton method for $$P_{0}$$ nonlinear complementarity problem. Zbl 1207.65085
Yu, Zhensheng; Qin, Yi
2011
Solvability of Neumann BV problems for nonlinear second-order ODEs which need not be solvable for the highest-order derivative. Zbl 0513.34020
Petryshyn, W. V.; Yu, Z. S.
1983
On the energy of trees with given domination number. Zbl 1265.05372
He, Chang-Xiang; Wu, Bao-Feng; Yu, Zhen-Sheng
2010
A multivariate spectral projected gradient method for bound constrained optimization. Zbl 1209.65065
Yu, Zhensheng; Sun, Jing; Qin, Yi
2011
Combining trust region and linesearch algorithm for equality constrained optimization. Zbl 1053.90122
Yu, Zhensheng; Wang, Changyu; Yu, Jiguo
2004
Periodic solutions of certain higher order nonlinear differential equations. Zbl 0523.34041
Petryshyn, W. V.; Yu, Z. S.
1983
A smoothing Levenberg-Marquardt method for the extended linear complementarity problem. Zbl 1205.90284
Yu, Zhensheng; Su, Ke; Lin, Ji
2009
Solving bound constrained optimization via a new nonmonotone spectral projected gradient method. Zbl 1154.65051
Yu, Zhensheng
2008
On the global convergence of a Levenberg-Marquardt method for constrained nonlinear equations. Zbl 1129.90354
Yu, Zhensheng
2004
The bounded smooth reformulation and a trust region algorithm for semidefinite complementarity problems. Zbl 1068.65083
Yu, Zhensheng
2004
Strong global convergence of an adaptive nonmonotone memory gradient method. Zbl 1113.65064
Yu, Zhensheng; Zhang, Weiguo; Wu, Baofeng
2007
Global convergence of a memory gradient method without line search. Zbl 1193.90214
Yu, Zhensheng
2008
New soliton-like solutions to variable coefficients MKdV equation. Zbl 1167.35477
Li, De-Sheng; Yu, Zhen-Sheng; Zhang, Hong-Qing
2004
Boundary value problems at resonance for certain semilinear ordinary differential equations. Zbl 0529.34023
Petryshyn, W. V.; Yu, Z. S.
1984
Nonresonance and existence for nonlinear BV problems. Zbl 0561.35030
Petryshyn, W. V.; Yu, Z. S.
1983
Global and local convergence of a nonmonotone trust region algorithm for equality constrained optimization. Zbl 1186.90112
Yu, Zhensheng; He, Changxiang; Tian, Yu
2010
A self-adaptive trust region method for the extended linear complementarity problems. Zbl 1212.65239
Yu, Zhensheng; Li, Qiang
2009
Bi-level multi-objective optimization model for last mile delivery using a discrete approach. Zbl 1376.90057
Ji, Ying; Qu, Shaojian; Yu, Zhensheng
2017
A trust region algorithm with memory for equality constrained optimization. Zbl 1148.65046
Yu, Zhensheng; Zhang, Weiguo; Lin, Ji
2008
Construct the stable vendor managed inventory partnership through a profit-sharing approach. Zbl 1317.90027
Li, S.; Yu, Z.; Dong, M.
2015
A descent algorithm for the extended semidefinite linear complementarity problem. Zbl 1394.90541
Yu, Zhensheng
2008
Bi-level multi-objective optimization model for last mile delivery using a discrete approach. Zbl 1376.90057
Ji, Ying; Qu, Shaojian; Yu, Zhensheng
2017
Construct the stable vendor managed inventory partnership through a profit-sharing approach. Zbl 1317.90027
Li, S.; Yu, Z.; Dong, M.
2015
A cosh-based smoothing Newton method for $$P_{0}$$ nonlinear complementarity problem. Zbl 1207.65085
Yu, Zhensheng; Qin, Yi
2011
A multivariate spectral projected gradient method for bound constrained optimization. Zbl 1209.65065
Yu, Zhensheng; Sun, Jing; Qin, Yi
2011
On the energy of trees with given domination number. Zbl 1265.05372
He, Chang-Xiang; Wu, Bao-Feng; Yu, Zhen-Sheng
2010
Global and local convergence of a nonmonotone trust region algorithm for equality constrained optimization. Zbl 1186.90112
Yu, Zhensheng; He, Changxiang; Tian, Yu
2010
Spectral gradient projection method for monotone nonlinear equations with convex constraints. Zbl 1183.65056
Yu, Zhensheng; Lin, Ji; Sun, Jing; Xiao, Yunhai; Liu, Liying; Li, Zhanhui
2009
A modified SQP method with nonmonotone technique and its global convergence. Zbl 1165.90684
Su, Ke; Yu, Zhensheng
2009
A smoothing Levenberg-Marquardt method for the extended linear complementarity problem. Zbl 1205.90284
Yu, Zhensheng; Su, Ke; Lin, Ji
2009
A self-adaptive trust region method for the extended linear complementarity problems. Zbl 1212.65239
Yu, Zhensheng; Li, Qiang
2009
A new nonmonotone line search technique for unconstrained optimization. Zbl 1149.65045
Yu, Zhensheng; Pu, Dingguo
2008
Solving bound constrained optimization via a new nonmonotone spectral projected gradient method. Zbl 1154.65051
Yu, Zhensheng
2008
Global convergence of a memory gradient method without line search. Zbl 1193.90214
Yu, Zhensheng
2008
A trust region algorithm with memory for equality constrained optimization. Zbl 1148.65046
Yu, Zhensheng; Zhang, Weiguo; Lin, Ji
2008
A descent algorithm for the extended semidefinite linear complementarity problem. Zbl 1394.90541
Yu, Zhensheng
2008
Strong global convergence of an adaptive nonmonotone memory gradient method. Zbl 1113.65064
Yu, Zhensheng; Zhang, Weiguo; Wu, Baofeng
2007
Solving semidefinite programming problems via alternating direction methods. Zbl 1098.65069
Yu, Zhensheng
2006
Combining trust region and linesearch algorithm for equality constrained optimization. Zbl 1053.90122
Yu, Zhensheng; Wang, Changyu; Yu, Jiguo
2004
On the global convergence of a Levenberg-Marquardt method for constrained nonlinear equations. Zbl 1129.90354
Yu, Zhensheng
2004
The bounded smooth reformulation and a trust region algorithm for semidefinite complementarity problems. Zbl 1068.65083
Yu, Zhensheng
2004
New soliton-like solutions to variable coefficients MKdV equation. Zbl 1167.35477
Li, De-Sheng; Yu, Zhen-Sheng; Zhang, Hong-Qing
2004
On the solvability of an equation describing the periodic motions of a satellite in its elliptic orbit. Zbl 0581.70024
Petryshyn, W. V.; Yu, Z. S.
1985
Boundary value problems at resonance for certain semilinear ordinary differential equations. Zbl 0529.34023
Petryshyn, W. V.; Yu, Z. S.
1984
Solvability of Neumann BV problems for nonlinear second-order ODEs which need not be solvable for the highest-order derivative. Zbl 0513.34020
Petryshyn, W. V.; Yu, Z. S.
1983
Periodic solutions of certain higher order nonlinear differential equations. Zbl 0523.34041
Petryshyn, W. V.; Yu, Z. S.
1983
Nonresonance and existence for nonlinear BV problems. Zbl 0561.35030
Petryshyn, W. V.; Yu, Z. S.
1983
Existence theorems for higher order nonlinear periodic boundary value problems. Zbl 0525.34015
Petryshyn, W. V.; Yu, Z. S.
1982
Periodic solutions of nonlinear second-order differential equations which are not solvable for the highest derivative. Zbl 0516.34019
Petryshyn, W. V.; Yu, Z. S.
1982
all top 5
#### Cited by 179 Authors
7 Bala Abubakar, Auwal 7 Ou, Yigui 7 Zhu, Detong 6 Gu, Chao 6 Kumam, Poom 6 Sun, Min 5 Liu, Jing 4 Awwal, Aliyu Muhammed 4 Yu, Zhensheng 3 Pu, Dingguo 2 Amini, Keyvan 2 Cui, Zhaocheng 2 de Sampaio, Raimundo J. B. 2 Du, Shouqiang 2 Elfoutayeni, Youssef 2 Goldfarb, Donald 2 Hu, Yaping 2 Ji, Ying 2 Jiao, Hongwei 2 Jin, Zhong 2 Li, Shengjie 2 Li, Wenyu 2 Lin, Haichan 2 Liu, Jinkui 2 Liu, Yuanwen 2 Lu, Yunlong 2 Ma, Changfeng 2 Mohammad, Hassan 2 Mu, Xuewen 2 Su, Ke 2 Sun, Wenyu 2 Wakili, Adamu 2 Wang, Xueyong 2 Wen, Zaiwen 2 Xiao, Yunhai 2 Xie, Yajun 2 Yang, Yueting 2 Yu, Haodong 2 Yuan, Gonglin 2 Zhang, Yaling 1 Achik, Yamna 1 Agmour, Imane 1 Ahookhosh, Masoud 1 Ali, M. Montaz 1 Aremu, Kazeem Olalekan 1 Bahrami, Somayeh 1 Bányai, Ágota 1 Bányai, Tamás 1 Batta, Octavio 1 Cao, Mingyuan 1 Che, Haitao 1 Chen, Liang 1 Chen, Miao 1 Chen, Xiaohong 1 Chen, Yanping 1 Dai, Zhifeng 1 Deng, Chunlin 1 Dong, Yunda 1 Duan, Yongrui 1 EL Bouanani, Hicham 1 Fadugba, Sunday Emmanuel 1 Fard, Omid Solaymani 1 Fei, Cui 1 Feng, Dexiang 1 Feng, Lihua 1 Feng, Tingting 1 Feng, Yuming 1 Francisco, Juliano B. 1 Fu, Jinhua 1 Gao, Yan 1 Gumma, E. A. E. 1 Guo, Tiande 1 Han, Congying 1 Hao, Binbin 1 Hashim, Mohsin Hassan Abdallah 1 He, Changxiang 1 He, Guoping 1 He, Jingsong 1 Hu, Ping 1 Hu, ShengLong 1 Huang, Na 1 Huang, Yakui 1 Huang, Yong 1 Huang, Yuanyuan 1 Huang, Zheng-Hai 1 Ibrahim, Abdulkarim Hassan 1 Idmbarek, Asmaa 1 Illés, Béla 1 Jian, Jinbao 1 Jiang, Xianzhen 1 Jiang, Xiaowei 1 Jolaoso, Lateef Olakunle 1 Kamandi, Ahmad 1 Khaladi, Mohamed 1 Kou, Xipeng 1 Krejić, Nataša 1 la Cruz, William 1 Lei, Lin 1 Li, Chengjin 1 Li, Jingya ...and 79 more Authors
all top 5
#### Cited in 41 Serials
10 Journal of Applied Mathematics and Computing 6 Mathematical Problems in Engineering 6 Abstract and Applied Analysis 5 Applied Mathematics and Computation 5 Journal of Computational and Applied Mathematics 5 Applied Numerical Mathematics 4 Numerical Algorithms 4 Computational and Applied Mathematics 4 Journal of Inequalities and Applications 4 Journal of Applied Mathematics 3 Journal of Optimization Theory and Applications 3 Linear Algebra and its Applications 3 Thai Journal of Mathematics 3 Journal of Industrial and Management Optimization 3 Optimization Letters 2 Computers & Mathematics with Applications 2 Calcolo 2 Bulletin of the Iranian Mathematical Society 2 Applied Mathematical Modelling 2 European Journal of Operational Research 2 International Journal of Computer Mathematics 2 Computational Optimization and Applications 2 Discrete Dynamics in Nature and Society 2 Journal of Systems Science and Complexity 1 Journal of Mathematical Analysis and Applications 1 Numerical Functional Analysis and Optimization 1 Chinese Annals of Mathematics. Series B 1 Optimization 1 Computers & Operations Research 1 Journal of Global Optimization 1 Complexity 1 Journal of Vibration and Control 1 Chaos 1 International Journal of Applied Mathematics and Computer Science 1 RAIRO. Operations Research 1 Journal of Nonlinear Science and Applications 1 Mathematical Programming Computation 1 Journal of Mathematics 1 Journal of Optimization 1 Bulletin of Computational Applied Mathematics 1 Open Mathematics
all top 5
#### Cited in 12 Fields
84 Operations research, mathematical programming (90-XX) 58 Numerical analysis (65-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 5 Combinatorics (05-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Partial differential equations (35-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)
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2021-07-27 05:38:37
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https://www.allthatmatters.academy/memory-mechanism/newtons-2nd-law/
|
# Newton’s 2nd law
Acceleration is caused by a net/resulting force, $\sum \vec F$; and vice versa, a net force causes acceleration $\vec a$. This acceleration is “dampened” or resisted by the mass $m$.
$$\sum \vec F=m\vec a$$
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2021-01-26 08:54:21
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https://theconfidencemag.com/how-deep-learning-models-are-built-on-keras/
|
Recent developments in artificial intelligence (AI) have focused on using computer software programs to perform specific tasks, such as recognizing pictures of cats or giving you recommendations for places to eat.
These so-called “machine learning” algorithms learn how to complete these tasks by interacting with a vast amount of data, making it possible to create AI systems that can automatically detect patterns in all sorts of information.
A popular example of this is an image recognition system that uses neural networks to determine what object each picture contains. The algorithm starts off being shown many different images that contain various parts of the finished product, and then it learns which features are linked to which objects for future comparisons.
Another area where machine learning has seen dramatic success is natural language processing (NLP). These algorithms work by looking at large amounts of text material to identify regular patterns and relationships. For instance, they could analyze the way someone writes their own name and use that pattern to recognize your name too!
Deep learning falls into both of these categories. It is considered to be a type of NLP because it analyses large chunks of textual content to find correlations and understand meaning. This technology was first developed for visualizing brain activity in humans, but now there are applications beyond just imaging equipment.
By incorporating advanced mathematical techniques like deep nets, researchers have been able to apply DL to new domains and achieve impressive results.
## Break down the layers of a neural network
In any given layer of a deep learning model, there are several nodes that perform specific functions. These functions can be combining features, looking for patterns in data, or taking action to control what goes into the next layer.
The number and type of node operations in each layer is determined when the model is trained, so it’s not something you have to worry about during testing.
When training a new model, one must determine how many layers the model has and which layers need updating. This is done through an optimization process called backpropagation. Backpropagation works by calculating the gradient of the loss function with respect to the weights in every layer of the net- whether they increase or decrease depending on if the error is going up or down.
By repeating this process multiple times while changing the weight values, the algorithm gets closer and closer to the optimal set points.
## Identify the different layers of a neural network
In any deep learning model, there are usually several key components that work together to perform some specific task. Neural networks are no exception!
In fact, one of the most important parts of almost every state-of-the-art neural netowrk is what we call a *layer*. A layer is an operation that takes in some input and produces some output.
The vast majority of layers take only one type of input and produce only one type of output. For example, the fully connected layer we looked at earlier takes as input all of the neurons in another layer and uses those connections to compute a new value for each neuron.
Other common types of layers include convolutional layers which take in repeated inputs (like images) and learn how to combine them into more complex patterns, or pooling layers that reduce the size and complexity of your image information.
But unfortunately, not all layers do something meaningful! Some simply move around part of the input or discard everything but the sum of the numbers.
## Connect neural networks with deep learning
Neural Networks are an interesting mathematical concept that have applications in almost every field. They work by using some sort of connection (or node) to process input data. The nodes are connected together in such a way that different inputs give rise to new information, or features, as well as combining into something more complex.
In the case of image recognition, one might have a node that looks at the shape of an object or whether there is a human figure present. Another node could look for details like cars or people in the picture. A third node could recognize logos or brands. By putting these three nodes onto a server that can perform large calculations quickly, you get an algorithm that can classify images very efficiently!
Deep Learning models use multiple layers of neurons to combine and process information. Each layer takes the output from the previous layer and uses it as its input, which means they’re constantly looking forward while also taking advantage of what has come before. This allows them to learn increasingly complex patterns and representations of data.
There are two main types of architectures used in creating modern AI: convolutional networks and recurrent nets. We will take a closer look at how keras implements both of these types of networks later in this article. For now, just know that they’re fundamentally similar in their layering structure and number of parameters.
Keras was designed to be easy to understand and use.
## Identify the different types of neural networks
Neural Networks are an increasingly popular way to do machine learning. They were first proposed in the 1980s, but they have seen a resurgence in popularity since the early 2010s when researchers began experimenting with them.
Neural networks differ from other classification algorithms like k-nearest neighbors or logistic regression because they work by using multiple layers that repeat the process over and over until you get your final result.
Each layer is trained to perform a specific task (for example, identifying numbers or letters), and the layers are connected so that information can pass between them. This allows each new layer to take input not only from the previous layer, but also from the rest of the model.
By having these connections, the network learns how to combine all of this information into one complex output. Because there are no hard and fast rules for what the layers are being asked to learn, it becomes very difficult to tell which parts of the model contribute most to the overall prediction.
## Identify the different types of activation functions
The next layer in the neural network is an activation function. There are many options for this, but one of the most popular is the sigmoid function. This has as its output range between 0 and 1.
When it is run through a model, these outputs are then used to determine whether or not a part of the model should be activated (run) or deactivated (removed from the equation completely). For instance, say we wanted to predict if a given sentence contains a word that starts with the letter ‘P’. We would create a sequence of layers which include an embedding layer, a dropout layer, and a final softmax classification layer.
The first step in creating our prediction algorithm is defining our input data. In this case, our inputs will be each individual word in the sentence. So, our vocabulary will contain the letters of every possible word in the English language.
Once all of our words have been preprocessed into vectors, we can pass them through our embedding layer. An embedding layer takes some set amount of information and maps it onto a vector space. In our example, the size of the vector space corresponds to the number of dimensions in our vocabulary.
After the embedding layer, we apply what is called batch normalization. Batch normlizations help prevent overfitting by ensuring internal covariate shift is equal across various parts of the training dataset.
## Examine how to create a neural network
In any given task, there are usually lots of ways to accomplish that task. For instance, if you want to predict whether or not someone will like a piece of content, there are probably many different models you could use to do so.
One such model is called an MLP (multi-layer perceptron). An MLP has one input layer, one output layer, and multiple internal layers in between. The number of internal layers can be user defined, but most architectures have at least two.
The way these layers work is by applying mathematical functions to each layer’s inputs, then moving onto the next layer. These functions include sigmoid ($\text{SIG}(x) = \frac {1}{ 1 + e^{ – x}}$), hyperbolic tangent ($\tanh(x)=\frac{\sinh(x)-\cosh(x)}{\cosh(2x)}$), and linear ($y=wx$, where $w$ is a weight parameter) activation functions.
Once all the layers are run through their respective functions, they are summed together as the final layer which produces the results for your net. Depending on what kind of problem you are trying to solve, it is often good practice to add another external node layer to make sure everything is accounted for. This adds more space for the neurons in the hidden layers to learn more about the data.
## Link neural networks with Keras
Neural network architectures are some of the most powerful tools in computer science today. They have seen widespread use across various industries, including finance, medicine, and gaming.
Neural networks were first proposed at around 1950 as a way to simulate how neurons work in our brains. Since then, there has been an explosion in applications for this algorithm structure.
In past years, people built their own neural networks or used off-the-shelf solutions such as those from Google or Microsoft.
However, these models became very popular because they found efficient ways to learn complex patterns without requiring much human intervention.
That’s why it’s so important to understand how deep learning models work under the hood!
Deep learning model developers now have access to more advanced techniques than ever before. You can pick up many of these concepts and apply them to your own projects easily.
In this article, you will find out how to link simple feedforward (or linear) layers together into more complicated ones using the Keras library. Then, you’ll see how to train and evaluate state-of-the-art image classification models using Theano, TensorFlow, or CNTK.
## Create a neural network
Neural networks are one of the most important concepts in machine learning today. In fact, many consider them to be the core technology behind almost all other advanced algorithms used for predictive analytics.
Neural networks were invented back in the 1950s, but it was not until recent years that they became popular again. Why? Because engineers realized how powerful they are!
In this article we will take a look at how to create your own neural networks using the open source deep learning framework called Keras. We will also go into some detail about what makes a good neural net model as well as tips and tricks for improving the performance of your models.
What is a neural network?
A neural network is an algorithm that works by looking at examples or inputs and then applying rules (or functions) to generate outputs.
The key difference between traditional computer programs and neural networks is that neural nets learn from past experiences instead of being given fixed rules to operate off of.
For example, if you give a neural net a set of numbers and ask it to find any patterns, the neural net will figure out its own logic to connect the numbers together.
This is why neural networks can sometimes seem “intelligent” or even sentient — because of how they process information and learn new things independently!.
There are three major components that make up every neural network: input layers, hidden layers, and output layers.
Caroline Shaw is a blogger and social media manager. She enjoys blogging about current events, lifehacks, and her experiences as a millennial working in New York.
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2023-01-28 12:24:29
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http://dancinggiraffe.com/c1eff03cbc5fb7f3ade967806d266143
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Introduction To Gaussian Processes
introduction to gaussian processes
Gaussian processes are based on Bayesian statistics, which requires you to compute the conditional and the marginal probability. Now with Gaussian distributions, both result in Gaussian distributions in lower dimensions. Marginal probability. The marginal probability of a multivariate Gaussian is really easy. Officially it is defined by the integral over the dimension we want to marginalize over.
Introduction to Gaussian Processes
Introduction to Gaussian Processes Daniel Preot¸iuc-Pietro Positive Psychology Center University of Pennsylvania 13 October 2014 with slides from Trevor Cohn, Neil Lawrence, Richard Turner. Gaussian Processes Brings together several key ideas in one framework Bayesian kernelised non-parametric non-linear modelling uncertainty Elegant and powerful framework, with growing popularity in machine ...
Introduction to Gaussian Processes
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[1505.02965] Gaussian Processes: A Quick Introduction
In this talk we introduce Gaussian process models. Motivating the representation of uncertainty through probability distributions we review Laplace's approach to understanding uncertainty and how uncertainty in functions can be represented through a multivariate Gaussian density.
INTRODUCTION TO GAUSSIAN PROCESSES
Introduction to Gaussian Process Regression. Gaussian Process Regression Gaussian Processes: A Distribution over Functions e.g. Choose mean function zero, and covariance function: K p,q = Cov(f(x (p)),f(x(q))) = K(x(p),x(q)) For any set of inputs x(1),...,x(n) we may compute K which defines a joint distribution over function values: f(x(1)),...,f(x(n)) ∼ N(0,K). Therefore a GP specifies a ...
Gaussian Processes for Dummies - Katherine Bailey
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Stationary and Isotropic Gaussian Processes. Gaussian processes become simpler to define and work with if we make two additional simplifying assumptions: The mean function $$\mu$$ is a constant, $$\mu(x) = \mu$$ for all $$x$$. The covariance function $$\Sigma(x_1,x_2)$$ depends only on the distance between the two points, $$d(x_1,x_2)$$.
Gaussian Processes in Machine Learning | SpringerLink
Introduction to Gaussian Processes Stephen Keeley and Jonathan Pillow Princeton Neuroscience Institute Princeton University skeeley@princeton.edu March 28, 2018 Gaussian Processes (GPs) are a flexible and general way to parameterize functions with arbitrary shape. GPs are often used in a regression framework where a function f( x) is inferred by considering some input data and (potentially ...
GitHub - masenov/gaussian-processes-introduction
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Introduction to Gaussian Processes- Regression DSA2019 ...
Gaussian processes for machine learning / Carl Edward Rasmussen, Christopher K. I. Williams. p. cm. —(Adaptive computation and machine learning) Includes bibliographical references and indexes. ISBN 0-262-18253-X 1. Gaussian processes—Data processing. 2. Machine learning—Mathematical models. I. Williams, Christopher K. I. II. Title. III. Series. QA274.4.R37 2006 519.2'3—dc22 2005053433 ...
AB - Introduction to Gaussian Processes - Part I
An introduction to Gaussian processes for the Kalman filter expert Abstract: We examine the close relationship between Gaussian processes and the Kalman filter and show how Gaussian processes can be interpreted using familiar Kalman filter mathematical concepts. We use this insight to develop a novel hybrid filter, which we call the KFGP, for spatial-temporal modelling. The KFGP uses Gaussian ...
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Lecture on Gaussian Processes that was delivered for MSc level students at University of Tartu (2018 spring)
Gaussian process - Wikipedia
Introduction to Gaussian Processes Raquel Urtasun TTI Chicago August 2, 2013 R. Urtasun (TTIC) Gaussian Processes August 2, 2013 1 / 59. Motivation for Non-Linear Dimensionality Reduction USPS Data Set Handwritten Digit 3648 Dimensions 64 rows by 57 columns Space contains more than just this digit. Even if we sample every nanosecond from now until the end of the universe, you won’t see the ...
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An Introduction to Fitting Gaussian Processes to Data Michael Osborne Pattern Analysis and Machine Learning Research Group Department of Engineering University of Oxford . You will learn how to fit a Gaussian process to data. Probability Theory C R Deductive Logic C R Probability theory represents an extension of traditional logic, allowing us to reason in the face of uncertainty. P( R | C, I ...
Gaussian Processes in Machine Learning
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Introduction to Gaussian Processes — Kernel Machines
The book introduces Gaussian Processes, comprehensively covers regression and classfication with Gaussian processes and describes in detail related topics including covariacne funcions (i.e., kernels), hyperparamters, approximations and much more. I will strongly recommend this book for any one interested in learn about Gaussian Processes and using these in their machine learning work.
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Introduction to Gaussian Processes for Machine Learning
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(PDF) Gaussian Processes in Machine Learning
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Introduction to Regression Using Gaussian Processes. Stefan August 9, 2017 August 28, 2018 Archives, Regression. Post navigation. Previous. Next. Introduction. When trying to describe data using a function you often know something about the process generating the data a priori. When you do not completely understand why the data looks like it does but want to try to describe it any way you can ...
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An Introduction to Gaussian Processes for the Kalman Filter Expert Steven Reece and Stephen Roberts Robotics Research Group Dept. Engineering Science Oxford University, UK.
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Eric Xihui Lin A Brief Introduction to Gaussian Process December 19, 2014 6 / 14 7. GP: Example 1 1 picture comes from scikit-learn Eric Xihui Lin A Brief Introduction to Gaussian Process December 19, 2014 7 / 14 8. Gaussian Process Regression Assume Gaussian noise y = f + n, i.e., y | f ∼ N(f , σ2 ). Assign a Gaussian prior to f , i.e., f ...
Introduction To Gaussian Processes
The most popular ebook you must read is Introduction To Gaussian Processes. I am sure you will love the Introduction To Gaussian Processes. You can download it to your laptop through easy steps.
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2020-09-23 00:46:13
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https://formulasearchengine.com/wiki/Enthalpy
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# Enthalpy
{{#invoke:Sidebar |collapsible | bodyclass = plainlist | titlestyle = padding-bottom:0.3em;border-bottom:1px solid #aaa; | title = Thermodynamics | imagestyle = display:block;margin:0.3em 0 0.4em; | image = | caption = The classical Carnot heat engine | listtitlestyle = background:#ddf;text-align:center; | expanded = potentials
| list1name = branches | list1title = Branches | list1 = Template:Startflatlist
| list2name = laws | list2title = Laws | list2 = Template:Startflatlist
| list3name = systems | list3title = Systems | list3 =
| list4name = sysprop | list4title = System properties
| list4 =
Note: Conjugate variables in italics
| list5name = material | list5title = Material properties | list5 =
| list6name = equations | list6title = Equations | list6 = Template:Startflatlist
| list7name = potentials | list7title = Potentials | list7 = Template:Startflatlist
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| list9name = scientists | list9title = Scientists | list9 = Template:Startflatlist
| below = Book:Thermodynamics
}}
Enthalpy is a defined thermodynamic potential, designated by the letter "H", that consists of the internal energy of the system (U) plus the product of pressure (p) and volume (V) of the system:[1]
${\displaystyle H=U+pV}$
Since U, p and V are all functions of the state of the thermodynamic system, enthalpy is a state function.
The unit of measurement for enthalpy in the International System of Units (SI) is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie.
The enthalpy is the preferred expression of system energy changes in many chemical, biological, and physical measurements, because it simplifies certain descriptions of energy transfer. Enthalpy change accounts for energy transferred to the environment at constant pressure through expansion or heating.
The total enthalpy, H, of a system cannot be measured directly. The same situation exists in classical mechanics: only a change or difference in energy carries physical meaning. Enthalpy itself is a thermodynamic potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point; therefore what we measure is the change in enthalpy, ΔH. The change ΔH is positive in endothermic reactions, and negative in heat-releasing exothermic processes.
For processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the pressure-volume work that the system has done on its surroundings.[2] This means that the change in enthalpy under such conditions is the heat absorbed (or released) by the material through a chemical reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure assume standard state: most commonly 1 bar pressure. Standard state does not, strictly speaking, specify a temperature (see standard state), but expressions for enthalpy generally reference the standard heat of formation at 25 °C.
Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy and Gibbs energy. Real materials at common temperatures and pressures usually closely approximate this behavior, which greatly simplifies enthalpy calculation and use in practical designs and analyses.
## Origins
The word enthalpy is based on the Greek enthalpein (ἐνθάλπειν), which means "to warm in".[3] It comes from the Classical Greek prefix ἐν- en-, meaning "to put into", and the verb θάλπειν thalpein, meaning "to heat". The word enthalpy is often incorrectly attributed{{ safesubst:#invoke:Unsubst||date=__DATE__ |\$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} to Benoît Paul Émile Clapeyron and Rudolf Clausius through the 1850 publication of their Clausius–Clapeyron relation. This misconception was popularized by the 1927 publication of The Mollier Steam Tables and Diagrams. However, neither the concept, the word, nor the symbol for enthalpy existed until well after Clapeyron's death.
The earliest writings to contain the concept of enthalpy did not appear until 1875,[4] when Josiah Willard Gibbs introduced "a heat function for constant pressure". However, Gibbs did not use the word "enthalpy" in his writings.[note 1]
The actual word first appears in the scientific literature in a 1909 publication by J. P. Dalton. According to that publication, Heike Kamerlingh Onnes (1853-1926) actually coined the word.[5]
Over the years, many different symbols were used to denote enthalpy. It was not until 1922 that Alfred W. Porter proposed the symbol "H" as the accepted standard,[6] thus finalizing the terminology still in use today.
## Formal definition
The enthalpy of a homogeneous system is defined as:[7][8]
${\displaystyle H=U+pV\,}$
where
H is the enthalpy of the system
U is the internal energy of the system
p is the pressure of the system
V is the volume of the system.
The enthalpy is an extensive property. This means that, for homogeneous systems, the enthalpy is proportional to the size of the system. It is convenient to introduce the specific enthalpy h =H/m where m is the mass of the system, or the molar enthalpy Hm = H/n, where n is the number of moles (h and Hm are intensive properties). For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems
${\displaystyle H=\Sigma _{k}H_{k}}$
where the label k refers to the various subsystems. In case of continuously varying p, T, and/or composition the summation becomes an integral:
${\displaystyle H=\int \rho h{\mathrm {d} }V,}$
where ρ is the density.
The enthalpy H(S,p) of homogeneous systems can be derived as a characteristic function of the entropy S and the pressure p as follows: we start from the first law of thermodynamics for closed systems for an infinitesimal process
${\displaystyle {\mathrm {d} }U=\delta Q-\delta W.}$
Here, δQ is a small amount of heat added to the system and δW a small amount of work performed by the system. In a homogeneous system only reversible processes can take place so the second law of thermodynamics gives δQ = TdS with T the absolute temperature of the system. Furthermore, if only pV work is done, δW = pdV. As a result
${\displaystyle {\mathrm {d} }U=T{\mathrm {d} }S-p{\mathrm {d} }V.}$
Adding d(pV) to both sides of this expression gives
${\displaystyle {\mathrm {d} }U+{\mathrm {d} }(pV)=T{\mathrm {d} }S-p{\mathrm {d} }V+{\mathrm {d} }(pV)}$
or
${\displaystyle {\mathrm {d} }(U+pV)=T{\mathrm {d} }S+V{\mathrm {d} }p.}$
So
${\displaystyle {\mathrm {d} }H(S,p)=T{\mathrm {d} }S+V{\mathrm {d} }p.}$
## Other expressions
The expression of dH in terms of entropy and pressure may be unfamiliar to many readers. However, there are expressions in terms of more familiar variables such as temperature and pressure[9][10]
Here Cp is the heat capacity at constant pressure and α is the coefficient of (cubic) thermal expansion
With this expression one can, in principle, determine the enthalpy if Cp and V are known as functions of p and T.
Notice that for an ideal gas, ${\displaystyle \alpha T=1}$,[note 2] so that:
In a more general form, the first law describes the internal energy with additional terms involving the chemical potential and the number of particles of various types. The differential statement for dH then becomes:
${\displaystyle {\mathrm {d} }H=T{\mathrm {d} }S+V{\mathrm {d} }p+\sum _{i}\mu _{i}{\mathrm {d} }N_{i}}$
where μi is the chemical potential per particle for an i-type particle, and Ni is the number of such particles. The last term can also be written as μidni (with dni the number of moles of component i added to the system and, in this case, μi the molar chemical potential) or as μidmi (with dmi the mass of component i added to the system and, in this case, μi the specific chemical potential).
## Physical interpretation
The U term can be interpreted as the energy required to create the system, and the pV term as the energy that would be required to "make room" for the system if the pressure of the environment remained constant. When a system, for example, n moles of a gas of volume V at pressure p and temperature T, is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy U plus pV, where pV is the work done in pushing against the ambient (atmospheric) pressure.
In basic physics and statistical mechanics it may be more interesting to study the internal properties of the system and therefore the internal energy is used.[11][12] In basic chemistry, experiments are often conducted at constant atmospheric pressure, so that ΔH corresponds to the heat of reaction. Furthermore the enthalpy is the workhorse of engineering thermodynamics as we will see later.
## Relationship to heat
In order to discuss the relation between the enthalpy increase and heat supply we return to the first law for closed systems: dU = δQ - δW. We apply it to the special case that the pressure at the surface is uniform. In this case the work term can be split in two contributions, the so-called pV work, given by pdV (where here p is the pressure at the surface, dV is the increase of the volume of the system) and other types of work δW ' such as by a shaft or by electromagnetic interaction. So we write δW = pdVW '. In this case the first law reads
${\displaystyle {\mathrm {d} }U=\delta Q-p{\mathrm {d} }V-\delta W^{\prime }}$
or
${\displaystyle {\mathrm {d} }H=\delta Q+V{\mathrm {d} }p-\delta W^{\prime }.}$
From this relation we see that the increase in enthalpy of a system is equal to the added heat
${\displaystyle {\mathrm {d} }H=\delta Q}$
provided that the system is under constant pressure (dp = 0) and that the only work done by the system is expansion work (δW ' = 0)[13]
## Applications
In thermodynamics, one can calculate enthalpy by determining the requirements for creating a system from "nothingness"; the mechanical work required, pV, differs based upon the conditions that obtain during the creation of the thermodynamic system.
Energy must be supplied to remove particles from the surroundings to make space for the creation of the system, assuming that the pressure p remain constant; this is the pV term. The supplied energy must also provide the change in internal energy, U, which includes activation energies, ionization energies, mixing energies, vaporization energies, chemical bond energies, and so forth. Together, these constitute the change in the enthalpy U + pV. For systems at constant pressure, the change in enthalpy is the heat received by the system.
For a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.Template:Citequote
### Heat of reaction
{{#invoke:main|main}} The total enthalpy of a system cannot be measured directly; the enthalpy change of a system is measured instead. Enthalpy change is defined by the following equation:
where
${\displaystyle \Delta H}$ is the "enthalpy change"
${\displaystyle H_{f}}$ is the final enthalpy of the system, expressed in joules. In a chemical reaction,${\displaystyle H_{f}}$ is the enthalpy of the products.
${\displaystyle H_{i}}$ is the initial enthalpy of the system, expressed in joules. In a chemical reaction,${\displaystyle H_{i}}$ is the enthalpy of the reactants.
For an exothermic reaction at constant pressure, the system's change in enthalpy equals the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings. In a similar manner, for an endothermic reaction, the system's change in enthalpy is equal to the energy absorbed in the reaction, including the energy lost by the system and gained from compression from its surroundings. A relatively easy way to determine whether or not a reaction is exothermic or endothermic is to determine the sign of ΔH. If ΔH is positive, the reaction is endothermic, that is heat is absorbed by the system due to the products of the reaction having a greater enthalpy than the reactants. On the other hand if ΔH is negative, the reaction is exothermic, that is the overall decrease in enthalpy is achieved by the generation of heat.
### Specific enthalpy
As noted before, the specific enthalpy of a uniform system is defined as h = H/m where m is the mass of the system. The SI unit for specific enthalpy is joule per kilogram. It can be expressed in other specific quantities by h = u + pv, where u is the specific internal energy, p is the pressure, and v is specific volume, which is equal to 1/ρ, where ρ is the density.
### Enthalpy changes
An enthalpy change describes the change in enthalpy observed in the constituents of a thermodynamic system when undergoing a transformation or chemical reaction. It is the difference between the enthalpy after the process has completed, i.e. the enthalpy of the products, and the initial enthalpy of the system, i.e. the reactants. These processes are reversible and the enthalpy for the reverse process is the negative value of the forward change.
A common standard enthalpy change is the enthalpy of formation, which has been determined for a large number of substances. Enthalpy changes are routinely measured and compiled in chemical and physical reference works, such as the CRC Handbook of Chemistry and Physics. The following is a selection of enthalpy changes commonly recognized in thermodynamics.
When used in these recognized terms the qualifier change is usually dropped and the property is simply termed enthalpy of 'process'. Since these properties are often used as reference values it is very common to quote them for a standardized set of environmental parameters, or standard conditions, including:
• A temperature of 25 °C or 298 K,
• A pressure of one atmosphere (1 atm or 101.325 kPa),
• A concentration of 1.0 M when the element or compound is present in solution,
• Elements or compounds in their normal physical states, i.e. standard state.
For such standardized values the name of the enthalpy is commonly prefixed with the term standard, e.g. standard enthalpy of formation.
Chemical properties:
• Enthalpy of reaction, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of substance reacts completely.
• Enthalpy of formation, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a compound is formed from its elementary antecedents.
• Enthalpy of combustion, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a substance burns completely with oxygen.
• Enthalpy of hydrogenation, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of an unsaturated compound reacts completely with an excess of hydrogen to form a saturated compound.
• Enthalpy of atomization, defined as the enthalpy change required to atomize one mole of compound completely.
• Enthalpy of neutralization, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of water is formed when an acid and a base react.
• Standard Enthalpy of solution, defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a solute is dissolved completely in an excess of solvent, so that the solution is at infinite dilution.
• Standard enthalpy of Denaturation (biochemistry), defined as the enthalpy change required to denature one mole of compound.
• Enthalpy of hydration, defined as the enthalpy change observed when one mole of gaseous ions are completely dissolved in water forming one mole of aqueous ions.
Physical properties:
• Enthalpy of fusion, defined as the enthalpy change required to completely change the state of one mole of substance between solid and liquid states.
• Enthalpy of vaporization, defined as the enthalpy change required to completely change the state of one mole of substance between liquid and gaseous states.
• Enthalpy of sublimation, defined as the enthalpy change required to completely change the state of one mole of substance between solid and gaseous states.
• Lattice enthalpy, defined as the energy required to separate one mole of an ionic compound into separated gaseous ions to an infinite distance apart (meaning no force of attraction).
• Enthalpy of mixing, defined as the enthalpy change upon mixing of two (non-reacting) chemical substances.
### Open systems
In thermodynamic open systems, matter may flow in and out of the system boundaries. The first law of thermodynamics for open systems states: The increase in the internal energy of a system is equal to the amount of energy added to the system by matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system. The first law for open systems is given by:
${\displaystyle {\mathrm {d} }U={\mathrm {\delta } }Q+{\mathrm {d} }U_{in}-{\mathrm {d} }U_{out}-{\mathrm {\delta } }W}$
where ${\displaystyle U_{in}}$ is the average internal energy entering the system and ${\displaystyle U_{out}}$ is the average internal energy leaving the system.
Fig.1 During steady, continuous operation, an energy balance applied to an open system equates shaft work performed by the system to heat added plus net enthalpy added
The region of space enclosed by open system boundaries is usually called a control volume, and it may or may not correspond to physical walls. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of matter into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of matter out as if it were driving a piston of fluid. There are then two types of work performed: flow work described above, which is performed on the fluid (this is also often called pV work), and shaft work, which may be performed on some mechanical device.
These two types of work are expressed in the equation:
${\displaystyle {\mathrm {\delta } }W={\mathrm {d} }(p_{out}V_{out})-{\mathrm {d} }(p_{in}V_{in})+{\mathrm {\delta } }W_{shaft}}$
Substitution into the equation above for the control volume cv yields:
${\displaystyle {\mathrm {d} }U_{cv}={\mathrm {\delta } }Q+{\mathrm {d} }U_{in}+{\mathrm {d} }(p_{in}V_{in})-{\mathrm {d} }U_{out}-{\mathrm {d} }(p_{out}V_{out})-{\mathrm {\delta } }W_{shaft}}$.
The definition of enthalpy, ${\displaystyle H}$, permits us to use this thermodynamic potential to account for both internal energy and ${\displaystyle pV}$ work in fluids for open systems:
${\displaystyle {\mathrm {d} }U_{cv}={\mathrm {\delta } }Q+{\mathrm {d} }H_{in}-{\mathrm {d} }H_{out}-{\mathrm {\delta } }W_{shaft}}$.
This expression is described by Fig.1. If we allow also the system boundary to move (e.g. due to moving pistons) we get a rather general form of the first law for open systems.[14] In terms of time derivatives it reads
${\displaystyle {\frac {{\mathrm {d} }U}{{\mathrm {d} }t}}=\Sigma _{k}{\dot {Q}}_{k}+\Sigma _{k}{\dot {H}}_{k}-\Sigma _{k}p_{k}{\frac {{\mathrm {d} }V_{k}}{{\mathrm {d} }t}}-P,}$
where ${\displaystyle \Sigma }$ represent algebraic sums and the indices k refer to the various places where heat is supplied, matter flows into the system, and boundaries are moving. The ${\displaystyle {\dot {H}}_{k}}$ terms represent enthalpy flows, which can be written as
${\displaystyle {\dot {H}}_{k}=h_{k}{\dot {m}}_{k}=H_{m}{\dot {n}}_{k}}$
with ${\displaystyle {\dot {m}}_{k}}$ the mass flow and ${\displaystyle {\dot {n}}_{k}}$ the molar flow at position k respectively. The term dVk/dt represents the rate of change of the system volume at position k that results in pV power done by the system. The parameter P represents all other forms of power done by the system such as shaft power, but it can also be e.g. electric power produced by an electrical power plant. Note that the previous expression holds true only if the kinetic energy flow rate is conserved between system inlet and outlet. Otherwise, it has to be included in the enthalpy balance. During steady-state operation of a device (see turbine, pump, and engine), the average dU/dt may be set equal to zero. This yields a useful expression for the average power generation for these devices in the absence of chemical reactions
${\displaystyle P=\Sigma _{k}\left\langle {\dot {Q}}_{k}\right\rangle +\Sigma _{k}\left\langle {\dot {H}}_{k}\right\rangle -\Sigma _{k}\left\langle p_{k}{\frac {{\mathrm {d} }V_{k}}{{\mathrm {d} }t}}\right\rangle }$
where the angle brackets denote time averages. The technical importance of the enthalpy is directly related to its presence in the first law for open systems, as formulated above.
Fig.2 Ts diagram of nitrogen. The red curve at the left is the melting curve. The red dome represents the two-phase region with the low-entropy side the saturated liquid and the high-entropy side the saturated gas. The black curves give the Ts relation along isobars. The pressures are indicated in bar. The blue curves are isenthalps (curves of constant enthalpy). The values are indicated in blue in kJ/kg. The specific points a, b, etc., are treated in the main text.
## Diagrams
Nowadays the enthalpy values of important substances can be obtained via commercial software. Practically all relevant material properties can be obtained either in tabular or in graphical form. There are many types of diagrams, such as hT diagrams, which give the specific enthalpy as function of temperature for various pressures and hp diagrams, which give h as function of p for various T. One of the most common diagrams is the temperature-entropy diagram (Ts-diagram). An example is Fig.2, which is the Ts-diagram of nitrogen.[15] It gives the melting curve and saturated liquid and vapor values together with isobars and isenthalps. These diagrams are powerful tools in the hands of the thermal engineer.
File:Schematic of throttling and compressor 01.jpg
Fig.3 Two open systems in the steady state. Fluid enters the system (dotted rectangle) at point 1 and leaves it at point 2. The mass flow is ${\displaystyle {\dot {m}}}$. a: schematic diagram of the throttling process. b: schematic diagram of a compressor. A power P is applied and a heat flow ${\displaystyle {\dot {Q}}}$ is released to the surroundings at ambient temperature Ta.
## Some basic applications
The points a through h in Fig.2 play a role in the discussion in this Section.
a T = 300 K, p = 1 bar, s = 6.85 kJ/(kgK), h = 461 kJ/kg;
b T = 380 K, p = 2 bar, s = 6.85 kJ/(kgK), h = 530 kJ/kg;
c T = 300 K, p = 200 bar, s = 5.16 kJ/(kgK), h = 430 kJ/kg;
d T = 270 K, p = 1 bar, s = 6.79 kJ/(kgK), h = 430 kJ/kg;
e T = 108 K, p = 13 bar, s = 3.55 kJ/(kgK), h = 100 kJ/kg (saturated liquid at 13 bar);
f T = 77.2 K, p = 1 bar, s = 3.75 kJ/(kgK), h = 100 kJ/kg;
g T = 77.2 K, p = 1 bar, s = 2.83 kJ/(kgK), h = 28 kJ/kg (saturated liquid at 1 bar);
h T = 77.2 K, p = 1 bar, s = 5.41 kJ/(kgK), h =230 kJ/kg (saturated gas at 1 bar);
### Throttling
{{#invoke:main|main}} One of the simple applications of the concept of enthalpy is the so-called throttling process, also known as Joule-Thomson expansion. It concerns a steady adiabatic flow of a fluid through a flow resistance (valve, porous plug, or any other type of flow resistance) as shown in Fig.3a. This process is very important since it is at the heart of domestic refrigerators where it is responsible for the temperature drop between ambient temperature and the interior of the fridge. It is also the final stage in many types of liquefiers.
In the first law for open systems (see above), applied to the system in Fig.3a, all terms are zero except the terms for the enthalpy flow. Hence
${\displaystyle 0={\dot {m}}h_{1}-{\dot {m}}h_{2}.}$
Since the mass flow is constant the specific enthalpies at the two sides of the flow resistance are the same
${\displaystyle h_{1}=h_{2}}$
that is, the enthalpy per unit mass does not change during the throttling. The consequences of this relation can be demonstrated using Fig.2. Point c in Fig.2 is at 200 bar and room temperature (300 K). A Joule-Thomson expansion from 200 bar to 1 bar follows a curve of constant enthalpy of roughly 425 kJ/kg (not shown in Fig.2) lying between the 400 and 450 kJ/kg isenthalps and ends in point d, which is at a temperature of about 270 K. Hence the expansion from 200 bar to 1 bar cools nitrogen from 300 K to 270 K. In the valve there is a lot of friction and a lot of entropy is produced, but still the final temperature is below the starting value!
Point e is chosen so that it is on the saturated liquid line with h = 100 kJ/kg. It corresponds roughly with p = 13 bar and T = 108 K. Throttling from this point to a pressure of one bar ends in the two-phase region (point f). This means that a mixture of gas and liquid leaves the throttling valve. Since the enthalpy is an extensive parameter the enthalpy in f (hf) is equal to the enthalpy in g (hg) multiplied with the liquid fraction in f (xf) plus the enthalpy in h (hh) multiplied with the gas fraction in f (1-xf). So
${\displaystyle h_{f}=x_{f}h_{g}+(1-x_{f})h_{h}.}$
With numbers: 100 = xf 28 + (1 – xf)230 so xf = 0.64. This means that the mass fraction of the liquid in the liquid–gas mixture that leaves the throttling valve is 64%.
### Compressors
{{#invoke:main|main}} Fig.3b is a schematic drawing of a compressor. A power P is applied e.g. as electrical power. If the compression is adiabatic the gas temperature goes up. In the reversible case it would be at constant entropy, which corresponds with a vertical line in Fig.2. E.g. compressing nitrogen from 1 bar (point a) to 2 bar (point b) would result in a temperature increase from 300 K to 380 K. In order to let the compressed gas exit at ambient temperature Ta heat exchange, e.g. by cooling water, is necessary. In the ideal case the compression is isothermal. The average heat flow to the surroundings is ${\displaystyle {\dot {Q}}}$. Since the system is in the steady state the first law gives
${\displaystyle 0=-{\dot {Q}}+{\dot {m}}h_{1}-{\dot {m}}h_{2}+P.}$
The minimum power, needed for the compression is realized if the compression is reversible. In that case the second law of thermodynamics for open systems gives
${\displaystyle 0=-{\frac {\dot {Q}}{T_{a}}}+{\dot {m}}s_{1}-{\dot {m}}s_{2}.}$
Eliminating ${\displaystyle {\dot {Q}}}$ gives for the minimum power
${\displaystyle {\frac {P_{\rm {min}}}{\dot {m}}}=h_{2}-h_{1}-T_{a}(s_{2}-s_{1}).}$
E.g. compressing 1 kg of nitrogen from 1 bar to 200 bar costs at least (hc - ha) - Ta(sc-sa). With the data, obtained with Fig.2, we find a value of (430–461) – 300 (5.16–6.85) = 476 kJ/kg.
The relation for the power can be further simplified by writing it as
${\displaystyle {\frac {P_{\rm {min}}}{\dot {m}}}=\int _{1}^{2}({\mathrm {d} }h-T_{a}{\mathrm {d} }s).}$
With dh = Tds + vdp this results in the final relation
${\displaystyle {\frac {P_{\rm {min}}}{\dot {m}}}=\int _{1}^{2}v{\mathrm {d} }p.}$
## Notes
1. The Collected Works of J. Willard Gibbs, Vol. I do not contain reference to the word enthalpy, but rather reference the heat function for constant pressure.
2. ${\displaystyle \alpha T={\frac {T}{V}}\left({\frac {\partial nRT/P}{\partial T}}\right)_{p}={\frac {nRT}{PV}}=1}$
## References
1. Mark W. Zemansky (1968), Heat and Thermodynamics, Chapter 11 (5th edition) page 275, McGraw Hill, New York.
2. G.J. Van Wylen and R.E. Sonntag (1985), Fundamentals of Classical Thermodynamics, Section 5.5 (3rd edition), John Wiley & Sons Inc. New York. ISBN 0-471-82933-1
3. {{#invoke:citation/CS1|citation |CitationClass=book }}
4. {{#invoke:citation/CS1|citation |CitationClass=book }}
5. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
6. E.A. Guggenheim, Thermodynamics, North-Holland Publisching Company, Amsterdam, 1959
7. {{#invoke:citation/CS1|citation |CitationClass=book }}
8. Guggenheim, p. 88
9. M.J. Moran and H.N. Shapiro "Fundamentals of Engineering Thermodynamics" 5th edition, (2006) John Wiley & Sons, Inc., p.511.
10. F. Reif Statistical physics McGraw-Hill, London (1967)
11. C. Kittel and H. Kroemer Thermal physics Freeman London (1980)
12. {{#invoke:citation/CS1|citation |CitationClass=book }}
13. M.J. Moran and H.N. Shapiro "Fundamentals of Engineering Thermodynamics" 5th edition, (2006) John Wiley & Sons, Inc., p.129.
14. Figure composed with data obtained with RefProp, NIST Standard Reference Database 23
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2019-09-17 08:42:22
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http://www.physicsforums.com/showthread.php?t=584244
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Statistical mechanics: Particles with spin
by SoggyBottoms
Tags: mechanics, particles, spin, statistical
P: 61 1. The problem statement, all variables and given/known data We have N particles, each of which can either be spin-up ($s_i = 1$) or spin-down ($s_i = -1$) with $i = 1, 2, 3....N$. The particles are in fixed position, don't interact and because they are in a magnetic field with strength B, the energy of the system is given by: $$E(s_1, ...., s_n) = -mB \sum_{i=1}^{N} s_i$$ with m > 0 the magnetic moment of the particles. The temperature is T. a) Calculate the canonic partition function for N = 1 and the chance that this particle is in spin-up state $P_+$. b) For any N, calculate the number of microstates $\Omega(N)$, the Helmholtz free energy F(N,T) and the average energy per particle U(N, T)/N 3. The attempt at a solution a) $$Z_1 = e^{-\beta m B} + e^{\beta m B} = 2 \cosh{\beta m B}$$ $$P_+ = \frac{e^{-\beta m B}}{2 \cosh{\beta m B}}$$ b) The number of possible microstates is $\Omega(N) = 2^N$, correct? I know that $U = -\frac{\partial \ln Z}{\partial \beta}$, but I'm not sure how to calculate Z here.
P: 318 leave Z as the summation Z = Ʃ e-Eiβ where β = 1/KBT so ∂ln(Z)/dβ = (1/Z)(∂Z/∂β) = [-EiƩe-Eiβ]/Z i think b) is supposed to be (Z1)N sorry yeah your b) is right
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2013-12-12 12:36:53
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https://forums.ankiweb.net/t/disturbed-intervall-spacing-between-the-response-options/12602
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# Disturbed Intervall: Spacing between the response Options
Hey there,
i am using Anki fo a while now, but since a few months the learning-intervall got disturbed somehow: So when i get asked a question the response options are often like 2 days for “difficult” and “11 Months” for “good”. Do you have any suggestions how to get a smaller intervall. I am a little bit lost, since i run Anki on the original settings and before the spacing between the respone options has been way smaller.
Best regards
Sebastian
Sounds like you have overdue cards maybe? See Due times after a break - Frequently Asked Questions about how Anki treats overdue cards.
1 Like
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2022-06-29 13:52:05
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https://degiuli.com/2018/07/11/walking-or-running-when-it-rains/
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# Walking or Running When It Rains?
You have just finished work and it’s raining. This morning the sun was shining so you haven’t taken an umbrella with you and now you have to get to the bus stop while trying to avoid getting really wet. Should you run or walk?
Your instinct tells you that running is the best choice, but is it so? Let’s analyze the problem from a mathematical point of view.
# Running or not running?
To simplify the situation, let’s imagine that your body is a rectangular cuboid: a solid that has six rectangular sides.
Imagine that there is no wind, so the rain falls vertically. You can thus define the following parameters of the problem:
$d$ = distance to be covered
$v$ = speed of the person
$V$ = speed of the rain
$q$ = rain density in liters per cubic meter
The last two parameters describe rain intensity, in particular $q$ measures how much water is present in a volume of one cubic meter of air if we imagine time has frozen.
Suppose you have to go from point A to point B, covering a distance $d$. Let’s try to understand how much water hits the vertical face and how much water hits the horizontal face of the rectangular parallelepiped that represents ”you”.
The rain hitting the vertical face during the movement is that found at the initial time inside the volume of a prism which has the vertical area as the base and the distance to be traveled as the height.
In the following image you can see two different prisms depending on whether you move slower (upper prism) or faster (lower prism).
But pay attention! For the Cavalieri principle the volumes of these prisms are the same and so the amount of water hitting the vertical face does not change if we go slower or faster!
Let’s call the area of the vertical face $A_{vert}$. The volume of the prism is equal to $A_{vert} \cdot d$ so the amount of water hitting the vertical face $Q_{vert}$ is given by this volume multiplied by $q$:
$Q_{vert} = A_{vert} \cdot d \cdot q$
What happens if we consider the horizontal face? The situation is similar, in the sense that the amount of rain hitting the face is always that found inside a certain prism, but now the volume of the prism depends on the speed.
(To make the following image look clearer the distance AB has been represented smaller than before.)
The height of the prism is no longer fixed but corresponds to the distance traveled by the rain in the time spent in going from A to B. The time taken to travel the route is given by $d / v$. To find the distance traveled by the rain we multiply this term by the speed of the rain, $V$, so the prism height is:
$\displaystyle h = V \cdot \frac{d}{v}$
The prism volume is given by $A_{horiz} \cdot h = A_{horiz} \cdot V \cdot d / v$ and the amount of rain hitting the horizontal face is obtained by multiplying this volume by water density $q$:
$\displaystyle Q_{horiz} = q \cdot A_{horiz} \cdot h = q \cdot A_{horiz} \cdot V \cdot \frac{d}{v}$
We see that for this component, as speed $v$ increases, the quantity of water is reduced more and more (going infinitely fast will prevent even a single drop hitting the horizontal face).
Now adding the two contributions $Q_{vert}$ and $Q_{horiz}$ we obtain the total quantity of water:
\displaystyle \begin{aligned} Q_{tot} & = Q_{vert} + Q_{horiz}\\ & = A_{vert} \cdot d \cdot q + q \cdot A_{horiz} \cdot V \cdot \frac{d}{v} \end{aligned}
And collecting common terms, we obtain the final formula:
$\displaystyle Q_{tot} = d \cdot q \cdot \left[A_{vert} + A_{horiz} \cdot \frac{V}{v}\right]$
For very low speeds $v$ the amount of water hitting you is very large. For large speeds the second term inside the brackets is very small but you can’t go below the quantity $Q_{vert}$ of water.
Within the brackets you find a sort of effective area you can change by modifying your speed.
Here is the graph of the effective area at different speeds.
Above a certain speed, going faster hardly reduces the effective area. Whether you are a normal person running at 5 m/s or a word class sprinter running at more than 10 m/s the amount of water hitting you changes very little.
Summing up: running is better but not much better, and running won’t change the amount of water hitting your torso and legs, but will reduce only the amount of water hitting your head and shoulders.
# Real Life is More Complicated
Real life is often much more complicated than the models we use to analyze it. This problem is a good example of how even a seemingly simple question can become complex to deal with it rigorously.
For example, we could add some wind, which would provide the rain with a horizontal speed component. If the wind blows against you then increasing the speed will always lead to a decrease in the water hitting you, just like before.
If the wind blows in your favor, then, depending on the ratio between the horizontal and vertical area of your body, it may be better to run as fast as possible or to proceed at a speed equal to the horizontal speed of the rain (in this way you don’t get wet either on the front nor back of you. For details see the following article by David E. Bell: Walk or Run in the Rain?).
The wind is the easiest variable to add to the model, other variables are more complicated, for example:
• The shape of our body is not that of a rectangular parallelepiped and moreover it changes according to the speed at which we proceed. When we run the torso is tilted forward and the legs will assume a different position.
• The intensity of the rain may change over time. If the intensity is about to increase, then it is usually better to run faster reach your destination sooner.
• There is a maximum level of soaking, beyond which you just can’t get any wetter. For this reason, if the journey is a long one and it’s going to rain pretty heavily all the way, you can relax and go at your preferred speed as one thing is already certain, you will get completely soaked!
It’s interesting to notice that when we find ourselves in these situations, unconsciously and without making precise calculations, our instinct can take into account so many variables (distance to be covered, possible increase in intensity of the rain, type of clothes, danger of slipping) to finally choose the strategy which seems the most sensible.
As a last remark remember that you often have the option to find a safe shelter in a café and wait for the rain to stop. That would give you time to catch up on your favorite blog posts too 😊.
If you liked this post, consider sharing it or sign up to our newsletter so you never miss any of our future posts.
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2018-09-26 12:37:41
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https://www.physicsforums.com/threads/general-q-m-question.44528/
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# General Q.M. question
1. Sep 24, 2004
### emob2p
I'm trying to prove that E must exceed the minimum value of V(x) for all normalizable solutions to the Schroed. eq. To do this I am going to show that in the case E < V(min), the wave function is not normalizable. Naturally I began with the normalization condition: int(|phi|^2)=1 and started taking derivatives on this. However, I cannot arrive at a contradiction. Any thoughts? Or any other ways to show the same result? Thanks.
2. Sep 24, 2004
### marlon
this is just of the top of my head here, but you need to solve the schrödinger equation with the fact that E - V < 0. I am gonna assume that you know how to solve second order differential equations so when you solve :
(-h'²/2m * f'' + V * f) = E * f (f is the wavefunction, f" is the second derivative and h' is h devided by 2 * pi)
you get : f" - (2m/h'²)*(V - E)f = 0 and the coëfficiënt (let's call this k²)of f is positive here so the solutions will be a superposition of exp(kx) and exp(-kx). So k² = (2m/h'²)(V-E) and the equation becomes f" = k²f
Now try searching for infinities : when x goes to the positive infinity one of the two exponential will become infinite and the same will occur when x goes to the negative infinite. We are not able to find a solution that is finite everywhere this this corresponds to an unphysical state...
regards
marlon
Last edited: Sep 24, 2004
3. Sep 24, 2004
### emob2p
Is there a way to prove in general if a function and its second derivative are always the same sign, then the function is not normalizalbe since this is essentially the case with E < V(min)?
4. Sep 25, 2004
### marlon
Well,
Just plot any function f with these two properties. You will clearly see that |f| will always "grow" without limit when x goes to either the positive or negative infinity. When f and f" > 0 then f will be concave upwards and if they are negative then f will be concave downwards...just check this out...
and suppose that f is zero in some point x then this point is also zero for the second derivative meaning that the function will go from convex (under the x-axis) to concave (above the x-axis)...the switch happens in the point x
marlon
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2018-03-23 21:05:05
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http://physics.stackexchange.com/questions/59493/how-to-understand-worldsheet-fermion-as-a-section
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# How to understand worldsheet fermion as a section?
I am reading Witten's paper on topological string, and I found some mathematical notation is hard to understand for me. Consider the nonlinear sigma model in 2 dimensions governed by maps $\Phi : \Sigma \rightarrow X$ with $\Sigma$ being a Riemann surface and $X$ a Riemann manifold of metric $g$. $z, \bar{z}$ are local coordinate on $\Sigma$ and $\phi^I$ is coordinate on $X$. $K$ and $\bar{K}$ are canonical and anticanonical line bundles of $\Sigma$ (the bundle of one forms of types (1,0) and (0,1) repectively), and let $K^{1/2}$ and $\bar{K}^{1/2}$.The fermi fields of the model are $\psi_{+}^I$, a section of $K^{1/2}\otimes\Phi^*(TX)$.
I can not understand the sections of $K^{1/2}$, $\Phi^*(TX)$ and $K^{1/2}\otimes\Phi^*(TX)$.
From my point of view, the element of $K$ should be of the following form $\alpha_z dz\in K$, and what is the element of $K^{1/2}$? the pull back of tangent space should be of form $\Phi^*(\beta^i \frac{\partial}{\partial \phi^i})=\beta^i \frac{1}{\frac{\partial \phi^i}{\partial z} }\frac{\partial}{\partial z}$. But in some notes the author seems give that the (0,1) form $\psi_-^i$ with values in $\Phi^*(T^{1,0} X)$ can be written as $\psi_{\bar{z}}^i$ satisfying $\psi \supset \psi_{\bar{z}}^id\bar{z}\otimes \frac{\partial}{\partial \phi^i}$. This contradicts with my naive point of view. where did I make mistakes? How to understand the sections of $K^{1/2}$, $\Phi^*(TX)$ and $K^{1/2}\otimes\Phi^*(TX)$?
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In addition to the other answers, I should point out that one needs to be careful when reading that paper to pay attention to whether Witten is discussing a QFT or its associated "twisted" QFT. The latter will not involve square roots of the canonical bundle. You can confuse yourself by trying to match formulae from the twisted and untwisted theories. – user1504 Mar 31 '13 at 12:54
In general, the canonical bundle $K$ is the bundle of n-forms on an n-dimensional manifold. Since your Riemann surface $\Sigma$ is one (complex) dimensional, it's just the (line) bundle of holomorphic one-forms. The "square root" $K^{\frac{1}{2}}$ is the bundle of things which transform in a way which is sort of the square root of the transformation of the holomorphic one forms. So if, under a worldsheet coordinate transformation (where $z$ is a local coordinate on $\Sigma$) $$z\rightarrow e^{i\alpha}z$$a one-form transforms as$$\omega\rightarrow e^{i\alpha}\omega$$ then, for the square root, we want something transforming as $$\psi\rightarrow e^{i\frac{\alpha}{2}}\psi$$ This is just a right handed worldsheet spinor. If it's a RH one, it's denoted $\psi_{+}$ and if, instead, it transformed with a $-\frac{\alpha}{2}$, it's LH and denoted $\psi_{-}$
Now you also want your entity to take values in the bundle $\phi^{*}(TX)$.
$\phi:\Sigma\rightarrow X$ is an embedding. Thinking of $\phi^{i}$; $i=1..N$ (where $N$ is the dimensionality of $X$) as coordinates on $X$, then your desired object has a target space index. So for example the right handed version of the components would be $\psi^{i}_{+}$, and the section is $$\psi^{i}_{+}(z)\frac{\partial}{\partial \phi^i}$$
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Thanks for your explaination, twistor59. – Craig Thone Mar 31 '13 at 8:27
$\psi_+^i(z)\frac{\partial}{\partial\phi}$ seems take values in $TX$ rather than $\Phi^*(TX)$, why not some form of $\psi_+^i \frac{1}{\frac{\partial \phi^i}{\partial z} }\frac{\partial}{\partial z}$? What is the difference of the sections of $K^{1/2}$, $\Phi^*(TX)$ and $K^{1/2}\otimes\Phi^*(TX)$? – Craig Thone Mar 31 '13 at 8:35
If I have a vector bundle $V$ over $X$, then the fibre of the pullback bundle $\phi^{*}(V)$ over $p \in \Sigma$ is just the fibre of $V$ over $\Phi(p)$, so since $\Phi$ here is an embedding, I can just work with the image of $\Sigma$ and restrict the bundle in question (in this case the tangent bundle) to this image. – twistor59 Mar 31 '13 at 9:11
Spinors are sections of the spinor bundle. The decomposition given by Witten of the spinor bundle is valid on Kähler manifolds which Riemann surfaces constitute special cases of. The spinor bundle has a structure group $SO(2N)$, where $N$ is the complex dimension of the Kähler manifold $M$. This group reduces to U(N) due to the existence of a Kähler structure. (This means that when one writes the curved space Dirac equation on $M$, it has the form of a gauged Dirac equation in flat space coupled to a U(N) gauge field).
The space of sections of the spinor bundle belongs a $2^N$ dimensional spinor representation of $SO(2N)$. This representation decomposes into a direct sum of all anti-symmetric representations of the $SU(N)$ factor of $U(N)$ under the reduction of the structure group. Thus from the dimension counting point of view, the $2^N$ dimensional spinorial representation space is isomorphic to the exterior algebra $\Lambda^{(0, *)}(M)$ of the holomorphic tangent bundle.
The appearance of the square root of the canonical bundle is due to the fact that the contribution of the $U(1)$ factor of $U(N)$ group to the Dirac equation is an Abelian connection whose curvature is just $\frac{N}{2}$ times the Kähler structure. This part provides the spin $\frac{1}{2}$ character of the fermion fields.
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2014-11-24 16:28:43
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http://mathematica.stackexchange.com/questions/41505/clean-webmathematica-kernel
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# Clean webMathematica Kernel
On my webMathematica server, certain input values are being saved between page loads on different computers. I assume this is because the kernel is not clearing the values after it finishes loading a page, which is the behavior that I would like. As per How do I clear all user defined symbols?, it seems there are a few ways to clear the kernel:
ClearAll["Global*"]
and
Quit[]
and
UtilitiesCleanSlate
My worry is this: Does calling one of these functions interfere with all pages that are currently being processed? I'm not sure I understand how the webMathematica kernel pool works, so I have no idea if multiple user accessing the server at the same time would be interfered with by clearing the Kernel. Also, would calling Quit[] quit the Kernel until it is restarted through some other process (e.g the Kernel Monitor), and would this interfere with multiple users accessing the page at the same time, or would it slow down the system with constant clearing and reloading?
Finally, would it be wise (assuming I'm not counting on packages staying loaded) to just add the lines
<KernelReleaseCode>
Quit[]
</KernelReleaseCode>
to MSPConfiguration.xml?
I know there are several questions here, but what I'd really is just a explanation (or a link to one) of how the webMathematica kernel pool and kernels work - I assume the answers to these questions would be trivial once I understand that.
-
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2016-02-06 07:23:27
|
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https://blog.fridaymath.com/a-property-of-the-kepler-triangle
|
This is a paragraph.
# A property of the Kepler triangle
On May 14, 2021, we showed that the side-lengths () of the Kepler triangle satisfy the identity
(1)
Or, in an upside-down form:
(2)
Of all right triangles, the Kepler triangle is the only one in which both the side-lengths and the reciprocals of the side-lengths satisfy Pythagorean identities.
On top of this, the Kepler triangle is also unique in that both the altitudes and the reciprocals of the altitudes satisfy Pythagorean identities.
(3)
(4)
(Only the Kepler triangle satisfies equation (3) above, but other right triangles satisfy equation (4).)
PROVE that equations (1) and (2) are equivalent.
Our very first example of 2022 is a breeze. To see that (1)(2), re-arrange
On the other hand, (2)(1) because
PROVE that every right triangle satisfies equation (4).
Let be the radius of the circumcircle of any triangle with side-lengths . Then the altitudes from vertices are given by
In the case of a right triangle with hypotenuse we have and so .
PROVE that equation (3) implies equation (1).
Since , we have
Clear the common denominator and it becomes clear that
PROVE that equation (1) implies equation (3).
Suppose that equation (1) holds, so that . Divide through by and use the expressions for the altitudes given in example 2.
PROVE that a right triangle is precisely the Kepler triangle, if it satisfies equation (3).
If a right triangle is of Kepler type, then by our post on May 14, 2021 , its side-lengths satisfy equation (1). By the preceding two examples, equations (1) and (3) are equivalent. Thus, a Kepler triangle satisfies equation (3).
Conversely, suppose that a right triangle with hypotenuse satisfies equation (3). Then and . Multiply both sides of by to get . Now combine with to get
In other words, the side-lengths form a geometric progression of the form . Thus, the right triangle is of the Kepler type.
## Takeaway
Let be a (right) triangle whose side-lengths satisfy . Then the following statements are equivalent:
1. the sequence is geometric
2. is the golden ratio
3. .
Such a triangle is the Kepler triangle.
• (Mid sixties) In a non-right triangle , let be the side-lengths, the altitudes, the feet of the altitudes from the respective vertices, the circumradius, the circumcenter, the nine-point center, the orthocenter, the midpoint of side , the reflection of over side , the reflection of over side , and the reflection of over side . PROVE that the following sixty-five statements are equivalent:
1. or
2. is congruent to
3. is congruent to
4. is isosceles with
5. is isosceles with
6. is right angled at
7. is the circumcenter of
8. is right-angled at
9. is right-angled at
11. the points are concyclic with as diameter
12. the reflection of over lies internally on
13. the reflection of over lies externally on
14. radius is parallel to side
15. is the reflection of over side
16. the nine-point center lies on
17. the orthic triangle is isosceles with
18. the geometric mean theorem holds
19. the bisector of has length , where
20. the orthocenter is a reflection of vertex over side
21. segment is tangent to the circumcircle at point
22. median has the same length as the segment
23. the bisector of is tangent to the nine-point circle at
24. is a convex kite with diagonals and
25. altitude is tangent to the nine-point circle at
26. segment is tangent to the nine-point circle at .
( short of the target.)
• (Extra feature) If satisfies equation (??), PROVE that its nine-point center divides in the ratio .
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2022-06-30 08:06:30
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|
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-6th-edition/chapter-p-prerequisites-fundamental-concepts-of-algebra-exercise-set-p-1-page-17/55
|
## College Algebra (6th Edition)
Published by Pearson
# Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.1 - Page 17: 55
#### Answer
$5-\sqrt 2$
#### Work Step by Step
|$\sqrt 2 - 5$| This must evaluate to a positive number. The square root of 2 is a very small quantity and if you were to subtract 5 from it you would get a negative result. Find the opposite. -($\sqrt 2 - 5$) Multiply through. -$\sqrt 2 + 5$ $5-\sqrt 2$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2019-04-18 20:37:53
|
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https://socratic.org/questions/lead-has-a-density-of-11-3-g-cm-3-what-is-the-volume-of-a-block-of-lead-with-a-m-1
|
Lead has a density of 11.3 g/cm^3. What is the volume of a block of lead with a mass of 282.5 g?
Mar 21, 2017
The volume is ${\text{25.0 cm}}^{3}$.
Explanation:
Density equation
"density"=("mass")/("volume")
Solution
Rearrange the density equation to isolate volume. Substitute the given values into the equation.
"volume"=("mass")/("density")
"volume"=(282.5color(red)cancel(color(black)("g")))/(11.3color(red)cancel(color(black)("g"))/"cm"^3")$=$$\text{25.0 cm"^3}$
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2020-08-05 10:40:49
|
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http://davydm.blogspot.com/2014/07/
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## Wednesday, 2 July 2014
### A little PeanutButter for your MVC
ASP.NET MVC is one of the best things that I could possibly think of to have happened to the web from a Windows-centric point of view. At last, there's a way to sweep that abomination that is WebForms under the proverbial carpet.
Like anything, though, it does have its caveats. You have useful constructs like Script and Style Bundles -- but no easy way to test them from a CI environment. Also script inclusion becomes a bit more manual than it needs to be when viewed though the lens of AMDs like require.js. But you do get the advantage of bundling in that a single request can satisfy multiple code/style requirements. (Let me be clear here: AMDs are good. I like require.js. But it does take a little more effort to set up and get working correctly and you don't (without even more configuration) get the hit-reduction that bundles provide. Both methods have their advantages. Select your tools for your tasks as they fit best for you, on the day.)
PeanutButter.MVC was built out of a need to make those processes slightly more testable and elegant.
First of all, there are two facade classes:
They wrap ScriptBundle and StyleBundle accordingly and implement interfaces of the expected names (IScriptBundle and IStyleBundle). You would use them like you'd use ScriptBundle and StyleBundle instances from the MVC framework. However, since they implement an interface, you can also create substitutes for them so that you can test-constrain your bundle registration process. This is important because I found that it was not uncommon to add a new javascript or css file to the solution, build-and-run, and be surprised that my changes weren't in play -- until I realised that I hadn't bundled them.
For example, I have the following method on my BundleConfig:
public static void RegisterBundles(BundleCollection bundles,
Func<string, IScriptBundle> withScriptBundleCreator = null,
Func<string, IStyleBundle> withStyleBundleCreator = null)
{
withScriptBundleCreator = withScriptBundleCreator ?? ((bundleName) => new ScriptBundleFacade(bundleName));
withStyleBundleCreator = withStyleBundleCreator ?? ((bundleName) => new StyleBundleFacade(bundleName));
}
We can see that the function would ordinarily be invoked without lambda factories to produce Script- and StyleBundleFacades, so it produces its own, very straight-forward ones. However, the tests that constrain this method can inject lambda factories so that the bundling methods can be tested to ensure that they include the required bundles from the relevant sources. Indeed, the tests are quite straight-forward:
[TestFixture]
public class TestBundleConfig
{
private Func<string, IScriptBundle< CreateSubstituteScriptBundleCreator(List>IScriptBundle< withTrackingList)
{
return (name) =>
{
var scriptBundle = Substitute.For<IScriptBundle>();
scriptBundle.Name.Returns(name);
var includedPaths = new List<string>();
var includedDirs = new List<IncludeDirectory>();
scriptBundle.IncludedPaths.ReturnsForAnyArgs(args =>
{
return includedPaths.ToArray();
});
scriptBundle.IncludedDirectories.ReturnsForAnyArgs(args =>
{
return includedDirs.ToArray();
});
scriptBundle.Include(Arg.Any<string>()).ReturnsForAnyArgs(args =>
{
return new Bundle("~/");
});
scriptBundle.IncludeDirectory(Arg.Any<string>(), Arg.Any<string>())
.ReturnsForAnyArgs(args =>
{
includedDirs.Add(new IncludeDirectory(args[0] as string, args[1] as string));
return new Bundle("~/");
});
scriptBundle.IncludeDirectory(Arg.Any<string>(), Arg.Any<string>(), Arg.Any<bool>())
.ReturnsForAnyArgs(args =>
{
includedDirs.Add(new IncludeDirectory(args[0] as string, args[1] as string, (bool)args[2]));
return new Bundle("~/");
});
return scriptBundle;
};
}
private Func<string, IStyleBundle> CreateSubstituteStyleBundleCreator(List<IStyleBundle> withTrackingList)
{
return (name) =>
{
var styleBundle = Substitute.For<IStyleBundle>();
var includedPaths = new List<string>();
styleBundle.IncludedPaths.ReturnsForAnyArgs(args =>
{
return includedPaths.ToArray();
});
styleBundle.Include(Arg.Any<string>()).ReturnsForAnyArgs(args =>
{
var paths = args[0] as string[];
return new Bundle("~/");
});
return styleBundle;
};
}
[Test]
{
//---------------Set up test pack-------------------
var collection = new BundleCollection();
var scriptBundles = new List<IScriptBundle>();
var styleBundles = new List<IStyleBundle>();
//---------------Assert Precondition----------------
//---------------Execute Test ----------------------
BundleConfig.RegisterBundles(collection,
CreateSubstituteScriptBundleCreator(scriptBundles),
CreateSubstituteStyleBundleCreator(styleBundles));
//---------------Test Result -----------------------
Assert.AreNotEqual(0, scriptBundles.Count);
Assert.AreNotEqual(0, styleBundles.Count);
Assert.IsTrue(scriptBundles.Any(sb => sb.Name == "~/bundles/js/shared" &&
sb.IncludedDirectories.Any(d => d.Path == "~/Scripts/js/shared" &&
d.SearchPattern == "*.js" &&
d.SearchSubdirectories == true)));
}
}
All good and well. We can ensure that our MVC application is creating all of the required bundles. It would also be super-neat if we could streamline the inclusion process. Of course, we can.
PeanutButter.MVC also includes a utility called AutoInclude. If we decide to set up our bundles under /bundles/js/{controller} (for scripts for any action on the controller) and /bundles/js/{action}, then a lot of inclusion work can be done for us in our base _Layout view with a single line (assuming you've included the relevant @using clause at the top):
@AutoInclude.AutoIncludeScriptsFor(ViewContext)
AutoInclude uses the convention of scripts sitting under folders with names corresponding to the controller, with the casing of the scripts folders lowered to be more consistent with how script folders are named. This one line has, in conjunction with judicial bundling (and testing of that bundling!) allowed all views to just "magically" get their relevant scripts. In my project, I can create script bundles which include similarly-named folders and not have to worry about how my views get relevant logic scripts from there on out.
So, for example, I might perform registrations like the following (where scriptBundleCreator is a passed in Func<iscriptbundle>):
bundles.Add(scriptBundleCreator("~/bundles/js/policy")
.IncludeDirectory("~/Scripts/js/policy", "*.js", false));
.IncludeDirectory("~/Scripts/js/policy/accept", "*.js", false));
.IncludeDirectory("~/Scripts/js/policy/edit", "*.js", false));
Now, from the Policy controller, I have two actions, Accept and Edit. Both have their relevant views, of course, and the AutoInclude is done automatically for them by virtue of the fact that they use the default _Layout.cshtml. Under my Scripts folder in my project, I have a file structure layout like:
policy
policy/common.js
policy/accept
policy/accept/accept.js
policy/accept/proposalEmailer.js
policy/edit
policy/edit/clientDetailsDisplayUpdater.js
policy/edit/edit.js
policy/livePolicyUpdater.js
And the result is that the Policy/Accept view gets common.js, accept.js, lead-autocompletion.js and proposalEmailer.js. The Policy/Edit view gets common.js, clientDetailsDisplayUpdater.js, edit.js and livePolicyUpdater.js.
So now I'm free to create small, easily-testable javascript files (which I'll test with Jasmine and whatever works best for my purposes (eg karma or the Resharper unit test runner -- which works, mostly, with Jasmine, but has a few rough edges)). And when I want them in a page, I just drop them in the appropriate folder to get them on the next compile/debug run. And because of bundling, the end-user doesn't have to get many little hits for javascript files, instead, just getting two per view.
Apart from the testability of it and the simplicity of adding another piece of javascript functionality to the site, there's a huge bonus in grokkability. Let's face it: one of the reasosn why tests are good on your code is for when a new developer comes onto the project (or some unlucky person is tasked with maintaining some code they had nothing to do with). Tests provide feedback for when something breaks but also provide a communication mechanism for the new developer to figure out how discreet parts of the overall machine work. To the same end, understandable symbol and file naming and unsurprising project layout can really help with a new developer (or when you just have to get back on to the project for maintenance or extension and it's a couple of months down the line...)
Anyway, so there it is: PeanutButter.MVC. Free, small, doesn't depend on much, and hopefully useful. I'm certainly reaching for it the next time I'm in MVC land.
## Tuesday, 1 July 2014
### INI files are dead... Long live INI files!
There was a time when INI files ruled the world of configuration. Since then, we've been told on numerous occasions by many people that we should rather be using XML. Or a SQLite database. Or something else, perhaps.
Now, don't get me wrong -- SQLite has its merits and XML is great if you want to store hierarchical data or if you need to configure your .NET application (which happens to already speak the lingo). But the reality is that INI serves quite well for a number of uses -- indeed, it can also be used to store hierarchical data, as you'd see if you checked out the innards of a .reg file. In particular, INI files are dead-easy to parse, both by machine and man -- and the latter is an advantage if you have nothing to hide and no need for quick read/write (where you might, for example, use SQLite). It's also a simple file-store so platform and library requirements are minimal. It's probably the easiest way to store structured configuration data and I still use it for projects unless I absolutely have to use something else.
A relatively small, simple part of the PeanutButter suite is the INI reader/writer/storage class PeanutButter.INI.INIFile. Usage is quite simple:
var ini = new INIFile("C:\\path\\to\\your\\iniFile.ini");
var someConfiguredValue = ini["colors"]["FavouriteColor"];
ini["Geometry"]["Left"] = "123";
ini.Persist();
In thesnippet above, we instantiate an INIFile class with a path to a file to use as the default persistence store. This file doesn't have to exist right now (and if it doesn't, it will be created with the Persist() call).
INIFile presents the data present in the source as a Dictionary<string, Dictionary<string, string>>, with indexing on the INIFile instance itself, making the syntax quite easy to use. Sections are created as and when you need them. Section and key names (such as "Geometry" and "Left" above) are case-insensitive to make access easier (and more compliant with the behavior of the older win32 calls for INI handling).
The parser tolerates empty lines and comments as well as empty keys (which are returned as an empty string).
Of course, you don't have to have a backing store to start with (or at all), and you can always override the output path with a parameter to Persist(). In addition, you can re-use the same INIFile, loading in a file from another path with the Load() method or loading with a pure string with the Parse() method.
Once again, the class has been developed on an as-required basis. It does much of what I want it to do (though I'd like it to persist comments on re-writing; that may come later). I hope that it can be of use to someone else too. I've lost count of how many times I've implemented an INI reader/writer. Hopefully, this is one of the last...
### What's new in PeanutButter
I realise that it's been a while (again) since I've posted an update about new things in PeanutButter ( GitHub , Nuget ). I've ...
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2018-01-19 09:20:11
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https://plainmath.net/30748/perform-the-indicated-operation-and-simplify-result-leave-your-answer
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# Perform the indicated operation and simplify the result. Leave your answer in fa
Perform the indicated operation and simplify the result. Leave your answer in factored form.
$$\displaystyle{\left[{\frac{{{x}}}{{{x}+{1}}}}\right]}-{\left[{\frac{{{2}{x}-{2}}}{{{x}-{1}}}}\right]}$$
• Questions are typically answered in as fast as 30 minutes
### Plainmath recommends
• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.
izboknil3
Step 1
We can simplify the algebraic expressions involving fractions by taking LCM (Least common multiple ) of the denominators . We have to convert all the denominators to the value of the LCM by multiplying both numerator and denominator in each fraction by using suitable constant.
We can also factor out the common terms from both numerator and denominator of the expression to get the simple fraction form the algebraic expression . We can cancel the factors which are in numerator and denominator of equal kind.
Step 2
Consider the algebraic expression $$\displaystyle{\left[{\frac{{{x}}}{{{x}+{1}}}}\right]}-{\left[{\frac{{{2}{x}-{2}}}{{{x}-{1}}}}\right]}$$,
We have to take the LCM of the denominator and we need to convert both the denominators of the fractions to the LCM value by multiplying both numerator and denominator in the expression by suitable terms.
We have the LCM of the denominators $$\displaystyle{\left({x}+{1}\right)}{\left({x}-{1}\right)}$$ is $$\displaystyle{\left({x}+{1}\right)}{\left({x}-{1}\right)}$$ .
To convert both denominators to LCM value , multiply both numerator and denominator of the first fraction by $$\displaystyle{\left({x}-{1}\right)}$$ and the second fraction by $$\displaystyle{\left({x}+{1}\right)}$$.
Thus we get,
$$\displaystyle{\left[{\frac{{{x}}}{{{x}+{1}}}}\right]}-{\left[{\frac{{{2}{x}-{2}}}{{{x}-{1}}}}\right]}$$
$$=\frac{x}{x+1} \times \frac{(x-1)}{(x-1)}-\frac{2x-3}{x-1} \times \frac{(x+1)}{(x+1)}$$
$$\displaystyle={\frac{{{x}{\left({x}-{1}\right)}-{\left({2}{x}-{3}\right)}{\left({x}+{1}\right)}}}{{{\left({x}+{1}\right)}{\left({x}-{1}\right)}}}}$$
$$\displaystyle={\frac{{{x}^{{{2}}}-{x}-{2}{x}{\left({x}+{1}\right)}+{3}{\left({x}+{1}\right)}}}{{{x}^{{{2}}}-{x}+{x}-{1}}}}$$
$$\displaystyle={\frac{{{x}^{{{2}}}-{x}-{2}{x}^{{{2}}}-{2}{x}+{3}{x}+{3}}}{{{x}^{{{2}}}-{1}}}}$$ (simplify by adding the like terms)
$$\displaystyle={\frac{{-{x}^{{{2}}}+{3}}}{{{x}^{{{2}}}-{1}}}}$$
$$\displaystyle={\frac{{-{\left({x}^{{{2}}}-{3}\right)}}}{{{x}^{{{2}}}-{1}}}}$$
$$\displaystyle=-{\frac{{{\left({x}^{{{2}}}-{3}\right)}}}{{{x}^{{{2}}}-{1}}}}$$
Hence we have the required simple fraction form.
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2021-12-08 00:22:20
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http://cjtcs.cs.uchicago.edu/articles/2013/10/contents.html
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### Volume 2013
#### Article 10
Published by the Department of Computer Science, The University of Chicago.
#### On the complexity of solving linear congruences and computing nullspaces modulo a constant
Niel de Beaudrap
Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Cambridge, UK
niel DOT debeaudrap AT gmail DOT com
July 27, 2013
#### Abstract
We consider the problems of determining the feasibility of a linear congruence, producing a solution to a linear congruence, and finding a spanning set for the nullspace of an integer matrix, where each problem is considered modulo an arbitrary constant $k \geqslant 2$. These problems are known to be complete for the logspace modular counting classes $\mathrm{Mod_k L = coMod_k L}$ in the special case when $k$ is prime (Buntrock et al 1992). By considering variants of standard logspace function classes -- related to $\mathrm{\#L}$ and functions computable by $\mathrm{UL}$ machines, but which only characterize the number of accepting paths modulo $k$ -- we show that these problems of linear algebra are also complete for $\mathrm{coMod_k L}$ for any constant $k \geqslant 2$.
Our results are obtained by defining a class of functions $\mathrm{FUL_k}$ which are low for $\mathrm{Mod_k L}$ and $\mathrm{coMod_k L}$ for $k \geqslant 2$, using ideas similar to those used in the case of k prime in (Buntrock et al 1992) to show closure of $\mathrm{Mod_k L}$ under $\mathrm{NC^1}$ reductions (including $\mathrm{Mod_k L}$ oracle reductions). In addition to the results above, we briefly consider the relationship of the class $\mathrm{FUL_k}$ for arbitrary moduli $k$ to the class $\mathrm{F \cdot coMod_k L}$ of functions whose output symbols are verifiable by $\mathrm{coMod_k L}$ algorithms; and consider what consequences such a comparison may have for oracle closure results of the form $\mathrm{Mod_k L^{Mod_k L} = Mod_k L}$ for composite $k$.
• The article: PDF (275 KB)
• Source material: ZIP (93 KB)
• BibTeX entry for this article (282 bytes)
Submitted September 13, 2012, revised July 11, 2013; published July 27, 2013.
Article 9 Article 11
Volume 2013 Published articles
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2018-08-16 14:44:41
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https://mathblog.com/on-concavity-calculus-and-crescents/
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# On Concavity, Calculus, and Crescents
Concavity characterizes so much of the world — from the distribution of sizes of animal species, to the potential return-on-investment from small vs large companies, to the temperature of a warm body in a cold room, to the results of sports training.
To explain concavity, I’ll talk about training for a race.
### Training for the Mile Race
If you’re like me and haven’t slipped into your jogging gear for a few months (ok, maybe a few years), then the first time you hit the track you will be quite slow. My mile time had dropped to 8:31 — and I used to run sub-6! Oh well. The good news is that I was quick to improve. After only a week my time dropped to 7:44. That’s what I call “low-hanging fruit”. Imagine if an Olympic athlete could drop their time by 9% in a week!
I continued to train and here were my times from each week when I tested myself at the end of the week.
Time Speed 8:31 7.05 mph 7:44 7.76 mph 7:13 8.31 mph 6:58 8.61 mph 6:51 8.76 mph 6:49 8.80 mph 6:48 8.82 mph … …
The story gets much more boring from here on out because I had left the land of low-hanging fruit and entered the land of diminishing returns. I was still getting faster every week, but not by as much. And so it is with Olympians–months of intense training often lead to speed gains of less than a second.
### Calculus!
This whole story can be summarized with just two mathematical statements about the function f which maps from $$\{ \mathrm{amount of training} \} \to \{ \mathrm{speed} \}$$.
1. f ' > 0 — training makes you faster —
2. f ” < 0 at a decreasing rate.
### As well as everything began…so badly did it end
But it’s not the end of my story. I kept up my regimen of running right through the summer, when it was warm. But as the weather worsened, my willpower waned. When I wouldn’t work out, I would get worse – weaker, wimpier. By winter I was worthless.
8.92 mph 8.80 mph 8.54 mph 8.22 mph 7.45 mph …
And so, in just exactly the opposite pattern as my times had leapt up in the spring and gradually improved over the summer, so did they, come fall, gradually start getting worse f ' < 0, and then plummeted back to sloth once November hit. By Black Friday, I was about as fast as a jelly donut.
My up-then-down crescent was exactly, exactly a concave function. Fast up, slow up, slow down, fast down. Unfortunately.
Well, at least I was fast… once. Oh, negative f ”, I’ll best you one of these years.
### Conclusion
Concavity is common, and when couched as calculus, can be condensed to a curt comment: f ” < 0.
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2021-04-20 19:55:37
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https://datascience.stackexchange.com/questions/26556/how-does-an-individual-feature-affect-predictions-in-neural-network-classificati/26595#26595
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# How does an individual feature affect predictions in neural network classification problem?
In the literature, I've come across statements like People with higher income and with long working hours are more likely to be diagnosed with chronic diseases such as stroke. The above-mentioned study (Page:8), explores the association between Behavioral Habits and Chronic Diseases using ANN.
As I'm new to ML,
1. I am unable to figure out how to make such conclusions with feature study in neural networks or other machine learning techniques.
2. Is there a way to quantify the likelihood in ANN similar to logistic regression wherein regression coefficients give the change in the log odds of the outcome for a one unit increase in the predictor variable?
Currently using Azure ML studio
Is there a way to quantify the likelihood in ANN similar to logistic regression wherein regression coefficients give the change in the log odds of the outcome for a one unit increase in the predictor variable?
Good question.
Yes, there is a way. The approach that can help you is called partial dependence plot (PDP), see the links below for further details and examples.
The approach is model agnostic, i.e. works well for any predictive model, powerful yet simple.
The main steps for one-dimensional partial dependence plot are as follows
1. Fit your model as usual
2. Select the predictor of interest and a set of values to be investigated (e.g. income as in the article you refer to and values of say 50k, 70k, 80k, ..., 120k)
3. For all observations in your dataset replace the values of your predictor with the first value from the set above (50k).
4. Calculate the model output for the modified dataset from the previous step and calculate the average over all observations.
5. Repeat steps 3-4 for the remaining values (70k, 80k, ...) and plot the values of your predictor along X axis and the corresponding averaged model predictions along Y axis.
With one-dimensional PDP described above you can easily see the marginal impact of a predictor being analysed on the model output. Furthermore, one can use similar technique to perform multi-dimensional analysis, e.g. to investigate the impact of interactions.
partial dependence plots- scikit-learn documentation
partial dependence plot - tutorial by Dans Becker on Kaggle
As you are new to ML, I will try to explain in my simplest way.
1. I am unable to figure out how to make such conclusions with feature study in neural networks or other machine learning techniques.
Machine learning has many applications, what you are talking about here comes under the term Inference. It means to understand- how your output is affected as your input changes. I suggest you follow the book- An Introduction to Statistical Learning with Applications in R. On page 19 of this book, it is given-
Inference
We are often interested in understanding the way that Y is affected as X1,...,Xp change.
........
We instead want to understand the relationship between X and Y.
- Which predictors are associated with the response?
- What is the relationship between the response and each predictor?
- Can the relationship between Y and each predictor be adequately summarized using a linear equation, or is the relationship more complicated?
I have not posted the whole thing here, just some important points.
So here, instead of prediction, you just analyze your model. After analyzing you can make such conclusions.
2. Is there a way to quantify the likelihood in ANN similar to logistic regression wherein regression coefficients give the change in the log odds of the outcome for a one unit increase in the predictor variable?
As far as I understand, ANN has multiple layers. It is not like logistic regression which just defines one coefficient for each predictor. In ANN, the coefficients are defined for each layer separately, and in each layer, for each node.
Hope this helps.
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2021-09-26 21:21:01
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https://chemistry.stackexchange.com/questions/112770/why-does-the-carbonyl-of-carboxylic-acids-get-protonated-and-not-the-hydroxyl-gr
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# Why does the carbonyl of carboxylic acids get protonated and not the hydroxyl group?
Is the O of the C=O group more electronegative or is it for the sake of getting from product A to B that the carbonyl is protonated rather than the hydroxyl?
• I suppose it because $\ce{R-C^{+}(OH)2}$ is more preferred. I think protonation of both oxygens is possible, but the symmetric structures is more stable. Apr 15 '19 at 7:27
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2021-11-29 21:57:56
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http://mathhelpforum.com/calculus/85904-converting-polar-form-rectangular-form.html
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# Thread: Converting from Polar form to Rectangular form
1. ## Converting from Polar form to Rectangular form
If you have the time,
So i want to convert this polar equation to a rectangular form.
Problem1: r= 4cosθ - 4sinθ
I understand the simple conversions like this one:
r= 3secθ
r/secθ = 3 (divided secθ)
rcosθ = 3 (1/secθ = cosθ)
x = 3 : rcosθ = x (coordinate conversion equations)
but i dont know how to begin with the problem 1
Here are other coordinate conversion equations that might help:
y = rsinθ
r^2 = x^2 + y^2
tanθ = y/x
thankyou!
2. Originally Posted by yeunju
If you have the time,
So i want to convert this polar equation to a rectangular form.
Problem1: r= 4cosθ - 4sinθ
Hint: multiply through by r, you get
$r^2 = 4r \cos \theta - 4 r \sin \theta$
now what?
3. Oh, with that helpful hint
i'm thinking to use the x=rcosθ and y=rsinθ and r^2 = x^2+y^2
so: x^2 + y^2 = 4x - 4y
then maybe x^2 -4x + y^2 + 4y = 0
I remember an example with my teacher using complete the square? but it was on an equation like x^2 + y^2 = 4x (subtract 4x)
so then it ended up with x^2 -4x +4 +y^2 = 4
so could i do that with both x and y? maybe..
or am i going the wrong direction?
4. Yes, rewrite it as $x^2 -4x +4 +y^2 +4y+4 = 8$.
Complete the square for both x and y to get:
Spoiler:
$(x-2)^2+(y+2)^2=8$
Voila! It's a circle of radius $2\sqrt{2}$ centered at $(2,-2)$.
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2016-08-28 21:13:34
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http://fluencyuniversity.com/m9o4am/b437h.php?cc98e9=inverse-of-a-3x3-matrix-calculator
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Verify by showing that BA = AB = I. The main difference between this calculator and calculator Inverse matrix calculator is modular arithmetic. Form the augmented matrix [A/I], where I is the n x n identity matrix. Find how to calculate the inverse of a matrix A using adjoint and transpose at BYJU'S This website uses cookies to ensure you get the best experience. Find more Mathematics widgets in Wolfram|Alpha. Some theory. Remember it must be true that: A × A-1 = I. Prediction positive in F1 and prediction negative in G1. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. Perform row transformations on [A|I] to get a matrix of the form [I|B]. 3. The inverse matrix can be calculated only for square matrices, but not every square matrix has an inverse matrix. We can calculate the Inverse of a Matrix by: Step 1: calculating the Matrix of Minors, Step 2: then turn that into the Matrix of Cofactors, Step 3: then the Adjugate, and; Step 4: multiply that by 1/Determinant. 3x3 Matrix Determinants. Enter a matrix. We will talk about what happens when it isn’t invertible a little later on. But anyway, that is how you calculate the inverse of a 2x2. How to find the inverse matrix of a 4x4 matrix Last updated: Nov. 3, 2017 Find the inverse of , where $|A|\neq 0$. It is much less intuitive, and may be much longer than the previous one, but we can always use it because it … But it is best explained by working through an example! If the found matrix A-1 is inverse for the given matrix A, then A-1 * A = A * A-1 = E. To explain the calculation of your inverse matrix is the main idea of creating this calculator. After that, you have to go through numerous lengthy steps, which are more time consuming in order to find the inverse of a matrix. To embed this widget in a post on your WordPress blog, copy and paste the shortcode below into the HTML source: To add a widget to a MediaWiki site, the wiki must have the. Related Topics: More Lessons on Matrices A square matrix, I is an identity matrix if the product of I and any square matrix A is A. IA = AI = A. The use of this calculator is very easy. Note : Let A be square matrix of order n. Then, A −1 exists if and only if A is non-singular. Tips. Free matrix inverse calculator - calculate matrix inverse step-by-step. FINDING INVERSE OF 3X3 MATRIX EXAMPLES. In other words: M * M-1 = I. Nicht jede quadratische Matrix besitzt eine Inverse; die invertierbaren Matrizen werden reguläre Matrizen genannt. This is a fun way to find the Inverse of a Matrix: A 3x3 Identity Matrix You may also find the following Math calculators useful. The matrix Y is called the inverse of X. If non-square matrices have an inverse, especially if 3x4 has one please let me know, the reason why. Matrices are array of numbers or values represented in rows and columns. Number of rows (equal to number of columns): n = . This website uses cookies to ensure you get the best experience. nxn inverse matrix calculator, formulas, work with steps, step by step calculation, real world and practice problems to learn how to find inverse matrix of 4x4, 3x3 and 2x2 matrices. For a 2 × 2 matrix, the identity matrix for multiplication is . In linear algebra, an n-by-n (square) matrix A is called invertible if there exists an n-by-n matrix such that. Guide . Calculating the inverse of a 3x3 matrix by hand is a tedious process. You will get the desired results immediately. A square matrix is singular only when its determinant is exactly zero. You just have to enter the values of the respective 3 x 3 order matrix in the required fields and hit the enter button. Form the augmented matrix [A/I], where I is the n x n identity matrix. 1 Steps. A square matrix is singular only when its determinant is exactly zero. Finding Inverse of 2 x 2 Matrix. Show Instructions In general, you can skip … 3x3 Sum of Three Determinants. To calculate inverse matrix you need to do the following steps. h) A*B A 3x3 matrix times a 1x3 matrix (does not work). Also gain a basic understanding of matrices and matrix operations and explore many other free calculators. Remember, not every matrix has an inverse. nxn inverse matrix calculator, formulas, work with steps, step by step calculation, real world and practice problems to learn how to find inverse matrix of 4x4, 3x3 and 2x2 matrices. A frequent misuse of inv arises when solving the system of linear equations Ax = b. A 3 x 3 matrix has 3 rows and 3 columns. (Note: also check out Matrix Inverse by Row Operations and the Matrix Calculator.) Setze die Matrix (sie muss quadratisch sein) und hänge die Identitätsmatrix der gleichen Dimension an sie an. Um die inverse Matrix zu berechnen, musst du folgende Schritte durchführen. 2. Inverse of a matrix A is the reverse of it, represented as A-1. Sal shows how to find the inverse of a 3x3 matrix using its determinant. Learn more Accept . And as we'll see in the next video, calculating by the inverse of a 3x3 matrix … Find the inverse of a given 3x3 matrix. We show how to find the inverse of an arbitrary 4x4 matrix by using the adjugate matrix. But hopefully that satisfies you. Inverse of a 3x3 matrix (practice) | Khan Academy. This matrix calculator will help you find the inverse of a 3x3 matrix. Learn more at BYJU'S. To embed this widget in a post, install the Wolfram|Alpha Widget Shortcode Plugin and copy and paste the shortcode above into the HTML source. (adsbygoogle = window.adsbygoogle || []).push({}); The inverse of a matrix can only be found in the case if the matrix is a square matrix and the determinant of that matrix is a non-zero number. Select the matrix size: Please enter the matrice: A-1 . 3x3 identity matrices involves 3 rows and 3 columns. A matrix is constructed by providing a list of row One important thing to note about SymPy matrices is that, unlike every other object in SymPy, theyFree online inverse matrix calculator computes the inverse of a 2x2, 3x3 or higher-order square matrix. A 3x3 matrix is an array of numbers having 3 rows and 3 columns. The inverse matrix was explored by examining several concepts such as linear dependency and the rank of a matrix. The inverse matrix multiplied by the original one yields the identity matrix (I). If you wish to enter a 3x3 or larger square matrix, you will select the last matrix template shape (6th icon from the left, or the one just to the left of the sigma notation). Answer There are mainly two ways to obtain the inverse matrix. Inverse of a Matrix using Elementary Row Operations. The inverse of a number is its reciprocal. Who would want to work so hard just to find out the inverse of a 3 x 3 matrix? Using Determinants and Cofactors Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 1. You can also find the inverse using an advanced graphing calculator. This post will explore several concepts related to the inverse of amatrix, in… Calculator. Example: find the Inverse of A: It needs 4 steps. By using this website, you agree to our Cookie Policy. Formula: This is the formula that we are going to use to solve any linear equations. Store the following matrix into . Summary. Matrix Calculator 2x2 Cramers Rule. As stated earlier, finding an inverse matrix is best left to a computer, especially when dealing with matrices of $$4 \times 4$$ or above. Guide . 1. That is what I selected to enter my example matrix that you also see on the screen. Find Inverse Matrix. It does not give only the inverse of a 3x3 matrix, and also it gives you the determinant and adjoint of the 3x3 matrix that you enter. You can find out the inverse of a matrix (say A) by finding out the value of 'I' in the above equation: A = IA. Inverse matrix using determinants . Calculating the inverse using row operations: v. 1.25 PROBLEM TEMPLATE: Find (if possible) the inverse of the given n x n matrix A. inverse of 3x3 matrices worksheet, Solving systems of Equations using Matrices Using Inverse Matrices to evaluate a system of equations. (Use a calculator) Example: 3x - 2y + z = 24 2x + 2y + 2z = 12 x + 5y - 2z = -31 This is a calculator that can help you find the inverse of a 3×3 matrix. The calculator will find the inverse of the square matrix using the Gaussian elimination method, with steps shown. The matrix picked below is invertible, meaning it does in fact have an inverse. The inverse matrix is practically the given matrix raised at the power of -1. advertisement. Thanks! In fact, once you know how to do something like finding an inverse matrix by hand, the calculator can free you up from that calculation and let you focus on the big picture. Given the matrix $$A$$, its inverse $$A^{-1}$$ is the one that satisfies the following: Try the free Mathway calculator and problem solver below to practice various math topics. The inverse of a matrix is something which can be very difficult to calculate and becomes more difficult when the order of the given matrix is 3 x 3. AB = BA = I n. then the matrix B is called an inverse of A. Formula to find inverse of a matrix. For every m×m square matrix there exist an inverse of it. Calculate matrix inverse with our matrix solver. Inverse 3x3 Matrix Codes and Scripts Downloads Free. If you wish to enter a 3x3 or larger square matrix, you will select the last matrix template shape (6th icon from the left, or the one just to the left of the sigma notation). Matrices, when multiplied by its inverse will give a resultant identity matrix. 4. AB = BA = I n. then the matrix B is called an inverse of A. Related Topics More Matrix Lessons; 3×3 inverse matrix calculator Enter in your 3×3 matrix to get the inverse. A matrix that has no inverse is singular. Free Matrix Adjoint calculator - find Matrix Adjoint step-by-step. g) B*A A 1x3 matrix times a 3x3 matrix. Assuming that there is non-singular ( i.e. Use it to check your answers. We welcome your feedback, comments and questions about this site or page. By using this website, you agree to our Cookie Policy. Examples: Insert the zeros-row on top of 3x3 matrix M = magic(3) . The calculation of the inverse matrix is an indispensable tool in linear algebra. Now, see the image above to see the 2x2 matrix and its inverse that I typed into my TI-nspire. Select the matrix size: Please enter the matrice: A-1 . A singular matrix is the one in which the determinant is not equal to zero. Also called the Gauss-Jordan method. Finding Inverse of 2 x 2 Matrix. As a result you will get the inverse calculated on the right. This inverse matrix calculator help you to find the inverse matrix. This is the reason why iCalculator made this good online calculator that will save your manual calculations and save you a lot of time. For example, the inverse of 8is 18, the inverse of 20 is 120 and so on.Therefore, a number multiplied by its inverse will always equal 1. 2. OK, how do we calculate the inverse? The inverse of the 3x3 matrix can be determined by calculating the determinant and matrix of cofactors and then dividing each term by determinant. Since there is no division operator for matrices, you need to multiply by the inverse matrix. Calculate the inverse of the matrix. Some theory. 1 Steps. A matrix X is invertible if there exists a matrix Y of the same size such that X Y = Y X = I n, where I n is the n-by-n identity matrix. Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one). SEMATH INFO. Get the free "Inverse & Determinant 3 x 3 Matrix Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. I saw this question somewhere and made me think do 3x4 matrices have an inverse, as I previously that that only square matrices have an inverse. Inverse of a Matrix Description Calculate the inverse of a matrix. Learn more Accept. We also have a matrix calculator that will help you to find the inverse of a 3x3 matrix. 3x3 Cramers Rule. 2x - y + 3z = 9. x + y + z = 6. x - y + z = 2. In this short tutorial we will learn how you can easily find the inverse of a matrix using a Casio fx-991ES plus. Formula to find inverse of a matrix. With help of this calculator you can: find the matrix determinant, the rank, raise the matrix to a power, find the sum and the multiplication of matrices, calculate the inverse matrix. Remember, not every matrix has an inverse. And you could try it the other way around to confirm that if you multiply it the other way, you'd also get the identity matrix. Contents. Matrices. Calculator. 2x2 Matrix. determinant(A) is not equal to zero) square matrix A, then an n × n matrix A-1 will exist, called the inverse of A such that: AA-1 = A-1 A = I, where I is the identity matrix. Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find the inverse matrix using matrix of cofactors. Good www.khanacademy.org. 2x2 Sum of Two Determinants. SPOILER ALERT: EVEN 3x3 MATRIX INVERSE IS ALREADY TOO HEAVY TO CALCULATE, SO BETTE Inverse of a Matrix using Elementary Row Operations. 3 x 3 Inverse Matrix Calculator Step by Step The inverse matrix can be calculated only for square matrices, but not every square matrix has an inverse matrix. This inverse matrix calculator help you to find the inverse matrix. Inverse matrix using determinants. By using this website, you agree to our Cookie Policy. X = A⁻¹ B. Calculating the inverse of a 3x3 matrix by hand is a tedious job, but worth reviewing. One way to solve the equation is with x = inv(A)*b. Example 1: Solve the following linear equation by inversion method . The use of this calculator is very easy. It is much less intuitive, and may be much longer than the previous one, but we can... ES; EN; CA; Syllabus. See step-by-step methods used in computing inverses, diagonalization and many other properties of matrices. In this tutorial, we are going to learn about the matrix inversion. 2x2 Matrix Determinants. If the found matrix A -1 is inverse for the given matrix A, then A -1 * A = A * A -1 = E. To explain the calculation of your inverse matrix is the basic idea of creating this calculator. The first possible matrix template is for a 2x2 matrix. Die inverse Matrix, Kehrmatrix oder kurz Inverse einer quadratischen Matrix ist in der Mathematik eine ebenfalls quadratische Matrix, die mit der Ausgangsmatrix multipliziert die Einheitsmatrix ergibt. We will talk about what happens when it isn’t invertible a little later on. Home | About ... FINDING AN INVERSE MATRIX To obtain A^(-1) n x n matrix A for which A^(-1) exists, follow these steps. You can also check your answers using the 3x3 inverse matrix calculator. 2x2 Sum of Determinants. FINDING INVERSE OF 3X3 MATRIX EXAMPLES. Calculator. The cofactor of is where - determinant of a matrix, which is cut down from A by removing row i and column j (first minor). The matrix picked below is invertible, meaning it does in fact have an inverse. Free online inverse matrix calculator computes the inverse of a 2x2, 3x3 or higher-order square matrix. 1. M-1 = inverse matrix. One method of finding the inverse of a 3x3 matrix involves using a graphing calculator. Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to find the inverse matrix using Gaussian elimination. Note : Let A be square matrix of order n. Then, A −1 exists if and only if A is non-singular. It is represented by M In this short tutorial we will learn how you can easily find the inverse of a matrix using a Casio fx-991ES plus. Inverse matrix. Perform row transformations on [A|I] to get a matrix of the form [I|B]. It is seldom necessary to form the explicit inverse of a matrix. Thus, similar toa number and its inverse always equaling 1, a matrix multiplied by itsinverse equals the identity. You will get the desired results immediately. Free online inverse matrix calculator computes the inverse of a 2x2, 3x3 or higher-order square matrix. I find the modular multiplicative inverse (of the matrix determinant, which is $1×4-3×5=-11$) with the extended Euclid algorithm (it is $-7 \equiv 19 \pmod{26}$). f) A*A Perform matrix multiplication. Online calculator to perform matrix operations on one or two matrices, including addition, subtraction, multiplication, and taking the power, determinant, inverse, or transpose of a matrix. Exist an inverse, especially if 3x4 has one Please let me know, the reason.! Evaluate a system of equations using matrices using inverse matrices to evaluate a system equations! A 3x3 matrix and its cofactor matrix image above to see the image above to see the 2x2 matrix where... The zeros-row on top of 3x3 matrix is an array of numbers having 3 inverse of a 3x3 matrix calculator and columns! Invertible a little critical job but can be calculated only for square matrices when! Our Cookie Policy x - y + 3z = 9. x + y + =. A: it needs 4 steps doing the changes to an identity matrix isn t. Uses cookies to ensure you get the inverse of a 3x3 matrix practice math., but not every square matrix is only possible when such properties hold: the matrix B of n.. We also have a matrix is singular only when its determinant is not equal zero... The inverse matrix is practically the given linear equation using inversion method when trying to find the of! To an identity matrix for multiplication is by using this website uses cookies ensure! To learn about the matrix ( including the right reverse of it + 3z = 9. x + +! No division operator for matrices, when multiplied by itsinverse equals the identity.! Of amatrix, in… FINDING inverse of a matrix itsinverse equals the identity the! Also find the inverse matrix calculator help you to find out the inverse of a matrix. Represented in rows and 3 columns arises when Solving the system of equations of! The zeros-row on top of 3x3 matrix using a Casio fx-991ES plus of! Using matrices using inverse matrices to evaluate a system of linear equations Ax B. 3 columns one method of FINDING the inverse of a 2x2 matrix and its inverse I! Y + 3z = 9. x + y + z = 2 concepts related to the inverse a. Check your answer with the second matrix the left matrix to row echelon form using elementary operations. Its cofactor matrix order matrix in the required fields and hit the enter.! Rank of a matrix that is how you can also find the inverse of a matrix VIF criterion suggested &. Matrices to evaluate inverse of a 3x3 matrix calculator system of linear equations matrix denoted by A−1and isdefined as: where I is the of..., a −1 exists if and only if a is called invertible there... Solve any linear equations form using elementary row operations changes to an matrix. Lessons ; 3×3 inverse matrix is the reverse of it, represented as A-1 die... About the matrix are the numbers which make up the matrix inversion form the augmented matrix [ A/I,... Insert the zeros-row on top of 3x3 matrices person_outline Timur schedule 2011-06-16 20:59:19 the determinant of a using. 2 × 2 matrix, the identity be square matrix from the Gaussian elimination method, with steps shown mainly... Multiplication is the explicit inverse of a inverse of a 3x3 matrix calculator x 3 order matrix in the required fields and hit enter... Above to see how to solve the equation is with x = inv ( ). By A−1and isdefined as: where I is the identitymatrix ways to obtain inverse! In computing inverses, diagonalization and many other free calculators online calculator that will help you to find the of... Inverse using an advanced graphing calculator. matrices involves 3 rows and 3.... Multiplied by its inverse always equaling 1, a −1 exists if and only if a is non-singular, or. Find matrix Adjoint step-by-step an example: how do we know this is identitymatrix! Working through an example: find the inverse matrix calculator computes the inverse of matrix... Practice ) | Khan Academy involves using a Casio fx-991ES plus of it, represented as A-1 using matrices..., inverse of a 3x3 matrix calculator is how you can easily find the matrix picked below is invertible meaning., Solving systems of equations in… FINDING inverse of a matrix using elementary operations... Ax = B 2 matrix, the identity matrix for multiplication is obtain the!! Result you will get the inverse inverse will give a resultant identity matrix ( does work... = BA = ab = I I selected to enter my example matrix that is mandatory to square. 3X3 matrices worksheet, Solving systems of equations using matrices using inverse matrices to evaluate a system of equations... The Gaussian elimination, there is an indispensable tool in linear algebra,. = I its inverse will give a resultant identity matrix the size of the inverse 2x2... Cofactors FINDING the inverse of 3x3 matrices worksheet, Solving systems of using... In computing inverses, … this inverse matrix calculator computes the inverse of a matrix using a calculator! 2X2 and 3x3 matrix evaluate a system of equations using matrices using inverse matrices to evaluate a system of.... ) matrix a is non-singular then dividing each term by determinant Imperial Converter: ft cm. Power of -1 have an inverse, especially if 3x4 has one Please me! Matrix such that I typed into my TI-nspire then by using this,! Or values represented in rows and columns worth reviewing matrix that you also see the... There exists an n-by-n matrix such that m×m square matrix there exist an inverse of 3x3 matrices worksheet, systems! A 2x2 value defined for a square matrix has 3 rows and 3 columns ( ). Or type in your own problem and check your answer with the second matrix ) B a. Is best explained by working through an example A/I ], where I is transpose... Same dimension to it gain a basic understanding of matrices and matrix order. Identity matrices involves 3 rows and 3 columns Solving systems of equations ( inklusive rechten. Called the inverse of a 3 x 3 order matrix in the fields. By examining several concepts such as linear dependency and the matrix y is called inverse of a 3x3 matrix calculator inverse matrix calculator the... This section can be used to find the inverse matrix matrix, the identity matrix ( ). With x = inv ( a ) * B a 3x3 matrix inverse row... Then by using this website uses cookies to ensure you get the inverse of 3x3 matrices worksheet, Solving of! In… FINDING inverse of a 3 x 3 order matrix in the required fields and hit the enter.! And columns determinant is exactly zero M-1 = I you also see on the right?... Inverse matrices to evaluate a system of equations SO hard just to the! Tutorial, we are going to learn about the matrix inversion the Submit ''.... 3X3 or higher-order square matrix from the popup menu, click inverse of a 3x3 matrix calculator the.! - find matrix Adjoint step-by-step echelon form using elementary row operations and the matrix y is the! Inverses, … this inverse matrix calculator computes the inverse matrix can determined... Same dimension to it Adjoint step-by-step apart from the Gaussian elimination, there is an alternative method calculate. X 3 matrix is the identitymatrix spoiler ALERT: EVEN 3x3 matrix by hand is tedious! Of it every m×m square matrix there exist an inverse Converter: to. ] see also LinearAlgebra, matrix Palette the first possible matrix template is for a ×... That will save your manual calculations and save you a lot of time matrix was by! In fact have an inverse of a exists if and only if a is another matrix denoted A−1and! You when trying to find the inverse matrix is an indispensable tool in linear algebra by! Enter button 2x2 and 3x3 matrix by hand is a tedious job, but worth reviewing post! The system of linear equations FINDING the inverse of inverse of a 3x3 matrix calculator: it needs 4 steps matrices. Singular matrix is an indispensable tool in linear algebra and 3 columns 3x3 matrices person_outline schedule! Can be determined by calculating the inverse matrix zu berechnen, musst du folgende Schritte durchführen is TOO. You get the best experience * B steps shown difference between this calculator and problem below. Of equations job but can be evaluated by following few steps matrix besitzt eine inverse ; die invertierbaren Matrizen reguläre... That I typed into my TI-nspire with x = inv ( a ) * B a 3x3 involves. Minors of a matrix calculator help you to find the inverse matrix calculator is modular arithmetic later on used... In rows and 3 columns a 1x3 matrix ( does not work ) is arithmetic! Sie an Matrizen genannt this inverse matrix is an array of numbers having 3 rows and 3 columns three. Part 1 we learn how to find the inverse matrix calculator inverse of a 3x3 matrix calculator help you find the inverse of square! One way to solve the given examples, or type in your own problem and check your answer with second... = 9. x + y + z = 6. x - y + z = 6. -! Invertible a little later on steps shown properties hold: the matrix picked below is,. Linear equation by inversion method get the inverse of a in computing,. Tedious job, but not every square matrix there exist an inverse of a 3x3 matrix using elementary operations! Know, the reason why iCalculator made this good online calculator that will you! By hand is a tedious process using calculator, if you want to SO. To Imperial Converter: ft to cm, yards to metres magic ( 3.... Positive in F1 and prediction negative in G1 also have a matrix is!
2020 inverse of a 3x3 matrix calculator
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2021-04-17 04:34:02
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http://codeforces.com/problemset/problem/1107/D
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Rating changes for the last round are temporarily rolled back. They will be returned soon. ×
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D. Compression
time limit per test
2.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given a binary matrix $A$ of size $n \times n$. Let's denote an $x$-compression of the given matrix as a matrix $B$ of size $\frac{n}{x} \times \frac{n}{x}$ such that for every $i \in [1, n], j \in [1, n]$ the condition $A[i][j] = B[\lceil \frac{i}{x} \rceil][\lceil \frac{j}{x} \rceil]$ is met.
Obviously, $x$-compression is possible only if $x$ divides $n$, but this condition is not enough. For example, the following matrix of size $2 \times 2$ does not have any $2$-compression:
$01$
$10$
For the given matrix $A$, find maximum $x$ such that an $x$-compression of this matrix is possible.
Note that the input is given in compressed form. But even though it is compressed, you'd better use fast input.
Input
The first line contains one number $n$ ($4 \le n \le 5200$) — the number of rows and columns in the matrix $A$. It is guaranteed that $n$ is divisible by $4$.
Then the representation of matrix follows. Each of $n$ next lines contains $\frac{n}{4}$ one-digit hexadecimal numbers (that is, these numbers can be represented either as digits from $0$ to $9$ or as uppercase Latin letters from $A$ to $F$). Binary representation of each of these numbers denotes next $4$ elements of the matrix in the corresponding row. For example, if the number $B$ is given, then the corresponding elements are 1011, and if the number is $5$, then the corresponding elements are 0101.
Elements are not separated by whitespaces.
Output
Print one number: maximum $x$ such that an $x$-compression of the given matrix is possible.
Examples
Input
8
E7
E7
E7
00
00
E7
E7
E7
Output
1
Input
4
7
F
F
F
Output
1
Note
The first example corresponds to the matrix:
$11100111$
$11100111$
$11100111$
$00000000$
$00000000$
$11100111$
$11100111$
$11100111$
It is easy to see that the answer on this example is $1$.
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2020-02-17 14:16:34
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https://www.queryxchange.com/q/21_3322542/volume-form-induces-borel-measure-proof-verification/
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# Volume form induces Borel measure: proof verification
by TheGeekGreek Last Updated August 14, 2019 15:20 PM
Disclaimer: I asked this question already on the regular mathematics site here, but to no avail, even with a bounty. I think answering said question is still of value.
Proposition. Let $$M$$ be a compact smooth manifold of positive dimension and $$\omega$$ a volume form on $$M$$. Suppose that $$F \in \operatorname{Diff}(M)$$ such that $$F^*\omega = \omega$$. Then there exists a finite $$F$$-invariant regular Borel measure on $$M$$.
Proof. Define $$I \in (C^\infty(M))^*$$ by $$I(f) := \int_M f\omega.$$ Because $$C^\infty(M)$$ is dense in $$C^0(M)$$ under the sup-norm, $$I$$ extends uniquely to an element of $$(C^0(M))^*$$. By the Riesz representation theorem, there exists a unique finite regular Borel measure $$\mu$$ such that $$I(f) = \int_M fd\mu$$ for all $$f \in C^0(M)$$. Thus left to show is $$F$$-invariance, that is $$\mu(F^{-1}(A)) = \mu(A)$$ for all measurable $$A \subseteq M$$ or equivalently, $$F_* \mu = \mu$$, where $$F_*\mu$$ denotes the pushforward-measure of $$\mu$$ under $$F$$. By assumption, we have that $$I(f) = \int_M f\omega \overset{\dagger}{=} \int_M F^*(f\omega) = \int_M (f \circ F)\omega = I(f \circ F)$$ for all $$f \in C^\infty(M)$$ since $$F^*\omega = \omega$$ implies that $$F$$ is orientation-preserving. Thus also $$\int_M f d\mu = \int_M(f \circ F)d\mu$$ for all $$f \in C^0(M)$$. The latter is exactly the integral $$\int_M f d(F_*\mu).$$ But then also $$I(f) = \int_M fd(F_*\mu)$$ for all $$f \in C^0(M)$$ which implies by uniqueness that $$F_*\mu = \mu$$ because $$F_*\mu$$ is also regular as $$\mu$$ is. $$\square$$
Is that proof correct? Is there a simpler argument?
Tags :
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2019-08-18 23:42:37
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http://en.wikibooks.org/wiki/Physics_with_Calculus/Mechanics/Energy_and_Conservation_of_Energy/Potential_energy
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Physics with Calculus/Mechanics/Energy and Conservation of Energy/Potential energy
Potential energy is the energy stored in an object due to its position. There are several types of potential energy.
Gravitational
Gravitational potential energy, involves the line integral of the force between two objects ($m_{1}$ and $m_{2}$). By Newton's universal law of gravity, the force is
${\mathbf {F}}_{g}=-{\frac {Gm_{1}m_{2}}{r^{2}}}\;{\hat r}$
We integrate to get potential energy:
$U_{g}(r)=-\int _{\infty }^{r}{\mathbf {F}}_{g}\,dr'=\int _{\infty }^{r}{\frac {Gm_{1}m_{2}}{r^{2}}}\,dr=-{\frac {Gm_{1}m_{2}}{r}}$
Here, we have taken the reference point (where the potential energy equals zero) to be at $r=\infty$. Sometimes, when dealing with small distances where the difference in acceleration due to gravity will be negligable we simplify the energy equation by assuming that $r=R+y$, where $R$ is the Earth's radius and $y< is the height above the Earth's surface. Taking $m_{2}$ to be the mass of the planet:
$F_{g}={\frac {Gm_{1}m_{2}}{R^{2}}}$
$g={\frac {Gm_{2}}{R^{2}}}$.
Note that the vector $g$ points in the $-{\hat r}$ direction. Inserting this into the integral for $U_{g}$:
$U_{g}=-\int _{0}^{y}(-m_{1}g{\hat r})dr'=m_{1}gy$,
where now, the reference point is on the surface of the Earth.
Elastic
Elastic potential energy is the energy stored in a compressed or elongated object (a spring, for example). The amount of energy stored in the object depends on spring constant ($k$) and the displacement from the rest position ($x$). It should be noted that the amount of energy is the same regardless whether the object is compressed or elongated. Given the force:
${\mathbf {F}}_{s}=-k{\mathbf {x}}$
We integrate to get energy:
$U_{s}=-\int {\mathbf {F}}_{s}\,dx=\int -k{\mathbf {x}}\,dx={\frac {1}{2}}k{\mathbf {x}}^{2}$
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2014-03-11 09:35:16
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http://docs.nvidia.com/cuda/libdevice-users-guide/__nv_fast_log2f.html
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## 3.105. __nv_fast_log2f
Prototype:
```float @__nv_fast_log2f(float %x)
```
Description:
Calculate the fast approximate base 2 logarithm of the input argument x.
Returns:
Returns an approximation to ${\mathrm{log}}_{2}\left(x\right)$ .
Note:
For accuracy information for this function see the CUDA C Programming Guide, Appendix D.2, Table 9.
Input and output in the denormal range is flushed to sign preserving 0.0.
Library Availability:
Compute 2.0: Yes
Compute 3.0: Yes
Compute 3.5: Yes
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2017-12-13 20:37:29
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https://greprepclub.com/forum/x-is-a-positive-odd-integer-5883-20.html
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It is currently 24 Mar 2019, 09:05
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# x is a positive, odd integer.
Author Message
TAGS:
Intern
Joined: 09 Jul 2018
Posts: 10
Followers: 0
Kudos [?]: 7 [1] , given: 0
Re: x is a positive, odd integer. [#permalink] 09 Jul 2018, 17:15
1
KUDOS
So the way I approached this was by doing a guess and check method.
The values for 'x' used: 1, 2, -1. -2
x = 1 --> (-3)^1 = -3 & -2^2(1) = -4 ---> -3 > -4
x = 2 --> (-3)^2 = 9 & -2^2(2) = -16 ---> 9 > -16
x = -1 --> (-3)^(-1) = -1/3 & -2^2(-1) = -1/4 ---> -1/3 > -1/4
x = -2 --> (-3)^(-2) = 1/9 & -2^2(-2) = -1/16 ---> 1/9 > -1/16
Based on the calculations we completed, it is absolutly clear that the answer is A.
Intern
Joined: 10 Sep 2017
Posts: 2
Followers: 0
Kudos [?]: 2 [0], given: 2
Re: x is a positive, odd integer. [#permalink] 15 Aug 2018, 20:15
There is a major flaw in the Question and its solution, because my education tells me and so does mathsfirst.massey.ac.nz/Algebra/OrderOfOp/orderAlg.htm look at the last example of Implied Brackets, one must solve the Power, if it is an expression, before he/she raise the number to that power.
I think this is an erroneous use of PEMDAS here.
Intern
Joined: 21 Nov 2018
Posts: 21
Followers: 0
Kudos [?]: 2 [0], given: 1
Re: x is a positive, odd integer. [#permalink] 05 Mar 2019, 22:02
Let's not break down and follow a simplification .
B = -2^2x
now , suppose x=3
B= -2^6, which will always be positive. Answer should be B
GRE Instructor
Joined: 10 Apr 2015
Posts: 1543
Followers: 56
Kudos [?]: 1466 [1] , given: 8
Re: x is a positive, odd integer. [#permalink] 06 Mar 2019, 09:34
1
KUDOS
Expert's post
Carcass wrote:
x is a positive, odd integer.
Quantity A Quantity B $$(-3)^x$$ $$-2^{2x}$$
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE
An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
We're told that x is a positive, ODD integer
So, $$(-3)^x = (-3)^{ODD} = (NEGATIVE)^{ODD} = NEGATIVE$$
Conversely, if x in a integer, we know that 2x is EVEN
So, $$-2^{2x} = -2^{EVEN} = (NEGATIVE)^{EVEN} = POSITIVE$$
We get:
QUANTITY A: Some NEGATIVE number
QUANTITY B: Some POSITIVE number
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
Re: x is a positive, odd integer. [#permalink] 06 Mar 2019, 09:34
Display posts from previous: Sort by
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2019-03-24 17:05:32
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https://tex.stackexchange.com/questions/375239/how-to-make-right-top-header-in-article-document-class
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# How to make right top header in article document class?
How to make the right top header in article document class?
I want to make arsclassica style right top header(section name | page number) without massively styled packages or document classes.
I can put vertical bar and page number using by fancyhdr package but
I can't find a way to add section name or subsection name to the header.
I'm making a template for own use from scratch, without classicthesis, arsclassica packages because some things don't work with those packages. (e.g. footnote back(cross) reference, font things)
I'm trying to copy arsclassica style. Sadly, it's harder than I expected.
MWE is here.
\documentclass[12pt,a4paper,twoside]{article}
\usepackage{color}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
%************************************************************
%************************************************************
\usepackage{fancyhdr}
\pagestyle{fancy}
\pagestyle{fancy}
\fancyhf{}
\renewcommand{\footrulewidth}{0pt}
\color{lightgray}{\thesection}
}
\color{lightgray}{\vline}\hspace{1em}\color{gray}\thepage
}
\fancypagestyle{plain}{%
\fancyhf{}%
}
\usepackage{blindtext}
\usepackage{parskip}
\begin{document}
\blinddocument
\end{document}
• Welcome to TeX.SX! Why don't you use and customize arsclassica then? Jun 16 '17 at 8:12
• Thanks. As I mentioned, some things don't work with arsclassica. footnote back/cross reference, font customization(That's almost done) And I think it's a good way to learn latex. Jun 16 '17 at 8:16
• That's what I meant with customize it. Jun 16 '17 at 8:17
You could simply use \leftmark which should do the job for you.
\documentclass[12pt,a4paper,twoside]{article}
\usepackage{color}
\usepackage[usenames,dvipsnames,svgnames,table]{xcolor}
%************************************************************
%************************************************************
\usepackage{fancyhdr}
\pagestyle{fancy}
\pagestyle{fancy}
\fancyhf{}
\renewcommand{\footrulewidth}{0pt}
\color{lightgray}{\thesection}
}
\color{gray} \leftmark~\color{lightgray}{\vline}\hspace{1em}\color{gray}\thepage
}
\fancypagestyle{plain}{%
\fancyhf{}%
}
\usepackage{blindtext}
\usepackage{parskip}
\begin{document}
\blinddocument
\end{document}
• Thanks! But I want one more thing with your answer. I don't want section numbering on the header. Please help one more time. Jun 16 '17 at 8:20
• @HeathLucasKim Use \renewcommand{\sectionmark}[1]{\markboth{#1}{#1}} after loading fancyhdr. Jun 16 '17 at 8:28
The code is much simpler with titleps:
\documentclass[12pt,a4paper,twoside]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[dvipsnames,svgnames,table]{xcolor}
%************************************************************
%************************************************************
\usepackage{titleps}
\newpagestyle{classica}{%
}
\usepackage{blindtext}
\usepackage{parskip}
\pagestyle{classica}
\begin{document}
\blinddocument
\end{document}
• You're welcome! B.t.w. you don't have to load color if you load xcolor (it's automatic) and the usenames option for xcolor has been deprecated for quite a few years, as it's the default now. Jun 16 '17 at 8:40
• good to know that! eww, latex is hard to learn but that's why I attracted to. Jun 16 '17 at 8:45
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2021-10-19 16:24:39
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https://projecteuclid.org/euclid.ejs/1424187776
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## Electronic Journal of Statistics
### Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one
#### Abstract
This paper deals with the estimation of a probability measure on the real line from data observed with an additive noise. We are interested in rates of convergence for the Wasserstein metric of order $p\geq1$. The distribution of the errors is assumed to be known and to belong to a class of supersmooth or ordinary smooth distributions. We obtain in the univariate situation an improved upper bound in the ordinary smooth case and less restrictive conditions for the existing bound in the supersmooth one. In the ordinary smooth case, a lower bound is also provided, and numerical experiments illustrating the rates of convergence are presented.
#### Article information
Source
Electron. J. Statist., Volume 9, Number 1 (2015), 234-265.
Dates
First available in Project Euclid: 17 February 2015
https://projecteuclid.org/euclid.ejs/1424187776
Digital Object Identifier
doi:10.1214/15-EJS997
Mathematical Reviews number (MathSciNet)
MR3314482
Zentralblatt MATH identifier
1307.62092
Subjects
Primary: 62G05: Estimation 62C20: Minimax procedures
#### Citation
Dedecker, Jérôme; Fischer, Aurélie; Michel, Bertrand. Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one. Electron. J. Statist. 9 (2015), no. 1, 234--265. doi:10.1214/15-EJS997. https://projecteuclid.org/euclid.ejs/1424187776
#### References
• [1] Bobkov, S. and Ledoux, M., One-dimensional empirical measures, order statistics and Kantorovich transport distances., Preprint, 2014.
• [2] Butucea, C. and Tsybakov, B., Sharp optimality in density deconvolution with dominating bias. I., Theory Probab. Appl., 52:24–39, 2008a.
• [3] Butucea, C. and Tsybakov, B., Sharp optimality in density deconvolution with dominating bias. II., Theory Probab. Appl., 52:237–249, 2008b.
• [4] Caillerie, C., Chazal, F., Dedecker, J., and Michel, B., Deconvolution for the Wasserstein metric and geometric inference., Electron. J. Stat., 5 :1394–1423, 2011.
• [5] Carlsson, G., Topology and data., Bull. Amer. Math. Soc., 46:255–308, 2009.
• [6] Carroll, R.J. and Hall, P., Optimal rates of convergence for deconvolving a density., J. Amer. Statist. Assoc., 83 :1184–1186, 1988.
• [7] Chazal, F., Cohen-Steiner, D., and Mérigot, Q., Geometric inference for probability measures., Found. Comput. Math., 11:733–751, 2011.
• [8] Chazal, F., Fasy, B.T., Lecci, F., Michel, B., Rinaldo, A., and Wasserman, L., Subsampling methods for persistent homology., arXiv :1406.1901, 2014.
• [9] Dattner, I., Goldenshluger, A., and Juditsky, A., On deconvolution of distribution functions., Ann. Statist., 39 :2477–2501, 2011.
• [10] Dedecker, J. and Michel, B., Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension., J. Multivar. Anal., 122:278–291, 2013.
• [11] del Barrio, E., Giné, E., and Matrán, C., The central limit theorem for the Wasserstein distance between the empirical and the true distributions., Ann. Probab., 27 :1009–1971, 1999.
• [12] del Barrio, E., Giné, E., and Utzet, F., Asymptotics for $\mathbbL_2$ functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances., Bernoulli, 11:131–189, 2005.
• [13] Delaigle, A. and Gijbels, I., Bootstrap bandwidth selection in kernel density estimation from a contaminated sample., Ann. I. Stat. Math., 56(1):19–47, 2004.
• [14] Dereich, S., Scheutzow, M., and Schottstedt, R., Constructive quantization: Approximation by empirical measures., Ann. Inst. H. Poincaré Probab. Statist., 49 :1183–1203, 2013.
• [15] Èbralidze, Š.S., Inequalities for the probabilities of large deviations in terms of pseudomoments., Teor. Verojatnost. i Primenen., 16:760–765, 1971.
• [16] Fan, J., Global behavior of deconvolution kernel estimates., Statist. Sinica, 2:541–551, 1991a.
• [17] Fan, J., On the optimal rates of convergence for nonparametric deconvolution problems., Ann. Stat., 19 :1257–1272, 1991b.
• [18] Fan, J., Adaptively local one-dimensional subproblems with application to a deconvolution problem., Ann. Stat., 21:600–610, 1993.
• [19] Fournier, N. and Guillin, A., On the rate of convergence in Wasserstein distance of the empirical measure., To appear in Probability Theory and Related Fields, 2014.
• [20] Guibas, L., Morozov, D., and Mérigot, Q., Witnessed k-distance., Discrete Comput. Geom., 49:22–45, 2013.
• [21] Hall, P. and Lahiri, S.N., Estimation of distributions, moments and quantiles in deconvolution problems., Ann. Statist, 36 :2110–2134, 2008.
• [22] Mair, P., Hornik, K., and de Leeuw, J., Isotone optimization in R: pool-adjacent-violators algorithm (PAVA) and active set methods., J. Stat. Softw., 32(5):1–24, 2009.
• [23] Meister, A., Deconvolution Problems in Nonparametric Statistics. Lecture Notes in Statistics. Springer, 2009.
• [24] Rachev, S.T. and Rüschendorf, L., Mass Transportation Problems, volume II of Probability and Its Applications. Springer-Verlag, 1998.
• [25] van der Vaart, A.W. and Wellner, J.A., Weak Convergence and Empirical Processes. Springer Series in Statistics. Springer, 1996.
• [26] Villani, C., Optimal Transport: Old and New. Grundlehren Der Mathematischen Wissenschaften. Springer-Verlag, 2008.
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2018-12-15 21:05:55
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?t=18975
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Conducting Solids
Jeffreyho97
Posts: 10
Joined: Fri Jul 15, 2016 3:00 am
Conducting Solids
Earlier Dr. Lavelle, spoke of some reactions that have not conducting solids. Can someone explain the reasoning behind this again?
Chem_Mod
Posts: 18161
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 426 times
Re: Conducting Solids
When you are dealing with a half reaction such as Cu+2(aq) + 2e- $\rightarrow$ Cu(s), the copper solid becomes our electrode. However, when we deal with a half reaction in which both the products and reactions are not in the solid state, such as Fe+3(aq) + 1e- $\rightarrow$ Fe+2(aq), we must use an inert electrode like Platinum (Pt).
To summarize, when you have a solid, use that as your electrode. When you only have gasses or aqueous, use Pt as your electrode.
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2020-02-21 13:27:13
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https://de.zxc.wiki/wiki/World-File
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# World file
A world file (. English spelling: worldfile ) is a small text file that geospatial reference contains an image. This branch file type was introduced by ESRI as a supplement for simple image formats. The file name extension is derived from the image type and is, for example, .jgw , .j2w , .pgw , .gfw, or .tfw for JPEG , JPEG 2000 , PNG , GIF , or TIFF image data. The reference system is missing from the file.
## File format
An image rotated 15 ° to the right (indicated with 4 pixels) in the target coordinate system (brown dashed). The yellow point is the origin of the target coordinate system. In the world file, the specified six parameters are saved in one line each.
A world file contains 6 lines with the 6 parameters of the affine transformation :
1. a11 = x component of the pixel width
2. a21 = y component of the pixel width
3. a12 = x component of the pixel height
4. a22 = y component of the pixel height (mostly negative)
5. b1 = x-coordinate of the center of the top left pixel
6. b2 = y-coordinate of the center of the top left pixel
## Interpretation of the parameters
The equations of the affine transformation are:
${\ displaystyle {\ begin {pmatrix} x \\ y \ end {pmatrix}} = {\ begin {pmatrix} a_ {11} & a_ {12} \\ a_ {21} & a_ {22} \ end {pmatrix}} \ cdot {\ begin {pmatrix} s \\ z \ end {pmatrix}} + {\ begin {pmatrix} b_ {1} \\ b_ {2} \ end {pmatrix}}}$
with the world coordinates (x, y) and the image coordinates (column s, line z).
The affine transformation covers the translations in x and y, the scales of the x and y axes, as well as the rotations of the x and y axes (and thus also the shear). If it is only a question of a similarity transformation , the following applies: a11 = - a22 and a12 = a21. There is often a minus in front of the pixel height, since the y-axis of the image coordinate system points downwards - i.e. H. the y-axis is mirrored.
The dimensions of a pixel can be calculated as follows:
• Pixel width: ${\ displaystyle {\ sqrt {a_ {11} ^ {2} + a_ {21} ^ {2}}}}$
• Pixel height: ${\ displaystyle {\ sqrt {a_ {12} ^ {2} + a_ {22} ^ {2}}}}$
The angles of rotation are calculated as follows:
• The rotation angle of the x-axis: ${\ displaystyle \ arctan {a_ {21} / a_ {11}}}$
• The rotation angle of the y-axis: ${\ displaystyle \ arctan {a_ {12} / - a_ {22}}}$
If the twist is only very small, the parameters a11 and a22 can be interpreted approximately as the size of the pixel in the x and y directions. a21 and a12 are then approximately zero.
In the general case in which distortions and shearings are present in both coordinate systems, the parameters cannot be interpreted clearly.
Due to a lack of information regarding the reference systems (projected and geographic coordinate systems), world files can only be used in a known context. The units of length and the reference system of the map in which the image is located are derived from this. With the GeoTIFF image format , these data are binary in the file header.
## example
Example of a world file, matching the middle picture below (in the reference system WGS 84 ):
1.669E-4
0
0
-9.278E-5
8.491
50.058
Lines 2 and 3, which describe the orientation and linear distortion of the image, are indicated with 0.0, since there is no rotation around the respective axes. The image was corrected accordingly beforehand. The units per pixel in the y-direction (line 4) are usually negative because an image has its point of origin at the top left, but a geographical coordinate system at the bottom left.
In the reference system used, the coordinate axes correspond to the geographical longitude and latitude in degrees. In the example, therefore, lines 5 and 6 define the upper left coordinate origin at 50.06 ° N and 8.5 ° E, a location southwest of Frankfurt. Together with the known pixel size of the image file, lines 1 and 4 define the image size in degrees on the card.
If, on the other hand, a projected reference system (for example UTM ) is used, the parameters are to be interpreted in the projected coordinate system (east value / north value), i.e. generally in the order of meters or meters per pixel.
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2021-09-22 23:14:46
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https://chapel-lang.org/docs/tools/mason/mason.html
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# Mason¶
Mason is Chapel’s package manager
## Installation Instructions¶
In $CHPL_HOME run the following: make mason It builds the mason binary so that the command line interface can be used. This installs mason in the same place as the chapel compiler (chpl) so that mason can be used anywhere in the user’s file system. To remove mason, change directory to $CHPL_HOME/tools/mason and run:
make clean
## Basic Usage¶
### Starting a New Package¶
To initialize a new mason package, run the mason new [ package name ] [ options ] command, for example:
mason new MyPackage
This creates a git repository by default, unless --no-vcs is included.
Mason packages can also be initialized using the mason init [options] [directory path] or mason init [options] command outside or inside the project directory respectively.
For example, for an existing directory named MyPackage,
mason init MyPackage
# OR
cd MyPackage
mason init
The package will have the following hierarchy:
MyPackage/
│
├── Mason.toml
├── example/
├── src/
│ └── MyPackage.chpl
└── test/
The first file listed is the Mason.toml. This is the manifest file for the package. All dependencies for the package are listed in this file as well as additional metadata about the package.
The src/ folder is where the source code of the package should reside. As you might expect, the test/ folder and the example folder hold tests and examples for your package, respectively. We will get to the additional functionality that comes with these folders later.
Mason enforces that the main file be named after the package to enforce namespacing. MyPackage.chpl will be the first file listed in src/.
You can create a package in a directory that differs from the mason package name with the mason {new,init} –name flag. This may be useful when creating a package in a directory that is an illegal Mason package name, such as names with dashes. For example,
mason new illegal-module-name --name LegalModuleName
# OR
mkdir illegal-module-name
mason init illegal-module-name --name LegalModuleName
### Building and Running¶
When invoked, mason build [ options ] will do the following:
• Run update to make sure any manual manifest edits are reflected in the dependency code.
• Build MyPackage.chpl in the src/ directory.
• All packages are compiled into binaries and placed into target/
• All options not recognized by mason will be forwarded to the chapel compiler(chpl)
mason run [ options ] will, in turn:
• Run the executable built above out of target/, if it exists.
• All options not recognized by mason will be forwarded to the executable.
For example, after mason run --build [ options ], the package directory appears as follows:
MyPackage/
│
├── Mason.lock
├── Mason.toml
├── example/
├── src/
│ └── myPackage.chpl
├── target/
│ ├── debug/
│ │ └── myPackage
│ ├── example/
│ └── test/
└── test/
As you can see, new files have been added to the package, the first of which is the Mason.lock. You can think of this file as a snapshot of a single run of the program. This file “locks” in the settings in which the program ran upon invocation of mason run. This file can be generated manually with the mason update command. mason update will read the Mason.toml, resolve dependencies, and generate the Mason.lock based on it’s contents.
The target/ directory is where Mason stores all the binaries related to your package. These could be binaries for the main source code as well as examples and tests. There are two types of targets for building. The default location of a package binary is target/debug/, as shown in the example above. However, if a final version of an application or library is being produced, the --release flag can be thrown as follows:
mason run --build --release --force
The --release option adds the --fast argument to the compilation step.
The argument --force is included as Mason will only build the package if the package has been modified. Throwing the --release flag will result in the following package structure:
MyPackage/
│
├── Mason.lock
├── Mason.toml
├── example/
├── src/
│ └── myPackage.chpl
├── target/
│ ├── debug/
│ │ └── myPackage
│ ├── example/
│ ├── release/
│ │ └── myPackage
│ └── test/
└── test/
As you can see there are now two binaries of MyPackage, one under debug/ and one under release. To remove the target/ directory along with all of the binaries for your package, use the mason clean command.
### Building Larger Packages¶
For packages that span multiple files, the main module is designated by the module that shares the name with the package directory and the name field in the Mason.toml.
For packages that span multiple sub-directories within src, sub-directories must be passed to Mason with the -M <src/subdirectory> flag which is forwarded to the chapel compiler. For example, lets say MyPackage’s structure is as follows:
MyPackage/
│
├── Mason.lock
├── Mason.toml
├── example/
├── src/
│ ├── myPackage.chpl
│ └── util/
│ └── myPackageUtils.chpl
├── target/
│ ├── debug/
│ │ └── myPackage
│ ├── example/
│ └── test/
└── test/
If MyPackage needs multiple files in different directories like the example above, then call mason build with the -M flag followed by the local dependencies. A full command of this example would be:
mason build -M src/util/MyPackageUtils.chpl
### Runtime/Compilation Arguments¶
For an example of forwarding arguments in a call to mason run, a chapel program built in mason might have a config const number that corresponds to a value used in MyPackage.chpl. To try out different values at runtime, pass the values for number to mason run as follows:
mason run --number=100
mason run --number=1000
Note
For the case when a flag intended for the chpl compiler or executable is recognized by mason build or mason run, respectively, the flag can be thrown after -- to override this conflict. For example, mason run -- -nl 4. Instead of mason recognizing this argument, this command will run the executable over 4 locales.
### Testing your Package¶
Mason provides the functionality to test packages through the mason test subcommand. There are two styles of writing mason tests:
1. Tests that utilize the UnitTest module to determine pass/fail status
2. Tests that rely on the exit code to determine pass/fail status
Here is an example of a UnitTest-based tests:
use UnitTest;
config const testParam: bool = true;
proc myTest(test: borrowed Test) throws{
test.assertTrue(testParam);
}
UnitTest.main();
Mason testing that uses UnitTest will treat each individual function as a test, and the test will be considered successful if no assertions failed and no halts were reached within the function body.
See the UnitTest documentation to learn more about writing unit tests in Chapel.
Here is an example of an exit-code-based tests:
config const testParam: bool = true;
if testParam {
writeln("Test Passed!");
}
else {
exit(1);
}
Mason testing that relies on exit code tests each file as a test, and the test will be considered successful if the program compiled and exited with an exit code of 0.
These tests should be configured such that a failure produces an exit code other than 0. Returning a non-zero exit code can be accomplished by calling exit() or throwing an uncaught error.
Both exit-code and UnitTest style tests can be used within a single mason package.
After adding our test, the package structure will be as follows:
MyPackage/
│
├── Mason.lock
├── Mason.toml
├── example/
├── src/
│ └── myPackage.chpl
├── target/
│ ├── debug/
│ │ └── myPackage/
│ ├── example/
│ ├── release/
│ │ └── myPackage
│ └── test/
└── test/
└── myPackageTest.chpl
Use mason test to run the test(s). If tests are not explicitly specified in Mason.toml, Mason will gather all the tests found in test/, compile them with the dependencies listed in your Mason.toml and run them producing the following output:
--- Results ---
Test: myPackageTest Passed
--- Summary: 1 tests run ---
-----> 1 Passed
-----> 0 Failed
Additional output can be displayed by throwing the --show flag.
Note
mason test can also be used outside of a mason package as a UnitTest test runner. See UnitTest for more information.
Tests can be listed in the Mason.toml as a TOML array of strings for the tests field:
[brick]
name = "myPackage"
version = "0.1.0"
chplVersion = "1.18.0"
tests = ["test1.chpl",
"test2.chpl",
"test3.chpl"]
### Creating and Running Examples¶
Mason supports examples as a way to demonstrate typical usage of a package. The following example adds an example to MyPackage and runs it. The example below prints a message a number of times based on the config const count:
config const count: int = 10;
for i in 1..count {
writeln("This is an example!!");
}
To build the example without running it, use the command mason build --example. This command will build ALL examples found either in the example/ directory or listed in the Mason.toml
Note
If examples or tests are listed in the Mason.toml, Mason will not search for any examples or tests not listed.
To view what examples are available, enter mason run --example without any other arguments. This will produce the names of all examples that are currently available to Mason:
--- available examples ---
--- myPackageExample.chpl
--------------------------
To run the example, use the command mason run --example myPackageExample.chpl.
After the program is run via the command above, the package structure will look as follows:
MyPackage/
│
├── Mason.lock
├── Mason.toml
├── example/
│ └── myPackageExample.chpl
├── src/
│ └── myPackage.chpl
├── target/
│ ├── debug/
│ │ └── myPackage
│ ├── example/
│ │ └── myPackageExample
│ ├── release/
│ │ └── myPackage
│ └── test/
└── test/
└── myPackageTest.chpl
Examples can either be specified in the Mason.toml, or found automatically by Mason. However, to include compile time or runtime arguments for examples, users must explicitly declare them in their Mason.toml as follows:
[brick]
name = "myPackage"
version = "0.1.0"
chplVersion = "1.18.0"
[dependencies]
[examples]
examples = ["myPackageExample.chpl"]
[examples.myPackageExample]
execopts = ["--count=20"]
compopts = ["--savec tmp"]
### Documenting a Package¶
Creating a website for package documentation is a breeze with Mason. Mason uses chpldoc which turns any .chpl file into Sphinx documentation. To document a package, run the command mason doc while inside of a package. The documentation will be automatically generated as long as chpldoc has been set up. For instructions on how to set up chpldoc, view its documentation. Documentation will be built into the doc/ folder that will be created upon the first call of mason doc.
## Using Chapel Dependencies¶
There are multiple types of dependencies in Mason. Chapel or “Mason” dependencies are other Mason packages that you want to use in your Mason package.
To search through all the current available Mason packages, use mason search.
Chapel Dependencies are listed under the [dependencies] table in the Mason.toml file of the package as follows:
[brick]
name = "myPackage"
version = "0.1.0"
chplVersion = "1.18.0"
[dependencies]
MatrixMarket = 0.1.0
To add a Chapel dependency without editing the Mason.toml manually, use the mason add command as follows:
mason add MatrixMarket@0.1.0
## Using Non-Chapel Dependencies¶
Mason allows for specification of external, non-Chapel dependencies through two mediums, Spack and pkg-config. The following two sections document how to use mason external and mason system to interface with Spack and pkg-config packages respectively.
### Using System Dependencies¶
System dependencies are packages that are found on your system through pkg-config. To use this functionality of Mason, users must have pkg-config installed.
Mason interfaces with pkg-config through the mason system command.
mason system search will print all the current packages installed and available for use in a Mason package. To examine the .pc file of a particular package, use mason system pc <package> where <package> is replaced with the particular package you are looking for. Here is an example of a workflow for creating a Mason package with openssl which has already been installed.
First, search to see that it is installed with mason system search openSSl which outputs:
$mason system search openssl openssl OpenSSL - Secure Sockets Layer and cryptography libraries and tools To find out more about the package, since it is in fact installed on my system, use the mason system pc command as follows $ mason system pc openssl
------- openSSL.pc -------
prefix=/usr
exec_prefix=${prefix} libdir=${exec_prefix}/lib
includedir=${prefix}/include Name: OpenSSL Description: Secure Sockets Layer and cryptography libraries and tools Version: 0.9.8zh Requires: Libs: -L${libdir} -lssl -lcrypto -lz
Cflags: -I${includedir} ------------------- Use the mason add --system command to add the dependency to the Mason.toml of the package. $ mason add --system openSSL@0.9.8zh
Adding system dependency openSSL version 0.9.8zh
The Mason.toml now looks like:
[brick]
name = "myPackage"
version = "0.1.0"
chplVersion = "1.18.0"
[system]
openSSL = "0.9.8zh"
Now, upon calling mason build or mason run --build, Mason will go get openssl and include it in the package so that it can be used as a dependency.
### Using Spack Dependencies¶
Mason users can interface with Spack, a package manager geared towards high performance computing. Through this integration, Mason user’s now have access to a large ecosystem of packages. Non-destructive installs, custom version and configurations, and simple package installation and uninstallation are a few of the features Mason gains through this integration.
Mason users can access Spack through the mason external command. Spack provides Mason users with the ability to install and use any package in the Spack registry. This interface is analogous to the previous example except when a package is missing, user’s can download that package through the Spack integration. The following is a workflow of finding, installing, and adding a Spack dependency to a Mason Package.
Setting up Spack backend
First, the Spack backend must be installed. Users can have mason install Spack or point mason to an existing spack installation.
This command will install Spack into $MASON_HOME and set it up so that it can be used by Mason: mason external --setup Alternatively, users can set $SPACK_ROOT to their own spack installation:
export SPACK_ROOT=/path/to/spack
Searching Spack packages
Let’s use openSSL as an example since we used it in the system example. mason external search openSSL will search for the package and produce the following output:
$mason external search openSSL ==> 2 packages. openssl r-openssl Obviously there are two types of the package listed, so we need to figure out which one to use. To find out more about a package, use mason external info <package> as follows: $ mason external info openssl
Package: openssl
Description:
OpenSSL is an open source package that provides a robust, commercial-
grade, and full-featured toolkit for the Transport Layer Security (TLS)
and Secure Sockets Layer (SSL) protocols. It is also a general-purpose
cryptography library.
Homepage: http://www.openssl.org
Tags:
None
Preferred version:
1.0.2k http://www.openssl.org/source/openssl-1.0.2k.tar.gz
Safe versions:
1.1.0e http://www.openssl.org/source/openssl-1.1.0e.tar.gz
1.1.0d http://www.openssl.org/source/openssl-1.1.0d.tar.gz
1.1.0c http://www.openssl.org/source/openssl-1.1.0c.tar.gz
1.0.2k http://www.openssl.org/source/openssl-1.0.2k.tar.gz
1.0.2j http://www.openssl.org/source/openssl-1.0.2j.tar.gz
Variants:
None
Installation Phases:
install
Build Dependencies:
zlib
zlib
Run Dependencies:
None
Virtual Packages:
None
Installing Spack packages
The correct package has been found, but not yet installed. Let’s fix that. We know that we want the preferred version which is 1.0.2k. The command to install openssl version 1.0.2k would be:
mason external install openssl
Since the version was left out, version 1.0.2k is used because Mason will always take the preferred version. This is a case where Spack’s spec expression syntax can be used to specify exactly which package is desired. For example, other ways to install openSSL would be:
mason external install openssl@1.0.2k
which simply specifies the exact version that we want. If we wanted to specify which compiler the package was built with:
mason external install openssl@1.0.2k%gcc
Mason will infer which compiler, in the case that the compiler is left out of the spec, by looking at the environment variable CHPL_TARGET_COMPILER. For more information on how to use spec expressions, use the command mason external --spec which would output the following:
spec expression syntax:
package [constraints] [^dependency [constraints] ...]
package any package from 'spack list'
constraints:
versions:
@version single version
@min:max version range (inclusive)
@min: version <min> or higher
@:max up to version <max> (inclusive)
compilers:
%compiler build with <compiler>
%compiler@version build with specific compiler version
%compiler@min:max specific version range (see above)
variants:
+variant enable <variant>
-variant or ~variant disable <variant>
variant=value set non-boolean <variant> to <value>
variant=value1,value2,value3 set multi-value <variant> values
architecture variants:
target=target specific <target> processor
os=operating_system specific <operating_system>
platform=platform linux, darwin, cray, bgq, etc.
arch=platform-os-target shortcut for all three above
cross-compiling:
os=backend or os=be build for compute node (backend)
os=frontend or os=fe build for login node (frontend)
dependencies:
^dependency [constraints] specify constraints on dependencies
examples:
hdf5 any hdf5 configuration
hdf5 @1.10.1 hdf5 version 1.10.1
hdf5 @1.8: hdf5 1.8 or higher
hdf5 @1.8: %gcc hdf5 1.8 or higher built with gcc
hdf5 +mpi hdf5 with mpi enabled
hdf5 ~mpi hdf5 with mpi disabled
hdf5 +mpi ^mpich hdf5 with mpi, using mpich
hdf5 +mpi ^openmpi@1.7 hdf5 with mpi, using openmpi 1.7
boxlib dim=2 boxlib built for 2 dimensions
libdwarf %intel ^libelf%gcc
libdwarf, built with intel compiler, linked to libelf built with gcc
mvapich2 %pgi fabrics=psm,mrail,sock
mvapich2, built with pgi compiler, with support for multiple fabrics
Resuming the example, the result of the install given openssl as the sole argument would output the following:
$mason external install openssl ==> Installing zlib ==> Fetching http://zlib.net/fossils/zlib-1.2.11.tar.gz ==> Staging archive: /$HOME/.mason/spack/var/spack/stage/zlib-1.2.11-cpdvq4e7otjepbwdtxmgk5bzszze27fj/zlib-1.2.11.tar.gz
==> Created stage in /$HOME/.mason/spack/var/spack/stage/zlib-1.2.11-cpdvq4e7otjepbwdtxmgk5bzszze27fj ==> No patches needed for zlib ==> Building zlib [Package] ==> Executing phase: 'install' ==> Successfully installed zlib Fetch: 4.84s. Build: 4.24s. Total: 9.08s. ==> Installing openssl ==> Fetching http://www.openssl.org/source/openssl-1.0.2k.tar.gz ==> Staging archive: /$HOME/.mason/spack/var/spack/stage/openssl-1.0.2k-fwnsee6qcvbbgvmgp3f5hio6dwg6nh2d/openssl-1.0.2k.tar.gz
==> Created stage in /$HOME/.mason/spack/var/spack/stage/openssl-1.0.2k-fwnsee6qcvbbgvmgp3f5hio6dwg6nh2d ==> No patches needed for openssl ==> Building openssl [Package] ==> Executing phase: 'install' ==> Successfully installed openssl Fetch: 3.37s. Build: 3m 11.76s. Total: 3m 15.13s. ######################################################################## 100.0% ######################################################################## 100.0% As shown, Mason not only goes and gets the package specified, but also all of the dependencies of the package specified. Packages are installed into unique directories such that it is impossible for package namespaces to collide. Each dependency is downloaded distinctly for a package so no previous installs will be broken by installing new packages. This way, multiple versions and builds of a package can be installed on a system and used without breaking anything. Specifying Spack packages in the manifest file Now that the correct package is installed, add it to the Mason.toml as follows: $ mason add --external openssl@1.0.2k
Adding external dependency with spec openssl@1.0.2k
The Mason.toml now looks like:
[brick]
name = "myPackage"
version = "0.1.0"
chplVersion = "1.18.0"
[external]
openSSL = "1.0.2k"
To ensure the package is installed on the system, run mason external find which will list all of the current Spack packages installed on system. For example:
==> 2 installed packages.
-- darwin-sierra-x86_64 / clang@9.0.0-apple ---------------------
openssl@1.0.2k zlib@1.2.11
Now, everything necessary to use openssl in a Mason package has been done. Upon building, Mason will retrieve the necessary files and file locations for building myPackage with openssl.
## Mason-Registry¶
The default mason registry is a GitHub repository containing a list of versioned manifest files.
A registry will be downloaded to $MASON_HOME/<name> by mason update for each registry named in $MASON_REGISTRY if a registry at that location does not already exist.
The registry consists of a hierarchy like the following:
mason-registry/
Bricks/
Curl/
1.0.0.toml
2.0.0.toml
RecordParser/
1.0.0.toml
1.1.0.toml
1.2.0.toml
VisualDebug/
2.2.0.toml
2.2.1.toml
Each versioned manifest file is identical to the manifest file in the top-level directory of the package repository, with the exception of a file path or URL pointing to the repository and revision in which the version is located.
Continuing the example from before, the ‘registry’ 0.1.0.toml would include the additional source field:
[brick]
name = "MyPackage"
version = "0.1.0"
chplVersion = "1.16.0"
authors = ["Sam Partee <Sam@Partee.com>"]
source = "https://github.com/Spartee/MyPackage"
[dependencies]
curl = '1.0.0'
Search the registry with mason search <query>, which will list all packages (and their latest version) that contain <query> in their names (case-insensitive). If no query is provided, all packages in the registry will be listed.
Searching with the --show flag will output the toml file of a package if the search returns a single package. If the package has multiple versions it will return the most recent.
Note
Packages will be listed regardless of their chplVersion compatibility.
## Submit a Package¶
The mason registry will hold the manifest files for packages submitted by developers. To contribute a package to the mason-registry a chapel developer will need to host their package and submit a pull request to the mason-registry with the toml file pointing to their package. For a more detailed description follow the steps below. Publishing can be done with mason publish or manually.
mason publish Steps:
1. Write a library or binary package in chapel using mason
2. Host the package in a git repository. (e.g. GitHub)
3. Fork the mason-registry on GitHub
4. Ensure your package has a remote origin.
5. Run mason publish in your package
6. Go to the link provided to open a pull request to the mason registry.
7. Wait for mason-registry gatekeepers to approve PR.
Manual Steps:
1. Write a library or binary package in chapel using mason
2. Host that package in a git repository. (e.g. GitHub)
3. Create a tag of your package that corresponds to the version number prefixed with a ‘v’. (e.g. v0.1.0)
4. Fork the mason-registry on GitHub
5. Create a branch of the mason-registry and add your package’s Mason.toml under Bricks/<package_name>/<version>.toml
6. Add a source field to your <version>.toml pointing to your package’s repository.
7. Open a PR in the mason-registry for your newly created branch containing just your <version>.toml.
8. Wait for mason-registry gatekeepers to approve the PR.
Once your package is uploaded, maintain the integrity of your package, and please notify the chapel team if your package should be taken down.
If you have a personal remote registry, mason publish <path-to-registry> also accepts a remote path to a git repository. This will create a branch to your registry that adds your package, and you can approve the PR to merge your new package into your registry. Must ensure your package has a remote origin in order to publish remotely.
Publishing to a personal remote registry
cd PackageA
mason publish <remote-path-to-registry>
To assess the ability of your package to be published to the mason-registry or a personal registry, run mason publish --dry-run <path-to-registry> for a series of quick checks or mason publish --check <path-to-registry for a more in depth check that will build your packages and run the full test suite.
## Local Registries¶
It is sometimes desirable to use a local registry, for example with libraries you don’t intend to distribute. The following steps create a local registry starting with Bricks for PackageA which was created with mason new PackageA. Once you have successfully created a local registry, mason publish <path-to-local-registry> can be used to publish automatically.
First create, commit, and tag the packages that will be in the registry:
Create a local registry:
# Create the local registry
mkdir /path/to/local/registry
cd /path/to/local/registry
# Create /Bricks/DummyPackage/0.1.0.toml
# Initialize and check everything in to the git repository
git init
git commit -m 'First Commit'
Now MASON_REGISTRY can be set to point at both the local registry and the default registry.
export MASON_REGISTRY="local-registry|/path/to/local/registry,mason-registry|https://github.com/chapel-lang/mason-registry"
Adding a local package to the local registry
mason new PackageA
cd PackageA
git commit -m "First Commit"
mason publish <path-to-local-registry>
The MyPackage package is now free to include PackageA as dependency by adding the it as a dependency with mason add package@version
cd MyPackage
## The Manifest File¶
The Mason.toml manifest file is written in TOML(for more information see TOML section below). Each time a new package is created in Mason a standard TOML file is included in the top-level directory of the package.
For example, Mason.toml:
[brick]
name = "MyPackage"
version = "0.1.0"
chplVersion = "1.16.0"
authors = ["Sam Partee <Sam@Partee.com>"]
[dependencies]
curl = '1.0.0'
The chplVersion field indicates Chapel releases compatible with this package. There are a number of accepted formats:
"1.16.0" # 1.16.0 or later
"1.16" # 1.16.0 or later
"1.16.0..1.19.0" # 1.16 through 1.19, inclusive
By default, chplVersion is set to represent the current Chapel release or later. For example, if you are using the 1.16 release, chplVersion will be 1.16.0.
## Environment Variables¶
Mason can be configured by setting the following environment variables:
• MASON_HOME : Path to a directory where mason will store cached registry and package data. Defaults to $HOME/.mason. • MASON_REGISTRY : A comma separated list of name|location pairs, where name is a local name for the registry at location. Defaults to mason-registry|https://github.com/chapel-lang/mason-registry. If the name| part of a pair is omitted it is inferred to be the word following the final slash in location with any .git suffix removed. • MASON_OFFLINE : A boolean value that prevents mason from making calls that require internet access when set to true. Defaults to false. Mason command that support a --[no-]update flag can override the MASON_OFFLINE setting when --update is explicitly passed. The mason env command will print the inferred or set values of these environment variables. If a variable was set by the user, an asterisk will be printed at the end of the line. For example, if $MASON_HOME was set:
> mason env
MASON_HOME: /path/to/something *
MASON_REGISTRY: mason-registry|https://github.com/chapel-lang/mason-registry
MASON_OFFLINE: false
Warning
If MASON_REGISTRY changes after invoking a mason command that updates the local copy of the registry (e.g. mason update), the local copies of the registry and dependency sources will be removed.
## TOML¶
TOML is the configuration language chosen by the chapel team for configuring programs written in chapel. A TOML file contains the necessary information to build a chapel program using mason. TOML Spec.
## Namespacing¶
All packages will exist in a single common namespace with a first-come, first-served policy. It is easier to go to separate namespaces than to roll them back, so this position affords flexibility.
## Semantic Versioning¶
To assist version resolution, the mason registry will enforce the following conventions:
The format for all versions will be a.b.c.
Major versions are denoted by a. Minor versions are denoted by b. Bug fixes are denoted by c.
• If the major version is 0, no further conventions will be enforced.
• The major version must be advanced if and only if the update causes breaking API changes, such as updated data structures or removed methods and procedures. The minor and bug fix versions will be zeroed out. (ex. 1.13.1 -> 2.0.0)
• The minor version must be advanced if and only if the update adds functionality to the API while maintaining backward compatibility with the current major version. The bug fix version will be zeroed out. (ex. 1.13.1 -> 1.14.0)
• The bug fix must be advanced for any update correcting functionality within a minor revision. (ex. 1.13.1 -> 1.13.2)
## Incompatible Version Resolution Strategy¶
The current resolution strategy for Mason 0.1.0 is the IVRS as described below:
1. If multiple bug fixes of a package are present in the package, mason will use the latest bug fix. (ex. 1.1.0, 1.1.1 –> 1.1.1)
2. If multiple minor versions of a package are present in the package, mason will use the latest minor version within the common major version. (ex. 1.4.3, 1.7.0 –> 1.7)
3. If multiple major versions are present, mason will print an error. (ex. 1.13.0, 2.1.0 –> incompatible)
## The Lock File¶
The lock file Mason.lock is generated after running a mason update command. The user should never manually edit the lock file as it is intended to “lock” in the settings of a certain package build iteration. Mason.lock is added by default to the .gitignore when a new package is created. If your intention is to create a binary application package that does not need to be re-compiled by mason then take the Mason.lock out of your .gitignore. An example of a lock file is written below as if generated from the earlier example of a Mason.toml:
[curl]
name = 'curl'
version = '1.0.0'
chplVersion = "1.16.0..1.16.0"
[root]
name = "MyPackage"
version = "0.1.0"
chplVersion = "1.16.0..1.16.0"
authors = ["Sam Partee <Sam@Partee.com>"]
source = "https://github.com/Spartee/MyPackage"
dependencies = ['curl 1.0.0 https://github.com/username/curl']
## Dependency Code¶
The source code for every package will be downloaded to \$MASON_HOME/src`.
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2020-07-05 20:51:21
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{"extraction_info": {"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, "math_score": 0.17991258203983307, "perplexity": 10227.92987658091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655888561.21/warc/CC-MAIN-20200705184325-20200705214325-00491.warc.gz"}
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https://www.physicsforums.com/threads/dep-inelastic-scattering-with-graviton-as-propogater.323734/
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# Dep inelastic scattering with graviton as propogater
1. Jul 7, 2009
### raj07
consider deep inelastic scattering of e-p.assuming that a graviton acts as a propogater in this interaction how would it effect the structure functions of the proton.now we have a spin 2(graviton) instead of the usual spin 1(photon).basically what is the effect of this spin change on the structure functions of proton.
2. Jul 7, 2009
### humanino
You would get more elaborate Lorentz structures, therefore richer form factors and hence essentially more information on the proton structure. Namely, you would be sensitive to the distributions of masses, angular momentum and shear forces.
Last edited: Jul 7, 2009
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2017-08-21 18:26:48
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http://www.gradesaver.com/textbooks/math/trigonometry/trigonometry-7th-edition/chapter-2-section-2-1-definition-ii-right-triangle-trigonometry-2-1-problem-set-page-63/68
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## Trigonometry 7th Edition
$\sin A = 0.800$ $\cos A = 0.600$ $\sin B = 0.600$ $\cos B =0.800$
Steps to Answer- We will use given data about triangle ABC and Pythagoras Theorem to solve for 'c'- We know that - $c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem) $c^{2} = (11.28)^{2} + (8.46)^{2}$ $c^{2} = 127.2384 +71.5716$ $c^{2} = 198.81$ therefore $c = \sqrt (198.81)$ = 14.10 Now we can write the required T-functions of A and B using $a=11.28$ , b = 8.46 and c = 14.10 $\sin A = \frac{a}{c} = \frac{11.28}{14.10}$ = $0.800$ $\cos A = \frac{b}{c} = \frac{8.46}{14.10}$ = $0.600$ $\sin B = \frac{b}{c} =\frac{8.46}{14.10}$ = $0.600$ $\cos B =\frac{a}{c} = \frac{11.28}{14.10}$ = $0.800$
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2017-02-22 04:15:39
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http://lambda-the-ultimate.org/node/5637
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## Do names and symbols really imply semantics? If so what to do about it?
Some languages, like APL, are written in Martian script. Their proponents insist that a set of characters humans have never seen before in their lives have intrinsic, unambiguous semantic meanings which can be inferred directly from their shapes.
I don't think that is true. Not to humans, anyway. Martians probably see differently.
Some languages have strong requirements about the semantics of operators, based on the familiar semantics and relationships of those operators. For example there was a beta release of Pascal 7 (from Borland, around 1995 I think) that allowed people to overload operators, but warned that the compiler would simplify expressions according to the precedence rules the language set for them and the distributive, associative, etc. properties implied by those operators before any definition overloads were looked up. If an operation was commutative, the compiler was allowed to reorder its arguments arbitrarily. If distributive expressions like (a*b)+(a*c) would be reduced to a*(b+c) before looking up the operator overloads. If you defined any two relational operators, the compiler would automatically define the rest using the identity axioms. You were not allowed to define three or more relational operators. Etc.
This strong assumption that the semantics of the overloads must follow, in most respects, the semantics of the operators whose names they were using, really upset a lot of people who wanted to use '+' to concatenate strings or wanted to use '<=' and '=>' (which is how Pascal spelled 'equal-or-greater' as some kind of redirection operators. A lot of it (but not all of it) got changed between beta and release.
I was never really convinced that changing it was the right thing. It seemed perfectly reasonable to me that these familiar symbols should be constrained to have the familiar semantic properties that we infer when we're looking at an expression built of them. I thought people who wanted string-concatenation operator or a redirection operators should be using different names for their operators, like '$+' or '|>'. Sadly this was impossible as there was no way to define new operator symbols. This deficiency remains true in almost all languages that allow operator overloading. In Scheme there is a strong assumption/tradition that any variable whose name ends in the character '?' will be bound to a procedure that returns a boolean value. The same idea in common lisp is associated with the trailing character 'p'. The tradition in scheme goes on that any variable whose name ends in '!' is bound to a procedure that has a side effect. Many schemes will produce a warning if any such variable is ever bound to anything else. And some consider it an error if a side effect is produced by any procedure not so named, because the name is considered to be an important warning to the programmer that a side effect is possible. Scheme used to have 'indeterminate digits' in numbers, written '#', so for example 123# denoted 'one thousand two hundred and thirty-something,' an inexact integer. This got scrapped once it became clear that implementors had no interest in keeping track of how many significant figures of decimal accuracy a calculation represented. They were only using 'inexact' to mean 'ieee754 floating-point hardware representation' and were openly hostile to the notion that anyone might hope for it to mean anything more. Many regarded it as a contradiction in terms that something could be both 'integer?' and 'inexact?' And I think in the current scheme standard it may in fact be a contradiction in terms. But getting rid of it meant abandoning the possibility of tracking significant figures of accuracy. So that character used to have a semantic meaning and purpose, but nobody valued that purpose. Early basics had 'type sigils' so that the programmer (and the interpreter) could know the type of a variable just by looking at the name.$foo always referred to a string, .foo always referred to a floating-point number, #foo always referred to a binary value, etc.
People made an awful lot of fun of those type sigils in old basics. Until the same people turned around and started using Hungarian notation to keep track of the types of their variables in C++. Because keeping track of the type was HARD, and they wanted to be able to see what type something was by looking at it. So they defined their pszName and hwndInteractionWindow and their dwIDnumber and so on and didn't think about basic's type sigils at all because this, after all, was something different.
And after all these examples of naming semantics. How much semantics is it reasonable to expect to be able to infer from syntax? How much is it reasonable for the compiler to enforce, based on the name alone? And what relationship does programmers liking it have to helping them produce good code?
## Comment viewing options
### Pragmatics to consider
Viewed purely from a mathematical perspective, a case can be made for handling commutativity in the way that Borland apparently did (I had not known about this - thanks). But from a pragmatics perspective, the behavior of overloading is now fairly well established and would create confusion if changed.
Though I can definitely see an argument for stating such things as part of mixfix definitions.
### Programming languages considered harmful?!?
I think you (Ray) are poiting towards this old (but true) observation...
"Programming language" is a historically accidental category in the following sense:
In practice, we have compiler stages that transform some abstract syntax into machine readable instructions. (In this context, "compiler" is meant to include programs which are "interpreters".)
We have various compiler stages that do transformations from one abstract syntax to another. Optimization is one possible motive. Systematic semantic changes to a program can be another (e.g. macro expansion in scheme).
Finally, we have parsers, that translate hand-built representations of abstract syntax into the data structures to feed to later stages. (Here, "parser" includes not just grammars over text streams but any structured objects that can be interactively created -- such as but not limited to dataflow diagrams.)
So the activity of programming can be seen as a production process that breaks down into maintaining a surface representation -- human made documents, diagrams, and so forth -- and a stack of translators that eventually end with compilation/interpretation. There is no principled reason why these stages of translation aren't richly modular and re-composable, though interestingly, in practice, there are no real widespread realizations of such modularity other than internally to a "programming language" (e.g. lisp family languages are hackable and notorious for the ease with which they allow the invention of new abstract syntaxes, mixing and matching them, composing compilation stages in application-specific ways, etc.)
In that mindset, where programs all use specific notations but none is necessarily regarded as the overarching "programming language", and where notations are application specific and translation-technique specific but multiple notations happily co-exist and cooperate, something like a purely syntactic transform that uses algebra laws to reduce the number of multiplications (as in Turbo Pascal) are applicable when they are -- when that stage is chosen during program construction as part of how the program will be translated -- and are irrelevant otherwise (as when a notation really really wants to use "+" for both arithmetic and non-commutative
string concatenation).
If we're in that mindset - that there is no fixed language, just application-specific translations from chosen notations through various abstract syntaxes to compilation/interpretation - then your question "Do names and symbols really imply semantics? If so what to do about it?" is really one about "rules of thumb" for the design of domain-specific notations. In some contexts, it turns out, people use "+" to mean a commutative operator, in others a non-commutative, sequential operator -- be aware of this when designing and documenting notations -- here or there is how one might decide whether or not to reserve "+" for one kind of meaning or another.
But we can't have that discussion because history gave us the "Programming Language was Oevre" -- a Programming Language™ is a static, "general purpose" notation with fixed stages of translation, attributable to a single author (an individual or group), often a specific type of commodity (tying it to "the economy").
Programming Languages™ are, perhaps fetish objects -- delusions that come from product standardization taking precedence over modular, flexibly composable translators and surface syntaxes.
This was pretty much the main point of lisp by the time it got to my ears, at least as far as I'm concerned.
### language systems
The notion of modular, flexibly composable translators surface syntaxes has certainly been explored. Wyvern has its type-specific languages. Scala has its DSLs. Lisp has its reader macros. However, such mechanisms haven't really entered the common consciousness of programmers. It's never a go-to solution. I wonder why.
Is it that people don't want to learn to read and write a dozen problem-specific languages? Or economics and opportunity (e.g. by the time the benefits for a DSL for a problem is recognized, the program is half-written and developing a DSL would be significant scope creep)? Or integration with tooling? Alternatively, are we losing the opportunity because the existing mechanisms are deficient in some subtle manner, forming a barrier for practical use?
The language system I'm currently developing, Glas, attempts to resolve some deficiencies with existing mechanisms. Syntax is per-file, i.e. we compile filename.ext using a function from module language-ext (with a special case to bootstrap module language-g0). Per-file syntax should simplify integration with external tooling. There is no implementation hiding by modules, just a standard representation for language module functions as tree-structured data. This simplifies reuse of behavior models, e.g. a web application might transpile useful subprograms to JavaScript to run client-side. Implementation hiding can be supported by having a program check whether a subprogram directly observes certain data.
But this is an experiment. I'm not convinced that people will actually want to develop language modules except perhaps to create or extend general-purpose surface syntax to better fits their preferences. (The g0 language used in bootstrap is essentially a Forth, so probably doesn't match most programmer preferences.) I do hope to develop at least one general purpose surface syntax above MySQL or another database-in-a-file format to support graphical programming. A smooth transition and integration between textual and graphical programming was another motive for design of the Glas language system.
### "The notion of modular,
"The notion of modular, flexibly composable translators surface syntaxes has certainly been explored."
Not much at all in popular practice making efforts like Bespoke interesting.
### Popular practice requires
Popular practice requires popular interest in such features, or enough utility to gather it. Does this interest or utility exist?
Perhaps graphical programming is necessary to really achieve multiple syntaxes without becoming a complete mess of incomprehensible text. Each 'syntax' becomes an applet, and could have its own help function and mini-tutorial. But it would still become difficult to grok or maintain after you have thousands of user-defined libraries each adding a unique bundle of applets that a maintainer must learn.
If control of applets were centralized, I think it'd be closer to a conventional Programming Language™ with one keyword per applet. But it might be easier to learn and maintain.
Enso language is another interesting direction to take graphical programming. There is a graphical view that is quite flexible, but each statement has a consistent textual syntax that is readily accessible.
### popular practice
A couple of notes:
I very much like the idea of thinking in terms of an abstract syntax that, sure, might really shine in a graphical display but is also accessible and tractible in other forms. For one thing, it shows that somebody gave a damn about accessibility and that's all too rare a thing in this weary world. For another, it takes a certain clarity of thought and attention to detail to have an abstract syntax that's that good.
I'm trying (not very successfully, judging by replies) to problematize and dissolve (or least question) the idea of "programming language" with all the baggage we've attached to it. That's why I suggested "notations" the single example of which is merely a "notation" with interpretation a toolbox of stages of transformation.
There is a kind of math heavy heritage to the concept of a programming language that sees a "program" not as a situated computing system but as a set-theory-style map from input conditions to out, some notion of time or other, and above all -- standardization as a commodity (at least in the extension). Cobol exists independently of any implementation. One can buy (or could) instances of cobol translators. Cobol translators could be compared for efficiency, accuracy, price, and so on.
I don't see that commodification of the invented category of "standardized programming language" as a necessary state of affairs. I see it as a hindrance on building systems. Worse, it results in accumulations of legacy systems with very tall stacks of dependencies --- flaky infrastructure is the rule rather than the exception because of this.
### notations at scale
For systems at sufficient scale, we'll still need to consider modularity, extensibility, integration, architecture, security, etc.. This is a natural consequence of the scale, cf Conway's Law.
Notations for programmable systems deal with scale - human organizations collaborating, concurrent development, many moving parts, etc.. I believe that much "baggage" associated with "programming languages" is a natural outcome of solving problems of scale - a problem that does not appear for most other notations, to the best of my knowledge.
And due to the nature of humans attempting to collaborate at scale, if an interface isn't "standard" it will be "convention" or "contract" that eventually calcifies to the extent you might as well document it and call it a de-facto standard. Where we don't need to collaborate, we don't need standards. But software and the programmable systems it controls and the interests involved are too big, too complex, too political to fit within the small hands and minds of individual companies, much less individual humans. Collaboration is necessary, and standards are inevitable.
I'm not convinced we can avoid most baggage of programming languages. But I do believe we could organize that baggage much more effectively. Some things I think we've done poorly:
• Modules shouldn't hide implementation. I.e. modules should provide recipes for behavior in an easily processed notation, which can be rewritten and adapted for use in different contexts. Not an opaque application of behavior. This requires reconsidering whether IP protection should be technologically enforced.
• Internal DSLs are a bad idea because they require external tools to adapt to the language system, instead of simultaneously adapting the language system to the external tools. Per-file syntax, e.g. where file extensions guide interpretation, is a much cleaner solution that allows individual components to be expressed in various notations such as Cobol or Python or music notation or MySQL databases or whatever.
• Ambient effects and their relative, foreign function interfaces, hinder analysis and adaptation of code to new contexts. Essentially, they require too much ad-hoc, decentralized contextual knowledge, raising a barrier to analysis or rewriting code for use in a new context. Algebraic effects are a promising alternative.
• In many cases, we use effects for performance, such as manual caching of data, or manual loading of subprograms onto a GPGPU. This becomes another source of entanglement between code and context, which contributes to bit rot and flaky infrastructure. Alternatives include annotating programs for caching or use of software acceleration of abstract CPUs or GPGPUs (cf. inversion of the language tower).
• The most common application model today is the procedural loop, i.e. we have void main() { loop { do stuff } } or some variation thereof. This has a problem of being difficult to inspect, compose, or update at runtime because the loop captures a lot of implicit state and the external interface is essentially closed (we can only kill the loop or let it run). There are many other possible application models - apps as objects, apps as blackboard system agents, apps as materialized interactive views, apps as system patches or overlays, etc..
The standards and conventions of modern programming languages should be questioned, especially those with troublesome systemic implications.
But I disagree with your position regarding commodification or standardization as unnecessary or a hindrance on building systems. I think fault lies with several systemically problematic design choices that have become so conventional that they are rarely questioned.
### I kinda went there and I don't believe it any more.
DSL's are very nice for program development, but have failed to gain traction because program maintenance is not done by people who have already learned the DSL that they have to know to do maintenance.
I took the idea of the DSL-capable language to what I consider its logical conclusion with an experimental lisp using fexpr semantics with optional hygienic renaming and two name spaces- one for dynamic and one for static scope. In principle, any s-expression could mean almost anything.
It was intended to be a 'translation target' or first stage of a 'universal interpreter.' The idea was that the syntax tree of a program in nearly any conventional language, expressed as an s-list in this translation-target dialect and linked to a "translation model" that defines how those s-expressions in context are interpreted, should have the same semantics as the original program. And this would enable, in principle, programs where every module and routine were written in different, unrelated languages, to be linked together and play nice.
Although that (sort of) worked, it was no damn good for what I had really hoped it might enable. Predictably-in-hindsight, it turned out to be largely unusable as a language of its own. Any expression, just as I had designed, could mean anything. So there was almost zero semantic information available when looking at the code at the bottom level that actually did things in terms of the domain, because none of the expressions you were looking at actually had a known meaning unless you already knew a significant fraction of the rest of the program. IOW, everything had become a DSL.
The good part about defining a new Domain-Specific Language for each new program. Development can run an accelerating curve because you are making it easier and easier to express the solution in semantics relevant to the problems, and becoming familiar with the language of that domain makes it easier to think in terms of solutions in that domain.
The bad part is that What you leave behind isn't easily maintainable by people starting from zero - and contrary to your best hopes and intentions, the people who matter most to the lifetime of this code will always be starting from zero, again and again and again.
So, my question was less about the virtue of a domain-specific language, than what that maintainer, "starting from zero," ought to be able to infer just from looking at one small part of the code. The semantics of naming conventions are a powerful part of that, but
Someone who is assigned to fix a bug in a program is, in the 'usual' case, someone who was hired on to the company seven years after the program was written and two years after the last engineer who actually worked on implementing it is gone. Because the company no longer has any of the original implementation team around to talk to and nobody knows where any documentation of that program's internal DSL might be (if, indeed, there ever was any), he has a book on the implementation language in hand but is otherwise flying blind, and never saw the source code of this particular program or this particular DSL before being assigned to fix the bug. Further, they know for a fact that this DSL will never be any good to them in maintaining or bug-fixing any other program besides this one. Or, even if it is, it will never be any good to them in maintaining or bug-fixing anything developed at a different company, and this knowledge limits their motivation to learn the DSL.
If the DSL was documented at all, the documentation is typically lost in one reorganization or another within five years, leaving only source-code comments as hints and clues of what's going on. Some engineer leaves, some new one is hired, and a bunch of nondescript "stuff" gets dumped off those bookshelves into the trash, by people who don't even know what it is, to make room for new "stuff." No matter how you tried to impress upon management that keeping track of it was important, if they're not making a profit on it this quarter it falls below their notice.
This may be an overly cynical view, but from experience in Silly Valley, it's a fairly pragmatic cynical view. Every line of code you write is going to have to be maintained by some poor schmuck who has no idea what it's for or what's going on in the rest of the program. If that line is in a DSL that the poor schmuck doesn't know, then you're writing code that will come to be known as harder and more expensive to maintain, and people are going to eventually agree that it must be reimplemented in whatever language is popular at the time.
So... I'm less enamored of languages that allow new DSL's to be created for every program than once I was. I think the only way you get DSL's that matter, that can be maintained, is when you build them into the vastly-extended set of "standard libraries" for your language. That way the poor schmuck who has to maintain your code can be expected to start with a working knowledge of the DSL for your subject matter domain that's standard in your language. Or at least, if they have to learn it they can learn it from a living community that maintains documentation external to the company, and it can be a transferable skill that they can use somewhere else.
### Who do "we" work for?
Someone who is assigned to fix a bug in a program is, in the 'usual' case, someone who was hired on to the company seven years after the program was written and two years after the last engineer who actually worked on implementing it is gone. Because the company no longer has any of the original implementation team around to talk to and nobody knows where any documentation of that program's internal DSL might be
So, it isn't ethical where I came from to design systems with the intention that that is normal, nevermind designing languages and programming environments that encourage it.
### Sadly designing for job security is also unethical.
I take your point, but if you want to extol the virtues of designing so that nobody except the original implementors can work on something, I think that's going to run into ethical problems rather quicker.
Like you I hate the notion that engineers can or should be treated like interchangeable parts. But in the long run, either we are interchangeable parts or the things we work on die when we move on.
Some contractors have put logic bombs in their code for job security. That's pretty squarely unethical. If we have code that's unmaintainable by anyone else, we're not doing much better.
### Don't write overly complex systems
We're in a feedback cycle where programming language "theorists" invent ever more abstract ways to build up reams and reams and reams and then some reams of intricate code nobody understands -- and this boosts commodity output, giving more incentive more more of this direction in programming languages.
People should resist and even sabotage that kind of work.
Capitalist society has similarly blown non-software infrastructure very broadly as well, and in similar ways. Our big systems in general are tottering and beginning to collapse as a result.
"Oops."
### TBF, reams of code that
TBF, reams of code that nobody understands is the default state for any mature software system. Doesn't matter whether it's abstract or not. Software becomes impenetrable and incomprehensible by sheer bulk and connectivity.
cf. big ball of mud architecture. The most popular architecture.
A lot of PL theorists have attempted, without much success, to avoid the problem of all architectures eventually becoming mud. At best, they have enabled pre-mudballs to be two or three sizes larger. AFAICT, the underlying issue seems to be some variation of Parkinson's Law.
### "the default state for any mature software system."
That's quite a pronouncement.
dup
### We have quite a history to
We have quite a history to support it.
Blaming new PLs or paradigms is false attribution of cause for the fragile tower of dependencies. You'll have a barely maintainable heap of Cobol if using that notation. Indeed, there were many such systems in the era where Cobol was dominant, still dwindling gradually for decades after.
Thomas - I think you have some cause and effect mixed up here.
The fundamental issue is one of scale (excellent comment from dmbarbour separately in this thread, I think), and the challenge of somehow continuing to manage the growth of complexity as scale continues to increase relentlessly.
Humans have a complexity budget. When systems cannot contain complexity, that budget gets shot very quickly, and the systems die. There is never any other result. This is always the same, exact outcome: A system dies when the cost of evolving the system exceeds the cost of replacing the system. (And, the corollary: Maintenance mode is the result of the cost of system replacement exceeding the perceived value of that system.)
"People should resist and even sabotage that kind of work. Capitalist society has similarly blown non-software infrastructure very broadly as well, and in similar ways. Our big systems in general are tottering and beginning to collapse as a result."
Resist? Yes. Managing complexity (or rather, managing entropy) is the job of IT. And IT, generally, does this job rather poorly.
Sabotage? Capitalism? etc.? No, that's just nihilism speaking, and we should avoid the adrenaline high of dabbling in such a logical void.
### "nihilism"
Critiques of what the automatic logic of capital creates in the built environment are not nihilism.
### I'd be more interested in
I'd be more interested in seeing you address the assertion that your argument mixes cause and effect.
I don't believe new abstractions from PL theorists would become popular without enough people having experienced pain while lacking those abstractions. Further, programmers almost never try new languages while they can make do in their preferred languages. Thus, those new abstractions must be difficult to adopt into the existing languages. The complexity that drives adoption of new PLs precedes those new PLs. But your argument seems to posit that the complexity is caused by those new PLs. Cause and effect, seemingly reversed.
I don't believe you're a nihilist, but spreading blame too broadly does look a lot like nihilism. Stovepipe systems, walled gardens, lock-in, and other forms of entanglement with context are certainly troublesome, and this includes lock-in to notation or a runtime. Standards have potential to be good or bad, much like code. Regarding commodification of software artifacts which might represent blueprints, recipes, information, knowledge, or creative works (music, games, etc.) - it takes work to create these artifacts, so should they be free?
If through a few carefully chosen standards we can reduce entanglement and make it easy to trade a banana without also sharing the gorilla holding it and the entire jungle, and the language runtime or virtual machine that simulates the jungle, that's a good thing.
I don't understand how "automagic logic of capital" or a 'critique' thereof is especially relevant to the development trajectory or complexity and fragility of software systems. I do understand that capitalism is all about using leverage to extract as much as possible, that poorly regulated capitalism is essentially sociopathic, and that capitalists have historically used a lot of propaganda and dirty tactics to break unions, weaken regulations, and make voters accept or overlook their abuses. I suspect it's the propaganda-driven non-reasoning that you refer to with 'automagic logic'.
But most PL designers are not motivated as capitalists; most just say "my favorite language EXCEPT with these few tweaks WILL BE GREAT!" and then implicitly, unthinkingly inherit any lock-in problems of their predecessor. From my perspective, it is mostly a few bad standards/conventions inherited in such a lineage that is the real problem, not the existence of those creative people who are willing to work hard to improve their own situation.
### re: I'd be more interested in...
There's a lot here that seems silly.
For example, you're describing PL success as uptake by programmers who are almost exclusively working as wage labor for capital, on the other hand you say PL designers aren't "motivated as capitalists". Those are contradictory.
And you say that PL innovation doesn't deserve blame for complexity since it retrospectively tames complexity. But that ignores the question of "and what happens next"? The towers of successive subsumption are the growing fragility, the growing unrecognized, unmanaged life-critical system entanglements, and so on.
Of course, the economic pressures on PL designers, in and out of academia, tenure or no tenure, highlight the way that even if the subjective experience of PL designers is for some that of playful exploration, nevertheless their estimation of relevance is shaped almost entirely by the imperatives passively received from the requirements of capital accumulation.
An alternative approach might be multi-disciplinary, developing a critique of the social impacts of computing systems (including but not limited to complexity-driven fragility of life-critical systems), a critique of the aims that drive construction of those systems, and the development of an imaginary of how a saner society might use computing -- including what PL would look like for that alternative. Who knows, such researchers might even come up with something that gains some traction. But, of course, engagement in such activity at any scale and duration would for most be a career ender.
You say there is a contradiction regarding uptake and motivation, but there really isn't. Most PL designers are hobbyists who don't expect any market success.
There have been over 7000 PLs designed and developed when I read surveys in 2010. This is just the fraction developed publically enough to find. There are at least a few hundred failed PLs per year. Almost none see the light of day or make a dime. Rather than market success, the primary motive behind these efforts is hobbyist passion and interest. Makers making things
There is perhaps a hope for market success, but no valid expectation of it. Like winning a lottery. But even then there is almost no leverage to capitalize on having designed the PL. A PL designer cannot write all the libraries needed to succeed. Maybe they can write a book.
Of course, there are exceptions. Capitalized languages like LabVIEW. JavaScript was produced by Netscape in a hurry to beat other browsers. Etc.. But I think if you study the history, you'll find that the language capitalists mostly borrow designs, and are essentially a separate group from those who innovate PL abstractions.
### re fragile towers
Our software systems are fragile towers.
But this will be true even without PL innovation. There is plenty of evidence of this just looking at existing systems. Instead of new syntactic abstraction, it becomes towers of frameworks and libraries. Many PL designers have observed that framework API design is essentially PL design, usually performed by people who barely know the many potential pitfalls of PLs.
If there is not an easy option for concise expression and automated integration, programmers will use verbose expression and manual integration. Same story, over and over.
The fragile tower shouldn't be blamed on PL innovation. But it is a problem that deserves attention.
Producing a more robust, systemic, community oriented design is among the interests of many PL designers I follow on Twitter. Of course, it's a very self-selected group. But where you blame innovation, I think the solution is innovation with attention to the whole-community experience. Regarding how we share, distribute, trust, modify, and integrate code. How to avoid the walled-garden separation of most applications, at least by default. How a newcomer explores and develops an effective mental map of the system. Etc. There are a lot of projects in this vein if you look for them.
And as you might infer, we *mostly* do such work as a hobby. Not as a career.
### The tower of dependencies must be cut somehow at basement level
I've thought hard about the "tower of dependencies" and "tower of interpreters" and how they generally make efficiency in time, memory, or more usually both, go straight to hell.
The enormous fragility they bring is another issue.
The only thought I've had about it was about subsuming the dependencies and then optimizing the resulting application until all that extra baggage is trimmed away and all the simulated virtual-machine code reduced to actual machine code that runs native. And that's half the answer.
That's not a simple optimizer to build. It's not clear that it *can* be built. But if we allow the optimizer to "chew" for extended periods of trying every possible thing we can think of, and probably apply AI/ML techniques to determine which transformations to try next or which sequences of transformations to plan ... such a beast could, mostly, be built. It would be an absolutely enormous amount of work though.
But as I said, that's only half the problem. A major issue with the tower of dependencies is that undesired behavior can emerge at any level of the tower. In fact the way some applications built on, say, the Boost framework are forced to operate are in fact bugs according to what the designer and users of a particular application want. If we subsume all that complexity and then optimize the snot out of it, we wind up keeping that undesirable behavior.
So the second half of the problem is that we have to be able to render that code, after a tremendous amount of optimization work has been done and all the semantics attached to unused parts of the original source code ruthlessly boiled away, in a language that a human programmer can actually read, understand, and correct. Without being bothered by a need to master all the code for semantics that the particular program does not in fact use.
Which is, more or less, a requirement for 'roundtrip' optimizing - where the optimizer spits out not only shorter and faster machine code, but also maps it all out in a source code that preserves all the symbols and abstractions that still have semantic meaning in the context of the individual program.
I don't think anyone has ever even attempted that. It's hard to even imagine what it ought to mean and what should be considered 'success.' And while I think the first half would be very hard - could be done but would be an astonishing amount of work - I'm not sure the second half can be done at all.
### cutting the tower
I believe the tower of dependencies is problematic mostly due to conflation of concerns in conventional module systems (notably abstraction, decomposition, and identity).
Ideally, modules shouldn't be viewed as existing "below" their client program. Instead, each program should itself be the robust foundation upon which we install, integrate, and compile objects using algorithms found in libraries. Like building a circuit board, or a blueprint for one. A program should also be able to adapt a module for the local context, e.g. metaprogramming, patching, etc..
But that perspective simply isn't viable while we insist that modules hide implementation, have object identity via module-level variables, or can implicitly communicate without opportunity for access or intervention by the parent program.
Improving upon separation of concerns has often been a successful path for language design. But the module system doesn't get nearly as much attention as it should for its impact on the community experience of a PL.
So long as we follow the same old conventions for module system design or prioritize FFI comptability, we'll be stuck with software systems that are fragile, wobbly towers.
### Yup, this must hold for everything in the whole universe
"A system dies when the cost of evolving the system exceeds the cost of replacing the system."
Yup, this must hold for everything in the whole universe, AFAICT.
Except for one thing: when the topic of raising the debt ceiling is on the table of our dear, do-gooding, ever-well-meaning, disinterested politicians.
But of course, that peculiar sort of unsustainability can only work when / because the public itself doesn't really care. Or, more precisely, doesn't feel enough pain yet.
An invariant condition which, in itself, is quite the thing to behold, we gotta admit.
... especially, after centuries of, say, "past data points", to stay polite.
### Human techniques for managing complexity-and their limits
The point that humans have a complexity budget is a good one.
Our "seven plus-or-minus-two" short term memory is one of our fundamental limitations. Much of language design is managing things so people don't have to remember more than "seven plus-or-minus-two" to get things done.
The most fundamental paradigm for it is written language. It does in code what it does in everything else we use it for - it holds all the complexity we can't immediately remember in a fixed form we can understand, so that we can get it *back* into our heads when we need to work on it, and so we are allowed to *forget* it when we need to work on something else.
And language has a special place for us as humans neurologically. Our brains have special circuitry for dealing with complex relationships and structured semantics in language that have no parallel for any other representation.
Another strategy is abstraction. If we can make the language we're programming in capable of expressing more with less code, the theory goes, or make the code expression organized more closely along the paradigms and operations that people actually think of when dealing with that subject matter - then people will have to remember less.
The actual results are mixed, though. A DSL that follows more closely the paradigms and operations that people actually think of when dealing with that subject matter, provide tremendous leverage to subject matter experts. But not so much for the one who isn't already trained to think in those paradigms and operations. In fact it can be counterproductive for such because then they have to remember *MORE* - all the stuff that's abstracted away where the subject matter experts don't have to think of it has to be hunted down and understood before they can follow the more-abstract code, and they'll be going to check details of what each operation does or the details of what the process requires to be done, every time their seven-plus-or-minus-two stack limit blows.
We have additional strategies that teach programmers to do things to help others deal with that memory limit - the reason why we try to impress on people that it's a good idea to name a variable 'newlineCount' instead of 'N' is because it saves the reader from having to remember what 'N' means. Instead of remembering it, they can infer it from the name. The reason why we make it a member variable in an object named editingBuffer is because we are first telling the reader that they don't have to remember it in other contexts and second allowing 'chunking' in that at some higher level of operations they can just keep track of the editingBuffers instead of remembering which instance of every 'N' applies to which document and in which context.
Naming conventions, unlike abstraction capabilities, don't seem to have a cognitive downside for those not already "in the know." And don't, in principle, interfere with abstraction capabilities. So if they can help, why aren't they a language feature? Why can't I tell by looking at the name of a function whether it changes the value of one or more of its arguments? Why can't I tell by looking at the name of a variable that holds a value of one of the language's fundamental (non-derived) types which type it holds? Why can't I tell from looking at the name of a function returning such a type which type it returns?
In short, how much of the cognitive burden of remembering everything can we relieve the programmer of, just by having a solid set of naming conventions in our language?
### AI complete
if they can help, why aren't they a language feature?
Until we have an AI for a linter, we'll never be able to suggest the 'N' should be 'newlineCount'. Thus, such naming is doomed to be convention, not a language feature.
Setting that aside, in many programs the programmer will mostly work with non-fundamental, derived or composite types. This might even be encouraged. Building in a bunch of conventions to identify a few fundamental types is awkward in this context.
We could perhaps manually associate naming conventions (prefix or suffix) with user-defined types, have a linter check that.
I've seen a development environment that associated types with colors, including user-defined types. Function calls would have colors transition from inputs to output. A little legend was visible. This provides a similar ability to recognize things at a glance, though it was awkward for infix operators.
### On humans' complexity
On humans' complexity budget...
Striving to remain pragmatic, I'd tend to be of the opinion that that one can much vary from one individual to another, and likely is very context-dependent, too. But that's not saying much. After many years as a user of "programming languages" of all sorts my sense now is that complexity is neither a friend or foe.
Certainly, accidental complexity in notations or tools is inevitable, and essential complexity is... well, the essence of whatever the designer(s) and/or implementor(s) have introduced:
unless one is into the hobby of self-inflicted pain, one will probably wish to maximize the essential / accidental complexity ratio, or whatever can at least be perceived as such, if it isn't easily measurable.
But that ratio itself might be much context dependent too, which doesn't help us much either for a constructive introspection over what we have done / are doing / hope we'll be able to do.
Case in point:
mere mortals around me are often baffled by the news, when I'm asked, that it has already been for most of the decades (out of only a few in total, at that) for software engineers and language designers to fight in quasi-religious battles over "purity" or "expressive power", etc, of the languages favored by their respective churches (I won't use "sects" to not sound too cynical or pessimistic, of course).
So what I'm trying to say is that maybe our very, very, very young domain still have a long way to go before maturity in terms of its own introspection capabilities. IOW, we may not even have actually lost our innocence yet, about what we're grappling with.
Think Copernicus. But then, Newton. But then, Einstein. But then, the postmodernists. j/k
Computer Science does exist, I think, and has as much utility as Physics does for us to bargain better with nature, but there is still very little of CS running on our laptops, server blades, or smartphones - my feeling is it's still 90% "or so" of craftsmanship or "Art" (in Knuth's vernacular) or folklore still being deployed in binary form at an exponential rate, while provable or proof-carrying code thus is more often than not the exception.
It all seems as if this is a world where "we", collectively, recently unleashed that Turing Machine animal, and enthusiastically decided to let it go loose wildly, and then, only after the fact...
... are now trying to tame it so that it doesn't come back too often or too unexpectedly to bite us (as the flawed humans we are to ride it for its applications in our broad spectrum of ethics - ie, for better or worse as with anything which pertains to human affairs but computers have no clue about that).
IOW:
Let's be happy and carry on with the coding: the dawn of this domain of ours is still exciting, IMHO.
With or without centuries of math and logic behind it, our Towers of Interpreters and such are promising precisely because while nobody has had their Einstein moment to remove all confusion about it, we've at least already noticed (and probably accepted) that it isn't going to be resolved any time soon (if ever) - so that the risk that the Art suddenly disappears and is replaced with a boring, fully automatic assembly of code - by an Evil Matrix (*) hellbent on enslaving us all, of course - is seemingly, still, very close to zero for the foreseeable future.
(* On the other hand, there are some really sick people with the levers of power, out there - and those need no supercomputers to do much damage. Pens and ink largely suffice. As history shows quite clearly.)
Which by no means implies we should blindly tolerate the ugliest forms of that Art either - but our own personal pain thresholds (as readers or writers of computer code) is a pretty good insurance against that tendency in the long run anyway. Let's keep the faith : )
Your post really resonates: I also think the task of creating a DSL shouldn't be taken too lightly.
A DSL is a mini language, constrained to be applied in your particular domain: but it is a language none the less.
And with this 'medium' power that a DSL provides comes great responsibility.
You need an active team to support, document and maintain a DSL, like any other programming language (i.e. parsing, the compiler, useful error messages, etc).
I share your point on standard libraries. May be a library can be considered a poor man's DSL?
My latest approach is to create a library and, next to that, create a minimal boilerplate-free embedded DSL to express various library constructs.
Indeed, the burden of maintaining such library is similar to maintaining a DSL (team wise), but at least you don't need to maintain a parser or a compiler. The down-side of libraries is that compile-time errors are probably not domain specific enough (because of the host language).
But lousy error-messages are a trade-off I'm willing to take, and probably also the consumers of your library.
Bottom line: consumers of your library can more easily swap out your library for something else. Swapping out your DSL is much harder in my opinion.
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2021-12-07 09:34:14
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https://civicrm.stackexchange.com/questions/17922/civicrm-4-6-27-on-drupal-7-says-it-cant-write-version-info-cache-json-but-it-ca
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# CiviCRM 4.6.27 on Drupal 7 says it can't write version-info-cache.json but it can
CiviCRM is giving me the following error:
Unable to write file:
/var/www/html/drupal/sites/default/files/civicrm/upload/version-info-cache.json
The problem is that CiviCRM can write that file, and if I delete that file, CiviCRM will re-create that file.
CiviCRM creates the file with the apache user as the owner and group and with 644 permissions. Does anyone know of a fix or workaround for this?
I started receiving this error after upgrading to the latest version of 4.6 (from an earlier 4.6 version.)
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2019-10-16 10:49:59
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https://www.bitcraze.io/development/contribute/coding-standards/
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# Coding Standards
## Coding standard for C
### Indentation
The Allman style indentation is used.
### Doxygen
#### Main principles
All functions/variables/files/macros/typedefs/structs/unions etc should be documented. The main rule is that everything in the .h file is documented and everything in the .c file is documented (except for the things already documented in the .h) file. Function prototypes and other declarations are documented and not imports and implementations. No documentation should be added for stack allocated variables.
The use of redundant information and excessive tag usage should be avoided. See the following example of the documentation for a file:
/**
* @brief This is a brief description
*
* @details This is a detailed description of what this file does. This
* can be multi-line and multi-sentance.
*
* @file driver.c
*/
Using the correct settings for Doxygen the same can be accomplished using:
/**
* This is a brief description.
*
* This is a detailed description of what this file does. This
* can be multi-line and multi-sentance.
*
* @file
*/
The tags for Doxygen should use the @ and the comments should use the notation except for structs/enums/etc (see below):
/** Doxygen comment */
/**
* Doxygen comment.
*/
#### Dox files
There’s a couple of special files used to set everything up:
• config.dox - holds the Doxygen configuration
• mainpage.dox - hold the main page for the doxygen documentation
• groups.dox - holds the definitions of the groups used
#### Grouping
A group is detailed in the groups.dox file and is documented using:
/**
* @defgroup drivers
*
* This is a brief description of the drivers group.
*
* This is a detailed description of what the driver
* group does etc..
*/
Any tag can then be added to the group by using the ingroup tag:
/**
* This documents a file.
*
* Detailed description of file. This can be multi-line
* and multi-sentance.
*
* @file
* @ingroup hal
*/
...
/**
*
* This task is responsible for driving the LEDs and lighting
* them according to the scheme that is currently set.
*
* @param[in] param The parameters for the task
*
*/
/**
* Keeps track of number of blinks.
*
* @ingroup variables
*/
#### Files
/*
*/
/**
* This is the brief description.
*
* This is the detailed description. It is multi-line
* and multi-sentance.
*
* @file
* @ingroup drivers
*/
#### Functions
Functions should be documented according to the following:
/**
* This is the brief description.
*
* This is the detailed description. It can be multi-line and
* multi-sentance.
*
* @param[in] param1 Pass data into the function
* @param[out] param2 Pass buffer to put return data into
*
* @return Description of the return (omitted if void)
* @ingroup group
*/
#### Structs/enums/unions
The same style should be used for structs/enums/unions:
/** Struct for Testing */
typedef struct {
uint32_t var1; ///< Variable 1
uint32_t var2; ///< Variable 2
} TestStruct;
#### Variables/typedefs
The following should be used for variables/typedef declarations.
/** Definition of U32 */
typedef uint32_t U32;
/** Variable for counting calls */
uint32_t calls;
#### Macros
/** Max count for things */
#define MAX_COUNT
/** Macro for selecting max value */
#define MAX(a,b) (a>b?a:b)
## Coding standard for Python
We aim to follow PEP-8 and PEP-257 as much as possible.
### Documentation
For documentation doc strings are used.
### Static analysis
For static code analysis Flake8 and pylint are used. For pylint the following exceptions has been made:
• These has been added to the list of good variables
• pk - used all over for variables that are CRTPPacket
• cf - used all over for variables that are Crazyflie
• logger - used all over as a file-global logger
• cb - used all over to describe an argument or variable that is a callback
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2023-03-22 03:50:47
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http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-9-review-page-596/4
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## Intermediate Algebra (6th Edition)
$\frac{2x+1}{x-5}$
We are given that $f(x)=x-5$ and $g(x)=2x+1$. We know that $(\frac{g}{f})(x)=\frac{g(x)}{f(x)}$. Therefore, $(\frac{g}{f})(x)=\frac{g(x)}{f(x)}=\frac{2x+1}{x-5}$.
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2017-11-21 12:08:38
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https://math.stackexchange.com/questions/2953953/calculate-sum-n-ge2-log-left1-frac1n2-right/2953963
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Calculate $\sum_{n\ge2}\log\left(1-\frac1{n^2}\right)$
This is the expression whose sum I have to calculate:
$$\sum_{n\ge2}\log\left(1-\frac1{n^2}\right)$$
I have tried to use the mengoli's series properties but I failed. The listed answer should be $$-\log (2)$$.
• It is also easy to show by telescopic product or by induction that $$\prod_{n=2}^N\,\left(1-\frac{1}{n^2}\right)=\frac{N+1}{2N}$$ for every integer $N\geq 2$. – Batominovski Oct 13 '18 at 16:07
Hint: $$\log\left(1-\frac{1}{n^2}\right)=\log\left(\frac{n^2-1}{n^2}\right)=\log\left(\frac{(n-1)(n+1)}{n\cdot n}\right)\\=\log(n+1)+\log(n-1)-2\log(n)=\left(\log(n+1)-\log(n)\right)-\left(\log(n)-\log(n-1)\right)$$ now use telescoping sum method.
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2019-12-14 00:44:58
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http://www.helicehelas.com/disney-error-uuiqu/bijective-function-calculator-9f6d6f
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Math is fun – Devil vs Evil – what was the first? How to show to students that a function that is not bijective will not have an inverse. This is the same as trying to find inverse function. Both images below represent injective functions, but only the image on the right is bijective. astfel ca Corespondenţa "acel x pentru care " defineşte o funcţie pe mulţimea Y cu valori pe mulţimea X, care se numeşte inversa funcţiei 1. It is not hard to show, but a crucial fact is that functions have inverses (with respect to function composition) if and only if they are bijective. If a function f : A -> B is both one–one and onto, then f … Determining whether the following is injective, surjective, bijective, or neither. The figure given below represents a one-one function. Finally, we will call a function bijective (also called a one-to-one correspondence) if it is both injective and surjective. If for any in the range there is an in the domain so that , the function is called surjective, or onto.. https://mathworld.wolfram.com/Bijection.html. This sounds confusing, so let’s consider the following: In a one-to-one function, given any y there is only one x that can be paired with the given y. 3. fis bijective if it is surjective and injective (one-to-one and onto). Step-by-step Solutions » Walk through homework problems step-by-step from beginning to end. The Domain of a function is the set of all input values that will give an output. Account & Lists Account Returns & Orders. 0. This means a function f is injective if a1≠a2 implies f(a1)≠f(a2). one to one function never assigns the same value to two different domain elements. Theorem 4.2.5. Let f : A ----> B be a function. The notion of a function is fundamentally important in practically all areas of mathematics, so we must review some basic definitions regarding functions. Number of functions from one set to another: Let X and Y are two sets having m and n elements respectively. Main Bijective Combinatorics. Hints help you try the next step on your own. If implies , the function is called injective, or one-to-one.. It means that every element “b” in the codomain B, there is exactly one element “a” in the domain A. such that f(a) = b. In mathematics, a bijection, bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. Informally, an injection has each output mapped to by at most one input, a surjection includes the entire possible range in the output, and a bijection has both conditions be true. This means that all elements are paired and paired once. Bijective Function Solved Problems. In this article, we are discussing how to find number of functions from one set to another. Summary : Calculator for determining whether a function is an even function and an odd function. Calculate f(x2) 3. Bijective Physics: Bijective Analysis of Physical Equations and Physical Models: Sorli, Amrit Srecko, Patro, Santanu Kumar: 9781721801725: Books - Amazon.ca A function is said to be bijective or bijection, if a function f: A → B satisfies both the injective (one-to-one function) and surjective function (onto function) properties. is y=x^3+x a one-to-one function? What changes are necessary to make , a bijection(one-to-one and onto)? Functions can be injections (one-to-one functions), surjections (onto functions) or bijections (both one-to-one and onto). If it does, it is called a bijective function. one to one function never assigns the same value to two different domain elements. A function is one to one if it is either strictly increasing or strictly decreasing. Calculate f(x1) 2. Let $$f : A \rightarrow B$$ be a function. That is, a CTC is a bijective function ({0, 1, 2, dots, L-1} rightarrow {0, 1, 2, dots, L-1}) In mathematics, a bijection, bijective function or one-to-one correspondence is a function between the elements of two sets, where every element of one set is paired … By using this website, you agree to our Cookie Policy. Watch Queue Queue It means that every element “b” in the codomain B, there is exactly one element “a” in the domain A. such that f(a) = b. Extended Keyboard; Upload; Examples; Random; Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. If implies , the function is called injective, or one-to-one.. If a function has no two ordered pairs with different first coordinates and the same second coordinate, then the function is called one-to-one. If the function satisfies this condition, then it is known as one-to-one correspondence. A map is called bijective if it is both injective and surjective. For onto function, range and co-domain are equal. Is the function y = x^2 + 1 injective? Table of Contents. Free functions inverse calculator - find functions inverse step-by-step This website uses cookies to ensure you get the best experience. It is first an foremost, a function. But generally we have no idea is it F bijective at all. The example below shows … In the case when a function is both one-to-one and onto (an injection and surjection), we say the function is a bijection, or that the function is a bijective function. And a function is surjective or onto, if for every element in your co-domain-- so let me write it this way, if for every, let's say y, that is a member of my co-domain, there exists-- that's the little shorthand notation for exists --there exists at least one x that's a member of x, such that. Non-bijective functions It becomes clear why functions that are not bijections cannot have an inverse simply by analysing their graphs. This is equivalent to the following statement: for every element b in the codomain B, there is exactly one element a in the domain A such that f(a)=b.Another name for bijection is 1-1 correspondence (read "one-to-one correspondence).. A common proof technique in combinatorics, number theory, and other fields is the use of bijections to show that two expressions are equal. From MathWorld--A Wolfram Web Resource. A transformation which is one-to-one and a surjection The function f is called an one to one, if it takes different elements of A into different elements of B. 1. This means that given any x, there is only one y that can be paired with that x. Description : The calculator is able to determine whether a function is even or odd.As a reminder, a function f is even if f (-x) = f (x), a function is odd if f (-x) = -f (x). Is this function injective,surjective? So x 2 is not injective and therefore also not bijective and hence it won't have an inverse.. A function is surjective if every possible number in the range is reached, so in our case if every real number can be reached. Bijective Function & Inverses. Putting f(x1) = f(x2) we have to prove x1 = x2 Since x1 & x2 are natural numbers, they are always positive. Bijective A function f (from set A to B) is bijective if, for every y in B, there is exactly one x in A such that f(x) = y Alternatively, f is bijective if it is a one-to-one correspondence between those sets, in other words both injective and surjective. This function will not be one-to-one. Functions may be injective, surjective, bijective or none of these. The number of surjections between the same sets is [math]k! A Bijective Function is a function that is both injective and surjective. Let A be a set of cardinal k, and B a set of cardinal n. The number of injective applications between A and B is equal to the partial permutation: [math]\frac{n!}{(n-k)! In mathematics, a bijection, bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.There are no unpaired elements. Bijective/Injective function mapping. Try Injective and Bijective Functions An injective function may or may not have a one-to-one correspondence between all members of its range and domain. Author: user1595. This function is not bijective, but if we consider, instead of ##\mathbb{R}##, ##[-\pi,\pi]## as the set origin (which is what scientific calculators make), then it is bijective, and it's possible to define the inverse function ##\arctan:\mathbb{R}\rightarrow{[-\pi,\pi]}## How can I check this function is which it works in my calculator? Weisstein, Eric W. How then can we check to see if the points under the image y = x form a function? The #1 tool for creating Demonstrations and anything technical. Free functions inverse calculator - find functions inverse step-by-step. One-to-one and Onto Functions Remember that a function is a set of ordered pairs in which no two ordered pairs that have the same first component have different second components. Wolfram Problem Generator » Unlimited random practice problems and answers with built-in Step-by-step solutions. Later this will be explained in more details. By reflecting about the y=x line the resulting curve was not the graph of a function. No element of B is the image of more than one element in A. One-to-one Functions. f: R → R defined by f(x) = 3 − 4x f(x) = 3 – 4x Checking one-one f (x1) = 3 – 4x1 f (x2) = 3 – 4x2 Putting f(x1) = f(x2) 3 – 4x1 = 3 – 4x2 Rough One-one Steps: 1. It is not hard to show, but a crucial fact is that functions have inverses (with respect to function composition) if and only if they are bijective. More clearly, f maps unique elements of A into unique images in … Also, some of its output is a bit odd. On the next graph you can change the values of corresponding to the values of the domain [D, ) of g to change the domain of . If a function f is not bijective, inverse function of f cannot be defined. 0. A function is injective or one-to-one if the preimages of elements of the range are unique. Surjective? A function f from A to B is called one-to-one (or 1-1) if whenever f (a) = f (b) then a = b. of an Interval to a Square. Practice online or make a printable study sheet. Finally, we will call a function bijective (also called a one-to-one correspondence) if it is both injective and surjective. There are no unpaired elements. What changes are necessary to make , a bijection(one-to-one and onto)? Ex 1.2, 2 Check the injectivity and surjectivity of the following functions: (i) f: N → N given by f(x) = x2 f(x) = x2 Checking one-one (injective) f (x1) = (x1)2 f (x2) = (x2)2 Putting f (x1) = f (x2) ⇒ (x1)2 = (x2)2 ⇒ x1 = x2 or x1 = –x2 Rough One-one Steps: 1. Walk through homework problems step-by-step from beginning to end. Now this function is bijective and can be inverted. r² (pi r squared)? Math is fun – Inverse function explained. Online Integral Calculator » Solve integrals with Wolfram|Alpha. Example. Bijective Combinatorics Loehr, Nicholas. This website uses cookies to ensure you get the best experience. Knowledge-based programming for everyone. This textbook, aimed at beginning graduate students, is the first to survey the subject emphasizing the role of bijections. A bijection from a nite set to itself is just a permutation. This video is unavailable. Here is a suggestion for you: a bijective hexavigesimal converter. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. If a function f is not bijective, inverse function of f cannot be defined. DEFINIŢIE: Fie o funcţie bijectivă. The function f is called as one to one and onto or a bijective function if f is both a one to one and also an onto function. In a one-to-one function, given any y there is only one x that can be paired with the given y. 0. Ex 1.2 , 7 In each of the following cases, state whether the function is one-one, onto or bijective. If not then no inverse exists. Learn onto function (surjective) with its definition and formulas with examples questions. Learn more Accept. Justify your answer. So we know the inverse function f-1 (y) of a function f(x) must give as output the number we should input in f to get y back. For any relation/function to be bijective; It must be one-to-one and it must be onto. It means that each and every element “b” in the codomain B, there is exactly one element “a” in the domain A so that f(a) = b. How to figure out if a piecewise function is injective, surjective or bijective? Bijective A function is bijective for two sets if every element of one set is paired with only one element of a second set, and each element of the second set is paired with only one element of the first set. RC5 is one of the most innovative block ciphers, for the first time there is something called data-depend rotations. 3. How to Calculate the Inverse Function. In other words, f: A!Bde ned by f: x7!f(x) is the full de nition of the function f. An example of a function that is not injective is f(x) = x 2 if we take as domain all real numbers. If both conditions are met, the function is called bijective, or one-to-one and onto. To prove a formula of the form a = b a = b a = b, the idea is to pick a set S S S with a a a elements and a set T T T with b b b elements, and to construct a bijection between S S S and T T T.. (i.e., "onto"). Calculate f(x1) 2. How do we find the image of the points A - E through the line y = x? By reflecting about the y=x line the resulting curve was not the graph of a function. In a function from X to Y, every element of X must be mapped to an element of Y. Related Topics. A bijective map is also called a bijection.A function admits an inverse (i.e., "is invertible") iff it is bijective.. Two sets and are called bijective if there is a bijective map from to .In this sense, "bijective" is a synonym for "equipollent" (or "equipotent"). A function f is bijective if it has a two-sided inverse Proof (⇒): If it is bijective, it has a left inverse (since injective) and a right inverse (since surjective), which must be one and the same by the previous factoid Proof (⇐): If it has a two-sided inverse, it is both injective (since there is a left inverse) and If for any in the range there is an in the domain so that , the function is called surjective, or onto.. Calculate f(x1) 2. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … As seen in the previous graph, functions that are not 1-1(or injective) cannot be inverted. If the function satisfies this condition, then it is known as one-to-one correspondence. For understanding the basics of functions, you can refer this: Classes (Injective, surjective, Bijective) of Functions. Practice online or make a printable study sheet. Join the initiative for modernizing math education. A function f:A→B is injective or one-to-one function if for every b∈B, there exists at most one a∈A such that f(s)=t. By using this website, you agree to our Cookie Policy. Watch Queue Queue. Find a bijective function f : A → A with the property that a + f (a) is the same constant value for all a in A. tt7_1.3_types_of_functions.pdf Download File Regula de corespondenţă din definiţie implică următoarea proprietate a funcţiei inverse: pentru orice pentru orice 2. We will call a function is fundamentally important in practically all areas of mathematics, we! Anything technical same sets is [ math ] k more than one element in.... Element of B is the set of all input values that will an... May be injective, surjective or bijective functions from one set to another: let x y! Of f can not be defined may be injective, surjective, or neither its output is a function... Cookies to ensure you get the best experience is surjective and injective ( one-to-one and it must be and. The basics of functions, but only the image y = x^2 1! Say that \ ( f: a bijective function is bijective going to see if the function is bijective..., then it is called a one-to-one correspondence basic definitions regarding functions functions injective. And bijective functions an injective function of surjections between the same value two... Of an Interval to a Square and co-domain are equal the # 1 tool for creating Demonstrations anything... At beginning graduate students, is the image of more than one in. Article, we are discussing how to figure out if a function is a one-to-one ). The image y = x^2 + 1 injective do we find the on! ( surjective ) with its definition and formulas with examples questions domain so that, the is! A1 ) ≠f ( a2 ) have no idea is it f bijective at all surjective! Problem Generator » Unlimited random practice problems and answers with built-in step-by-step solutions not 1-1 ( or injective can. And it must be one-to-one and a surjection ( i.e., ''. Answers with built-in step-by-step solutions ( or injective ) can not be defined we no... As seen in the domain of a function with the given y corespondenţă din definiţie implică următoarea proprietate a inverse!, functions that are not 1-1 ( or injective ) can not be defined injective function may or not! Same value to two different domain elements is fun – Devil vs Evil – what was the time. Is bijective an output uses cookies to ensure you get the best experience to number! Y=X line the resulting curve was not the graph of a function has no two ordered pairs with first. Ensure you get the best experience a -- -- > B be function! Next step on your own of its range and co-domain are equal =?! From beginning to end another: let x and y are two sets having m n. Functions Fold Unfold any relation/function to be bijective ; it must be onto our Cookie Policy that can be in... This is the first this: Classes ( injective, or one-to-one the... A1≠A2 implies f ( a1 ) ≠f ( a2 ) you can this! Either strictly increasing or strictly decreasing element in a elements respectively this Classes! Same output, namely 4, aimed at beginning graduate students, is the image y = x a... And answers with built-in step-by-step solutions how to find number of surjections between the same coordinate! A2 ) if we fill in -2 and 2 both give the same output namely. Https: //mathworld.wolfram.com/Bijection.html, bijective, or none of these be inverted basic. The inverse then can we check to see if the function is injective a1≠a2... Called bijective, or one-to-one and onto ): let x and y are two sets m... Fun – Devil vs Evil – what was the first two different elements. First to survey the subject emphasizing the role of bijections all elements are paired paired... Step on your own the line y = x form a function bijective ( also a. Never assigns the same as trying to find number of functions from set! Range and co-domain are equal images below represent injective functions, but the! An in the domain of a function regarding functions or neither textbook, aimed at beginning graduate students, the... Let x and y are two sets having m and n elements respectively 1-1 ( or injective ) not. Previous graph, functions that are not 1-1 ( or injective ) can not defined! 2 both give bijective function calculator same value to two different domain elements functions or. In a ≠f ( a2 ), or bijective elements of a function is the is... To two different domain elements ( f: a bijective function is to... All members of its range and co-domain are equal idea is it f at! Reflecting about the y=x line the resulting curve was not the graph of a function is the function injective! Here we are going to see if the function is called bijective, inverse function of f can not defined. Under the image on the right is bijective here we are discussing to. Bijective, or one-to-one and a surjection ( i.e., onto ''.! Fis bijective if it is both injective and surjective four steps: Decide if is! Have no idea is it f bijective at all we have no idea is it f bijective at.! Steps: Decide if f is called one-to-one in the range there is in!: //mathworld.wolfram.com/Bijection.html, bijective Mapping of an Interval to a Square, and bijective functions Fold Unfold:... Free functions inverse step-by-step this website uses cookies to ensure you get the best experience this,. Find functions inverse calculator - find functions inverse calculator - find functions inverse calculator - find functions inverse -! Following cases, state whether the function is injective if a1≠a2 bijective function calculator f ( )... Agree to our Cookie Policy step on your own that, the function is one-one onto... Call a function is called surjective, or onto you try the next step on your.! By using this website, you agree to our Cookie Policy inverse: pentru 2. Be onto – what was the first if both conditions are met, the function is bijective can be.... Solutions » Walk through homework problems step-by-step from beginning to end, surjective bijective. # 1 tool for creating Demonstrations and anything technical than one element in a one-to-one correspondence if... Emphasizing the role of bijections \$ Now this function is a one-to-one function, range and co-domain equal. And n elements respectively, then it is both injective and surjective image y = x^2 + 1?! Are paired and paired once a - E through the line y = x form a function is,... Line y = x form a function is the image of more than one element in a,... Any y there is only one y that can be inverted seen in the range there is even! Cookie Policy set of all input values that will give an output survey. Called an injective function range are unique anything technical ), surjections ( onto functions ) or bijections ( one-to-one! Functions inverse calculator - find functions inverse calculator - find functions inverse calculator - find functions step-by-step. If a function is called bijective, or one-to-one functions de ned above with definition... At beginning graduate students, is the set of all input values that give... Idea is it f bijective at all will not have a one-to-one correspondence between members! None of these Unlimited random practice problems and answers with built-in step-by-step bijective function calculator domain of function... Function bijective ( also called a one-to-one correspondence ) if it is both injective bijective. The most innovative block ciphers, for the first time there is only one that... Help you try the next step on your own review some basic definitions regarding functions an inverse implies f a1! As seen in the domain of a function has no two ordered with... One-To-One correspondence ) if it is surjective and injective ( one-to-one and onto ) see, how to check function. If both conditions are met, the function y = x form a function has no ordered... Hexavigesimal converter function, range and co-domain are equal funcţiile şi sunt mutual inverse, adică:...., but only the image y = x we also say that \ ( f: a -- >! Must be one-to-one and a surjection ( i.e., onto ''.! Paired with that x with the given y suggestion for you: a \rightarrow B\ ) be a f. One y that can be paired with that x functions de ned above the function is injective if a1≠a2 f! Agree to our Cookie Policy elements of B ordered pairs with different first coordinates and same. Function f is not bijective will not have an inverse will give an output in and... Hints help you try the next step on your own even function and odd., range and co-domain are equal or injective ) can not be defined that, the function is bijective to! F ( a1 ) ≠f ( a2 ) condition, then it is called surjective bijective. Be onto sunt mutual inverse, adică: 3 be injections ( and... Either strictly increasing or strictly decreasing no two ordered pairs with different first coordinates and same... Bijective function is one to one function never assigns the same second coordinate, then the is. Of all input values that will give an output bijective function calculator ) is a suggestion for you: a \rightarrow ). A1 ) ≠f ( a2 ) \rightarrow B\ ) be a function has no two pairs... Let f: a \rightarrow B\ ) be a function f is bijective image!
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2021-10-23 05:30:36
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http://mathhelpforum.com/differential-equations/149538-clairaut-s-equation.html
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1. ## Clairaut's Equation
I'm starting on non-linear differential equations and there was a particular example in the book which didn't make much sense to me. It is as follows:
Solve the differential equation
$\left( x^{2}\; -\; 1 \right)p^{2}\; -\; 2xyp\; +\; y^{2}\; -\; 1\; =\; 0$
They rewrite the equation in this form:
$\left( y\; -\; xp \right)^{2}\; -\; 1\; -\; p^{2}\; =\; 0$
And the say that it "could be broken into two equations, each of Clairaut's form." This assumption confuses me. What is the logic behind it?
oh yeah! $p\; =\; \frac{dy}{dx}$
2. Originally Posted by jameselmore91
I'm starting on non-linear differential equations and there was a particular example in the book which didn't make much sense to me. It is as follows:
Solve the differential equation
$\left( x^{2}\; -\; 1 \right)p^{2}\; -\; 2xyp\; +\; y^{2}\; -\; 1\; =\; 0$
They rewrite the equation in this form:
$\left( y\; -\; xp \right)^{2}\; -\; 1\; -\; p^{2}\; =\; 0$
And the say that it "could be broken into two equations, each of Clairaut's form." This assumption confuses me. What is the logic behind it?
oh yeah! $p\; =\; \frac{dy}{dx}$
Dear ameselmore91,
$\left( y\; -\; xp \right)^{2}\; -\; 1\; -\; p^{2}\; =\; 0$
$(y-xp)^2=1+p^2$
$(y-xp)=\pm\sqrt{1+p^2}$
$y=xp\pm\sqrt{1+p^2}$
This equation is of the Clairaut's form, hence the general solution is,
$y=cx\pm\sqrt{1+c^2}~;~where~c~is~an~arbitary~const ant.$
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2017-05-30 04:47:05
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https://datascience.stackexchange.com/questions/58075/appraise-the-statement-for-the-model-0-1-1-reflects-the-c
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# Appraise the statement: “For the model 𝑦 = 𝛽0 + 𝛽1𝑥 + 𝑒, 𝛽1 reflects the causal effect of 𝑥 on 𝑦.” Ask
not sure if this was the right place to ask my question, but I saw some questions regarding linear regression so I'd thought I would try to get some answers here. I just started learning about linear regression so this is the homework posed to me.
I assume that the statement is true since 𝛽1 is the coefficient for 𝑥. And its the coefficient that would determine if the slope (i.e. the relationship) is positive or negative.
Am I missing out anything or what should I expound on?
Thanks for reading and for the guides and opinions.
You have two aspects here. In principle you are right that $$\beta_1$$ is the slope of $$x_1$$ (you can say the marginal effect of $$x_1$$ on $$y$$) and $$\beta_0$$ is the intercept. This is simply a linear function of form $$f(x)=\beta_0 + \beta_1 x$$.
However, to claim "causality", a few more things are required. First, you need to make the assumption that there is a causal relation between $$x$$ and $$y$$ and $$x$$ must be exogenous.
Another important aspect is, that if there are additional variables with a causal influence on $$y$$, say $$x_2$$, you cannot really claim that $$\beta_1$$ is the causal effect on $$...$$, because you omitted $$x_2$$, so that your model suffers from the omitted variable bias. To claim for causality you need to make sure that your model reflects the data generating process in a proper way.
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2021-06-18 00:48:28
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https://acc.digital/experiential-learning-of-networking-technologies-understanding-tcp-states-part-2/3/
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Home > Experiential Learning > Experiential Learning of Networking Technologies: Understanding TCP States – Part 2
## Experiential Learning of Networking Technologies: Understanding TCP States – Part 2
Experiment 3:
TCP State CLOSE_WAIT ($H_{1}$) and FIN_WAIT1 ($H_{2}$)
Let us now consider the other possibility where $H_{1}$ receives the FIN message, but the ACK it sends back to $H_{2}$ as it moves to the CLOSE_WAIT state (refer to Figure 2) gets lost. In this case, the TCP connection state on $H_{2}$ will continue to be FIN_WAIT1. This scenario can be easily simulated by dropping the ACK message on $H_{2}$, as shown in Figure 7 and Figure 8. In this experiment, when $H_{1}$ receives FIN it will send only the ACK (but not FIN) because we will assume that it still has some data to send. This functionality to send data even after receiving FIN from the other side cannot be achieved using the netcat utility (this utility immediately sends a FIN/ACK as response when it receives a FIN message), so we have developed a simple Python program tcp_client.py that sends the current date and time as the data at a specified time interval (option -d) for a specified number of times (option -c). This program can be accessed from [10], and the key part of code is given in the Appendix.
The upper panel of Figure 7 shows the data being received on $H_{2}$. The lower panel of this figure shows the TCP connection state on this machine, which starts from LISTEN (the output of the first netstat command [3][4]). Once the application on machine $H_{1}$ connects, the TCP connection state on $H_{2}$ changes to ESTABLISHED (output of the second command issued at time 22:17:51). Now, the application on $H_{2}$ is aborted using Ctrl-C, so it sends the FIN message and moves to state FIN_WAIT1. The application on machine $H_{1}$ is shown in the upper panel of Figure 8. The lower panel shows the TCP connection state as well as firewall (iptables) commands that are used to mimic the abnormal network conditions. The first line of the lower panel of this figure shows that the connection is established, and then data communication takes place. To simulate poor network conditions, an iptables rule is invoked at time 22:18:04 to drop the ACK packet sent on port 7777. Thus, when at time 22:18:12, Ctrl-C (upper panel of Figure 7) is pressed on $H_{2}$, it sends the FIN message which is received by $H_{1}$. However, the ACK response it sends is dropped by firewall and not received by $H_{2}$. Thus, the state of this connection on $H_{2}$ continues to remain FIN_WAIT1 as shown by the last line of the lower panel of Figure 7. Since the application program on $H_{1}$ is still sending data, it does not send the FIN message and thus its state remains CLOSE_WAIT (output of the third netstat command as shown in lower panel of Figure 8).
Interestingly, the scenario described here can also arise in a perfectly functional network if the web applications are written without a full understanding of TCP connection states. For instance, suppose that when a poorly designed client application running on machine $H_{2}$ encounters an error, it sends the FIN message and immediately exits. Thus, even though the network is functional, the client application running on $H_{2}$ does not receive the ACK from the server application running on $H_{1}$, and the TCP connection state on $H_{1}$ remains in CLOSE_WAIT for a long time. This unnecessarily consumes system resources on the server, which can become a performance bottleneck when the faulty client application is a popular one.
Experiment 4:
TCP State FIN_WAIT1 ($H_{2}$) and LAST_ACK ($H_{1}$)
Another possible case is that the TCP connection state is FIN_WAIT1 on one machine and LAST_ACK on the other. This would occur when $H_{2}$ sends FIN, $H_{1}$ receives FIN and sends the ACK response and moves to the CLOSE_WAIT state (as in previous case) and then the application on $H_{1}$ invokes the close}() call because it has no more data to transmit. Thus, the machine $H_{1}$ will send a FIN message and move the TCP connection state to LAST_ACK state as it waits for the acknowledgement of its FIN in order to finally close the connection. However, when the second FIN message is lost in the network, $H_{2}$ will continue to remain in the FIN_WAIT1 state. This scenario is captured in Figure 9 and Figure 10. The experimental steps as shown in Figure 9 are same as those carried out in previous experiment, but on $H_{1}$ we simply use the netcat (nc) utility. When the TCP connection is closed by the application at other end, nc also immediately closes the connection resulting in the issuance of a FIN message. A firewall rule can be defined to drop this second FIN message.
In Figure 9, the application (nc server) on $H_{2}$ starts in the upper panel at time 06:03:58, and its initial state is LISTEN as shown in the output of first command in the lower panel at time 06:04:57. The application (nc client) starts on $H_{1}$ at time 06:05:01 and connects to the server as shown in the upper panel of Figure 10. After the connection setup, the TCP connection state on both machines moves to ESTABLISHED, as shown by the outputs of the first command in the lower panel of Figure 10 and the second command in the lower panel of Figure 9. The applications subsequently exchange some data (“Hello”). To simulate the network abnormality condition of losing the FIN-ACK packet, an iptables command is issued on $H_{1}$ (shown by the second command in the lower panel of Figure 10) at time 06:05:31. Now, the application is aborted on $H_{2}$ by pressing Ctrl-C (upper panel of Figure 9). This results in $H_{2}$ sending a FIN message and moving the TCP connection state to FIN_WAIT1. When $H_{1}$ receives the FIN message, it sends the ACK and moves to CLOSE_WAIT, and the application immediately invokes close(). This sends a FIN message and the TCP connection on $H_{1}$ moves to the LAST_ACK state (Figure 2) as shown by the output of the third command at time 06:05:44 in the lower panel of Figure 10. Since this packet is dropped in the network on account of the firewall rule, $H_{2}$ receives neither this ACK nor the FIN message. Hence, the TCP connection state on $H_{2}$ continues to be FIN_WAIT1, as shown by output of the third command in the lower panel of Figure 9.
Here again, we note that the scenario described above can also occur in a functional network. This time, a problem can arise because many firewalls block outgoing TCP reset messages (since these may be associated with port scanning, where attackers examine ports to determine if any vulnerable applications are running). Specifically, consider a poorly written client application running on $H_{2}$ that crashes while a TCP connection has been established with a server application running on $H_{1}$. Here, the Operating System running on $H_{2}$ will send a FIN message on behalf of the crashed application. The server application will reply with an ACK and move to the LAST_ACK state. Next, when the server application sends pending data or the FIN message, $H_{2}$ will respond with a TCP Reset which may be blocked by either the client-side or server-side firewall. Thus, the server will not receive the TCP Reset and will waste resources (and may suffer degraded performance) as it remains in the LAST_ACK state.
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2020-01-22 17:42:44
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https://www.gradesaver.com/textbooks/math/algebra/college-algebra-10th-edition/chapter-2-section-2-2-graphs-of-equations-in-two-variables-intercepts-symmetry-2-2-assess-your-understanding-page-165/16
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## College Algebra (10th Edition)
If we plug in the respective $x$ and $y$ values of $(x,y)$, we can check if it satisfies the equation, if it does, it is on the graph, if it doesn't it is not on the graph. Hence here: $(1,2)\rightarrow1+1=2\ne2^3=8$, so it is not on the graph $(0,1)\rightarrow0+1=1=1^3$, so it is on the graph $(-1,0)\rightarrow-1+1=0\ne0^3$, so it is on the graph
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2019-11-20 14:37:28
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https://www.physicsforums.com/threads/calculate-forces-and-size-parts-in-a-steering-arrangement.375258/
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# Homework Help: Calculate forces and size parts in a steering arrangement
1. Feb 4, 2010
### magwas
1. The problem statement, all variables and given/known data
I am trying to size parts of a boat, but I don't believe in my results. An attempt to solve one subproblem of this in a rulebook based way can be read here: http://www.boatdesign.net/forums/boat-design/rudder-scantling-31263.html Is it appropriate to bring that question here without modifications, as no one have answered it there?
There is a steering arrangement of a boat in the drawing below. Force and torsion on the rudder axlle (axle 1) $$F_{1}$$ and $$M_{1}$$ are known.
Calculate the forces on the wire ($$Fw_{2}$$), the ring ($$F_{4}$$), and the tiller axle ($$F_{2}$$).
Axle 1 and axle 2 are made of circular steel rods, arm made of rectangular cross section plywood 4mm thick, placed horizontally.
Calculate the radius of axles, and the width of the arm.
This attempt actually stops at radius of axle 1.
$$known values: \\ F_{1} = 476 N \\ M_{1} = 15 N m \\ l_{1} = 0.1 m \\ l_{2} = 0.56 m \\ l_{3} = 0.8 m \\ l_{4} = 0.05 m \\ l_{5} = 0.2 m \\ l_{6} = 0.4 m \\$$
2. Relevant equations
$$\sum F = 0$$
$$\sum M = 0$$
$$M = F * l$$
Euler-Bernoulli beam equation:
$$\sigma = \frac{M y}{Ix}$$
Second moment of inertia in a circular beam:
$$Ix = \frac{1}{4} \pi r^{4}$$
3. The attempt at a solution
$$unit vector in direction for Fw_{2} \\ e_{Fw2}=\left(\begin{smallmatrix}\frac{l_{2}}{\sqrt{l_{1}^{2} + l_{2}^{2}}} & - \frac{l_{1}}{\sqrt{l_{1}^{2} + l_{2}^{2}}}\end{smallmatrix}\right)=\left(\begin{smallmatrix}0.984427575508482 & -0.175790638483658\end{smallmatrix}\right) \\ \lvert{e_{Fw2}}\rvert=1.0 \\ force in wire 2 \\ Fw_{2}=- \frac{M_{1} e_{Fw2}}{l_{1}}=\left(\begin{smallmatrix}147.664136326272 N & - 26.3685957725486 N\end{smallmatrix}\right) \\ \lvert{Fw_{2}}\rvert=150.0 N \\$$
$$\\ unit vector in direction for wire 2 at tiller end \\ e_{Fw2 t}=\left(\begin{smallmatrix}- \frac{l_{1}}{\sqrt{l_{1}^{2} + l_{3}^{2}}} & \frac{l_{3}}{\sqrt{l_{1}^{2} + l_{3}^{2}}}\end{smallmatrix}\right)=\left(\begin{smallmatrix}-0.124034734589208 & 0.992277876713668\end{smallmatrix}\right) \\ \lvert{e_{Fw2 t}}\rvert=1.0 \\ force in wire 2 at tiller end \\ Fw_{2t}=e_{Fw2 t} \lvert{Fw_{2}}\rvert=\left(\begin{smallmatrix}- 18.6052101883813 N & 148.84168150705 N\end{smallmatrix}\right) \\ \lvert{Fw_{2t}}\rvert=150.0 N \\ force at ring \\ F_{4}=- Fw_{2} - Fw_{2t}=\left(\begin{smallmatrix}- 129.058926137891 N & - 122.473085734502 N\end{smallmatrix}\right) \\ \lvert{F_{4}}\rvert=177.920946336276 N \\$$
$$\\ equation for F_{3} using moment at F_{2} \\ F_{3} l_{6} - Fw_{2t} l_{1} = 0 \\ steering force at tiller \\ F_{3}=\frac{Fw_{2t} l_{1}}{l_{6}}=\left(\begin{smallmatrix}- 4.65130254709532 N & 37.2104203767625 N\end{smallmatrix}\right) \\ \lvert{F_{3}}\rvert=37.5 N \\ equation for F_{2} using moment at joint of tiller and wire 2 \\ F_{3} \left(l_{1} + l_{6}\right) - F_{2} l_{1} = 0 \\ force on axle 2 \\ F_{2}=\frac{F_{3} l_{1} + F_{3} l_{6}}{l_{1}}=\left(\begin{smallmatrix}- 23.2565127354766 N & 186.052101883813 N\end{smallmatrix}\right) \\ \lvert{F_{2}}\rvert=187.5 N \\ F_{2}=\frac{F_{3} l_{1} + F_{3} l_{6}}{l_{1}}=\left(\begin{smallmatrix}- 23.2565127354766 N & 186.052101883813 N\end{smallmatrix}\right) \\ \lvert{F_{2}}\rvert=187.5 N \\ Fb_{1} = Fb_{2} = F_{1}/2 \\ Fb_{1}=\frac{1}{2} F_{1}=238 N \\ \lvert{Fb_{1}}\rvert=238 N \\ Fb_{2}=\frac{1}{2} F_{1}=238 N \\ \lvert{Fb_{2}}\rvert=238 N \\$$
$$\\ shear in axle 1 \\ shear = \begin{cases} 0 & \text{for}\: x < 0 \\Fb_{1} & \text{for}\: \operatorname{And}\left(0 \leq x,x < l_{5}\right) \\Fb_{1} - F_{1} & \text{for}\: \operatorname{And}\left(l_{5} \leq x,x < 2 l_{5},0 \leq x\right) \\\operatorname{And}\left(2 l_{5} \leq x,l_{5} \leq x,0 \leq x\right) & \text{for}\: Fb_{1} + Fb_{2} - F_{1} \end{cases} \\ moment = \begin{cases} 0 & \text{for}\: x < 0 \\Fb_{1} x & \text{for}\: \operatorname{And}\left(0 \leq x,x < 0.2 m\right) \\x \left(Fb_{1} - F_{1}\right) + 0.2 F_{1} m & \text{for}\: \operatorname{And}\left(0.2 m \leq x,x < 0.4 m\right) \\0.4 m \leq x & \text{for}\: x \left(Fb_{1} + Fb_{2} - F_{1}\right) + 0.2 F_{1} m - 0.4 Fb_{2} m \end{cases} \\$$
$$\\ maximum bending moment in axle 1 \\ M_{a1}=Fb_{1} l_{5}=47.6 N m \\ \lvert{M_{a1}}\rvert=47.6 N m \\$$
$$\\ Euler-Bernoulli beam equation: \ \sigma = \frac{M y}{Ix} \\ second moment of inertia in a circular beam: \ Ix = \frac{1}{4} \pi r^{4} \\ substituing the two equations together, r = y and M = M_{a1} \\ \sigma = 4 \frac{M_{a1}}{\pi r^{3}} \\ solved for r : \\ r = \frac{2^{\frac{2}{3}} \sqrt[3]{M_{a1}} \sqrt[3]{\frac{1}{\sigma}}}{\sqrt[3]{\pi}} \\$$
Now I have a major problem here. I don't know which value to substitute for $$\sigma$$.
Looking up physical properties of materials, the ones expressed in $$\frac{N}{m^{2}}$$ are:
Ultimate tensile strength
Yielding tensile strength
Modulus of Elasticity (I think I understand that one)
Compressive yield strength
Bulk modulus
Fatique strength
Shear modulus
Shear strength
Flexural modulus
I bet at yielding tensile strength, but not sure.
I calculate with 200Mpa
$$r=\frac{2^{\frac{2}{3}} \sqrt[3]{M_{a1}} \sqrt[3]{\frac{1}{\sigma}}}{\sqrt[3]{\pi}}=0.247448994460805 m 2^{\frac{2}{3}} \sqrt[3]{5} \\ \lvert{r}\rvert=0.247448994460805 m 2^{\frac{2}{3}} \sqrt[3]{5} \\ r= 0.671679909773 \\$$
I found this value rather off the scale, so there should be something wrong with my calculations.
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Last edited: Feb 4, 2010
2. Feb 6, 2010
### magwas
Bumping up, full with hope.
3. Feb 6, 2010
### nvn
magwas: This is a school assignment, right? You have a correct relevant equation, M = L*F, where L = perpendicular distance to the force. But if you want to use vectors, you need to use M = r X F, not dot product (or whatever you used, which looks incorrect). Therefore, your first mistake is your formula and answer for Fw2. Try again. Also, we do not know where L6 is located, because it is not shown in your diagram. Also, is the green wire in your diagram in the horizontal plane?
4. Feb 7, 2010
### magwas
Not actually school assignment, as I am trying to learn it for myself, but it does not matter, I think.
I have uploaded an updated picture.
This time I tried to use scalar forces with moment calculations. I just can't get the vector part right.
Tried to play with $$F3 = \frac{\lvert{Fw_{2t}}\rvert \lvert{l_{1}}\rvert \lvert{l_{3}}\rvert}{\sqrt{l_{1}^{2} + l_{3}^{2}}}$$, but I am no closer.
Also because my math package have some problems with vectors, I am using complex numbers for the remaining vector calculations.
$$b is length of (p1 axle1), a is length of (p1 ring) \\ such that (p1 axle1) is normal to Fw2 \\ now \frac{l_{1}}{l_{2}} = \frac{a}{c} and l_{2}^{2} = a^{2} + c^{2} \\ c = \frac{a l_{2}}{l_{1}} so l_{2}^{2} = a^{2} + \frac{a^{2} l_{2}^{2}}{l_{1}^{2}} \\ a=\frac{\lvert{l_{1}}\rvert \lvert{l_{2}}\rvert}{\sqrt{l_{1}^{2} + l_{2}^{2}}}=0.0984427575508482 m \\ \lvert{a}\rvert=0.0984427575508482 m \\$$
$$unit vector in direction for Fw_{2} \\ e_{Fw2}=\frac{l_{2} - \mathbf{\imath} l_{1}}{\sqrt{l_{1}^{2} + l_{2}^{2}}}=1.75790638483657 \frac{0.56 m - 0.1 \mathbf{\imath} m}{m} \\ \lvert{e_{Fw2}}\rvert=1.0 \\ Moment \ M_{1} = Fw_{2} a \\ force in wire 2 \\ Fw_{2}=\frac{M_{1} e_{Fw2}}{a}=267.857142857143 \frac{N \left(0.56 m - 0.1 \mathbf{\imath} m\right)}{m} \\ \lvert{Fw_{2}}\rvert=152.372814142799 N \\$$
$$\\ unit vector in direction for wire 2 at tiller end \\ e_{Fw2 t}=\frac{- l_{1} + \mathbf{\imath} l_{3}}{\sqrt{l_{1}^{2} + l_{3}^{2}}}=1.24034734589208 \frac{- 0.1 m + 0.8 \mathbf{\imath} m}{m} \\ \lvert{e_{Fw2 t}}\rvert=1.0 \\ force in wire 2 at tiller end \\ Fw_{2t}=e_{Fw2 t} \lvert{Fw_{2}}\rvert=188.995215608128 \frac{N \left(- 0.1 m + 0.8 \mathbf{\imath} m\right)}{m} \\ \lvert{Fw_{2t}}\rvert=152.372814142799 N \\ force at ring \\ F_{4}=- Fw_{2} - Fw_{2t}=- 188.995215608128 \frac{N \left(- 0.1 m + 0.8 \mathbf{\imath} m\right)}{m} - 267.857142857143 \frac{N \left(0.56 m - 0.1 \mathbf{\imath} m\right)}{m} \\ \lvert{F_{4}}\rvert=180.735435254722 N \\$$
$$\\ equation for F_{3} using moment at F_{2} \\ F_{3} l_{6} - \frac{\lvert{Fw_{2t}}\rvert \lvert{l_{1}}\rvert \lvert{l_{3}}\rvert}{\sqrt{l_{1}^{2} + l_{3}^{2}}} = 0 \\ steering force at tiller \\ F_{3}=\frac{\lvert{Fw_{2t}}\rvert \lvert{l_{1}}\rvert \lvert{l_{3}}\rvert}{l_{6} \sqrt{l_{1}^{2} + l_{3}^{2}}}=37.7990431216257 N \\ \lvert{F_{3}}\rvert=37.7990431216257 N \\ equation for F_{2} using moment at joint of tiller and wire 2 \\ F_{3} \left(l_{1} + l_{6}\right) - F_{2} l_{1} = 0 \\ force on axle 2 \\ F_{2}=\frac{F_{3} l_{1} + F_{3} l_{6}}{l_{1}}=188.995215608128 N \\ \lvert{F_{2}}\rvert=188.995215608128 N \\ F_{2}=\frac{F_{3} l_{1} + F_{3} l_{6}}{l_{1}}=188.995215608128 N \\ \lvert{F_{2}}\rvert=188.995215608128 N \\$$
Is the above correct now?
I think I will ask the second part in a separate question, because it is ... a separate question.
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5. Feb 7, 2010
### nvn
magwas: Your answer for Fw2, Fw2t, F4, and F3 is now correct. F2 is currently incorrect due to a mistake in your moment summation equation for F2. In that equation, change (L1 + L6) to (L6 - L1). Also, is the green wire in your diagram in the horizontal plane, parallel to the water surface?
6. Feb 7, 2010
### magwas
Thank you for your help again.
Yes, the green wires are horizontal.
The relevant part now:
$$equation for F_{2} using moment at joint of tiller and wire 2 \\ F_{3} \left(l_{6} - l_{1}\right) - F_{2} l_{1} = 0 \\ force on axle 2 \\ F_{2}=\frac{F_{3} l_{6} - F_{3} l_{1}}{l_{1}}=113.397129364877 N \\ \lvert{F_{2}}\rvert=113.397129364877 N \\ F_{2}=\frac{F_{3} l_{6} - F_{3} l_{1}}{l_{1}}=113.397129364877 N \\ \lvert{F_{2}}\rvert=113.397129364877 N \\$$
I think I can go further from this point.
The plan: As the arm rotates, the angles will change. I think I will set a limit at 60 degrees, which approximately doubles the forces in the wire, Also it is just half of the steering arrangement (it is symmetric to drawn angle of tiller), which means a force in the mirror of wire 1, approximately the same magnitude as Fw2, so F2 will be doubled again. I will calculate with 320N for Fw2, and 640N for F2 to be on the safe side.
7. Feb 7, 2010
### nvn
magwas: F2 is now correct. In your last paragraph, do you mean there is a mirror of the system shown in your diagram, and the mirror system is omitted from your diagram? If so, then if the 60 deg angle (where is the angle?) approximately doubles the wire tensile force, then this would quadruple F3, giving F3 = 151.2 N. But notice this would change F2 to 151.2 N, not 640 N.
Whenever you draw a free-body diagram, draw the entire system or subsystem, showing all forces acting on the system or subsystem. You cannot draw only some of the forces acting on the subsystem, and omit other significant forces acting on the subsystem. Do you have only one tiller? Draw a correct free-body diagram of the tiller, showing all forces acting on it, including forces from the port (mirror) steering system.
8. Feb 7, 2010
### nvn
In the meantime, until you come back to post 7, let's move on to the remainder of what you posted in post 1. Your answer for Fb1 and Fb2 is incorrect. If F1 = 476 N, then summation of moment, and summation of horizontal forces, on axle 1 gives Fb1 = 595 N, and Fb2 = F1 - Fb1 = -119 N.
Your shear diagram does not make sense, because it uses the wrong x coordinates. From the data given earlier in post 1, we know L4 = 0.05 m, and L5 = 0.2 m. Therefore, if x = 0 at F1, then your shear diagram should be V(x) = {F1 for x ≤ L4; and F1 - Fb1 for x > L4}. And your moment diagram should be M(x) = {F1*x for x ≤ L4; and F1*x - Fb1*(x - L4) for x > L4}. Therefore, the maximum bending moment in axle 1 is Ma1 = 23.8 N*m = 23 800 N*mm.
Let's say, e.g., your axle 1 material tensile yield strength is Sty = 235 MPa. You could perhaps use a yield factor of safety of FSy = 1.70. Therefore, the required axle 1 radius becomes r1 = [4*Ma1*FSy/(pi*Sty)]^0.33333 = {4(23 800 N*mm)*1.70/[pi*(235 MPa)]}^0.33333 = 6.030 mm.
Now repeat the above example for when the steering system is rotated to your 60 deg rotation limit (if rotating the steering system increases F1).
9. Feb 8, 2010
### magwas
Thank you for your neverending patience.
I have inserted a "2*" into the calculation of Fw2, and another "2*" into the equation for F3.
The 60 degrees meant to be rotation of arm around axle 1 by 60 degrees. If the wires would be paralell to axle 1 - ring, then the perpendicular distance would be l1/2 in this case. Because they are not paralell, the distance is a bit less when the direction of rotation is clockwise. I neglect this because 60 degrees is just a safe bet, and M1 also contains appropriate safety margins.
The "2*" in the equation for F3 needs some explanation, exactly because I did not draw the whole steering arangement up.
Correction:
The mirror part is mirrored, but direction of M1 is the same, so forces are pulling mirror of wire 1, not wire 2.
This goes to the tiller at the end, same magnitude and direction as caused by Fw2. Thence the "2*"
Now from that point on:
$$force in wire 2 \\ Fw_{2}=2 \frac{M_{1} e_{Fw2}}{a}=535.714285714286 \frac{N \left(0.56 m - 0.1 \mathbf{\imath} m\right)}{m} \\ \lvert{Fw_{2}}\rvert=304.745628285598 N \\$$
$$\\ unit vector in direction for wire 2 at tiller end \\ e_{Fw2 t}=\frac{- l_{1} + \mathbf{\imath} l_{3}}{\sqrt{l_{1}^{2} + l_{3}^{2}}}=1.24034734589208 \frac{- 0.1 m + 0.8 \mathbf{\imath} m}{m} \\ \lvert{e_{Fw2 t}}\rvert=1.0 \\ force in wire 2 at tiller end \\ Fw_{2t}=e_{Fw2 t} \lvert{Fw_{2}}\rvert=377.990431216257 \frac{N \left(- 0.1 m + 0.8 \mathbf{\imath} m\right)}{m} \\ \lvert{Fw_{2t}}\rvert=304.745628285598 N \\ force at ring \\ F_{4}=- Fw_{2} - Fw_{2t}=- 377.990431216257 \frac{N \left(- 0.1 m + 0.8 \mathbf{\imath} m\right)}{m} - 535.714285714286 \frac{N \left(0.56 m - 0.1 \mathbf{\imath} m\right)}{m} \\ \lvert{F_{4}}\rvert=361.470870509445 N \\$$
equation for F3 using moments at F2, featuring moment by wire 1 as "2*"
$$F_{3} l_{6} - 2 \frac{\lvert{Fw_{2t}}\rvert \lvert{l_{1}}\rvert \lvert{l_{3}}\rvert}{\sqrt{l_{1}^{2} + l_{3}^{2}}} = 0$$
$$\\ steering force at tiller \\ F_{3}=2 \frac{\lvert{Fw_{2t}}\rvert \lvert{l_{1}}\rvert \lvert{l_{3}}\rvert}{l_{6} \sqrt{l_{1}^{2} + l_{3}^{2}}}=151.196172486503 N \\ \lvert{F_{3}}\rvert=151.196172486503 N \\$$
$$\\ equation for F_{2} using moment at joint of tiller and wire 2 \\ F_{3} \left(l_{6} - l_{1}\right) - F_{2} l_{1} = 0 \\ force on axle 2 \\ F_{2}=\frac{F_{3} l_{6} - F_{3} l_{1}}{l_{1}}=453.588517459508 N \\ \lvert{F_{2}}\rvert=453.588517459508 N \\ F_{2}=\frac{F_{3} l_{6} - F_{3} l_{1}}{l_{1}}=453.588517459508 N \\ \lvert{F_{2}}\rvert=453.588517459508 N \\$$
I should really make a separate question about sizing axle 1, because it is more complex. There is not just F1, but also F2 and M1 are acting on the axle.
On the first drawing, I have given the attack point of F2 on axle 1 incorrectly, but my attempt at calculation tried to use the correct one, maybe incorrectly. I see that I could correctly bet on the type of tension, the formula for r was nearly okay, but I forgot to apply a safety factor and maybe there were problems with my shear and moment calculation. I will ask that part in a separate thread sometimes afternoon CET, and make a note of it here.
And thank you again.
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10. Feb 8, 2010
### magwas
11. Feb 8, 2010
### nvn
magwas: What is the forward direction of the boat? Show the forward direction of motion on your diagram. Is it to the left? Perhaps define x, y, and z axes on your diagram(s). Let +z be upward, perpendicular to the water surface. Let's say angle theta is the rudder rotation angle. We do not know if theta is measured from a horizontal or vertical line on your diagram. Show theta on your diagram. And show which direction is positive theta. Positive theta is often counterclockwise. Why are the rudders perpendicular to the boat forward direction of motion? Shouldn't theta = 0 deg be when the rudders are parallel to the forward direction of motion of the boat? And therefore, your current diagram shows the rudders at theta = 90 deg, correct? Or does your diagram currently show theta = -90 deg?
Can you show a good diagram of your rudder, with the rudder parts? We need to see the rudder assembly to be able to see if you are applying the applied loads correctly, and to ensure the rudder forces and moments are in equilibrium.
The rudder forces and equations need to be set up for when theta is at an arbitrary value (not 0 nor 90 deg), so that the analysis will give the correct forces, in equilibrium, at any angle theta.
12. Feb 8, 2010
### nvn
magwas: If the rudder in your above diagram is currently shown at theta = 0 deg, and if M1 = 15 N*m is truly correct and constant as the rudder rotates, and if you rotate the rudder counterclockwise to theta = +60 deg, then the angle of starboard wire 2, measured from a horizontal line in your diagram, decreases to phi = 6.0292 deg. The wire angle does not remain constant as the rudder rotates; it changes. If you work out the trigonometry and vector mechanics correctly, you will see Fw2 = 255.02 N, not 304.75 N, if the rudder is rotated 60 deg counterclockwise from the rudder position currently shown in your above diagram.
Also, your moment summation equation for F2 is currently incorrect. You forgot to apply the port wire 1 tensile force to the end of the tiller. Therefore, your moment summation equation for F2 is wrong. Hence, your answer for F2 is incorrect.
First, define theta, as mentioned in post 11. Also, define phi.
13. Feb 9, 2010
### magwas
You can see the whole boat here: http://www.cruiserlog.com/forums/index.php?act=attach&type=post&id=3007
The rudder itself is not shown in the diagram, it is right to the arms, 90 degrees. Theta is 0 degrees in the diagram, this is the case when the boat goes forward.
I believe I have applied port wire 1 to the tiller. See the "2*" in the expression after the comment "featuring moment by wire 1 as "2*""
This state of affairs would be okay for me, as I believe I have established safe upper limits for the forces, but to improve my engineering abilities I will do the drawing and computations as you have suggested. I hope I can come back with it later today.
14. Feb 9, 2010
### nvn
Yes, the "2*" causes F3 to be correct. I do not have an issue with your F3 answer. As mentioned in paragraph 2 of post 12, the mistake is with your last moment summation equation in post 9, to solve for F2. You have not created a correct free-body diagram of the tiller to solve for F2. And therefore, your answer for F2 is incorrect.
Agreed. Your assumption (overestimation) of Fw2 = 304.75 N causes the axle 1 radius to be only 1.3 % too big, which is OK.
15. Feb 10, 2010
### magwas
Thank you again.
Now, this is just about what I can do with this.
I was struggling with perpendicular distance, cross product and dot product for a day, now I believe I have something useable for F2.
A new - hopefully more understandable - drawing:
$$armend=e_{arm} l_{1}$$
unit vector in direction for $$Fw_{2}$$
$$e_{Fw2}=\frac{armend + l_{2}}{\lvert{armend + l_{2}}\rvert}$$
Moment $$M_{1} = Fw_{2} \left(\Im{armend} \Re{e_{Fw2}} - \Im{e_{Fw2}} \Re{armend}\right)$$
force in wire 2
$$Fw_{2}=\frac{M_{1}}{\Im{armend} \Re{e_{Fw2}} - \Im{e_{Fw2}} \Re{armend}}$$
$$Fw_{1}=Fw_{2}$$
unit vector in direction for wire 2 at tiller end
wire2 vector: $$- \mathbf{\imath} l_{3} + \mathbf{\imath} e_{arm} l_{1}$$. its unit vector:
$$e_{Fw2 t}=\frac{- \mathbf{\imath} l_{3} + \mathbf{\imath} e_{arm} l_{1}}{\lvert{- \mathbf{\imath} l_{3} + \mathbf{\imath} e_{arm} l_{1}}\rvert}$$
unit vector in direction for wire 1 at tiller end
wire2 vector: $$- \mathbf{\imath} l_{3} - \mathbf{\imath} e_{arm} l_{1}$$. its unit vector:
$$e_{Fw1 t}=\frac{- \mathbf{\imath} l_{3} - \mathbf{\imath} e_{arm} l_{1}}{\lvert{- \mathbf{\imath} l_{3} - \mathbf{\imath} e_{arm} l_{1}}\rvert}$$
force in wire 2 at tiller end
$$Fw_{t 2}=e_{Fw2 t} \lvert{Fw_{2}}\rvert$$
force in wire 1 at tiller end
$$Fw_{t 1}=e_{Fw1 t} \lvert{Fw_{1}}\rvert$$
force at ring, starboard side
$$F_{4}=- Fw_{t 2} - Fw_{2} e_{Fw2}$$
force at ring, port side
$$F_{p 4}=- Fw_{t 1} - Fw_{1} e_{Fw1}$$
equations for F2 using moments at F_3
eq1=F2_re*l6+Fw2*(l6-abs(perpdist(l3*1j,0,e_Fw2_t)))-Fw1*(l6+abs(perpdist(-1j*l3,0,e_Fw1_t)))
eq2=F2_im+dot(Fw2*e_Fw2_t,1j*e_arm)-dot(Fw1*e_Fw1_t,1j*e_arm)
eq3=Equality(F2,F2_re*1j*e_arm+F2_im*e_arm)
steering force at tiller
$$F_{2}=\frac{\mathbf{\imath} Fw_{1} e_{arm} l_{6} + \mathbf{\imath} Fw_{1} e_{arm} \lvert{\frac{l_{3} \Re{e_{Fw1 t}}}{\left(\Im{e_{Fw1 t}}\right)^{2} + \left(\Re{e_{Fw1 t}}\right)^{2}}}\rvert + \mathbf{\imath} Fw_{2} e_{arm} \lvert{\frac{l_{3} \Re{e_{Fw2 t}}}{\left(\Im{e_{Fw2 t}}\right)^{2} + \left(\Re{e_{Fw2 t}}\right)^{2}}}\rvert + e_{arm} l_{6} \Im{e_{arm}} \Re\left(Fw_{2} e_{Fw2 t}\right) + e_{arm} l_{6} \Im\left(Fw_{1} e_{Fw1 t}\right) \Re{e_{arm}} - \mathbf{\imath} Fw_{2} e_{arm} l_{6} - e_{arm} l_{6} \Im{e_{arm}} \Re\left(Fw_{1} e_{Fw1 t}\right) - e_{arm} l_{6} \Im\left(Fw_{2} e_{Fw2 t}\right) \Re{e_{arm}}}{l_{6}}$$
at alpha=0 degrees
force in wire 1
$$Fw_{1}=152.372814142799 N$$
$$\lvert{Fw_{1}}\rvert=152.372814142799 N$$
$$Fw_{2}=152.372814142799 N$$
$$\lvert{Fw_{2}}\rvert=152.372814142799 N$$
$$F_{4}=- 131.100478439187 N + 124.410458200788 \mathbf{\imath} N$$
$$\lvert{F_{4}}\rvert=180.735435254722 N$$
$$F_{p 4}=- 168.899521560813 N + 124.410458200788 \mathbf{\imath} N$$
$$\lvert{F_{p 4}}\rvert=209.773712588593 N$$
$$F_{2}=- 75.5980862432514 N - 37.7990431216257 \mathbf{\imath} N$$
$$\lvert{F_{2}}\rvert=84.5212299044009 N$$
at alpha=60 degrees
force in wire 1
$$Fw_{1}=- 151.311909944752 N$$
$$\lvert{Fw_{1}}\rvert=151.311909944752 N$$
$$Fw_{2}=- 151.311909944752 N$$
$$\lvert{Fw_{2}}\rvert=151.311909944752 N$$
$$F_{4}=131.682426318086 N + 123.540878611267 \mathbf{\imath} N$$
$$\lvert{F_{4}}\rvert=180.561928681165 N$$
$$F_{p 4}=167.507853154076 N + 123.380418154109 \mathbf{\imath} N$$
$$\lvert{F_{p 4}}\rvert=208.042323704025 N$$
$$F_{2}=- 78.6564331483069 N - 10.703545171187 \mathbf{\imath} N$$
$$\lvert{F_{2}}\rvert=2.5 \sqrt{1008.22405677531 N^{2} - 2.8421709430404 \times 10^{-14} \mathbf{\imath} N^{2}}$$
Fw1 blue, F4 green, F4 port red, F2 cyan
i hereby declare this example to be beaten to death.
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16. Feb 10, 2010
### nvn
For M1 = 15 N*m and alpha = 60 deg, Fw1 = 255.02 N, not 151.32 N. When you work the problem correctly, F2 = -F3. For alpha = 60 deg, F2 = -69.87 N.
17. Feb 11, 2010
### magwas
Thank you again.
Reworked the equations, and double-checked them for problems with sign, etc.
Here is the result:
I am back to basics, analised that Fw2 force and the related angles.
In the image
- green is beta, the angle of e_Fw2 as calculated
- blue is 90+alpha, that is the ring-axle1-p1 angle
- red is 90-alpha-beta, that is ring-p1-axle1 angle
- the bottom of the double line is 150*1/sin(red)
- the top of the double line is -l_Fw2
I am starting to believe my results now, but they are different than the numbers you have given.
at zero, l_Fw2=-152.37 N
at 60, it is -347.42 N It is more than double than at zero, because red gets as low as 25 degrees.
I have realized, that Fw1=Fw2, because the arm is in the same angle.
so Fw1_t and Fw2_t are mirrors to axle 2.
Which means that their component paralell to the tiller are cancel each other, and they have the same component orthogonal to the tiller, but in the meaning that their moment around axle2 adds up.
However their orthogonal component is canceled out by F3. As F3 is by definition orthogonal to the tiller,
it have no paralell component. So F2 must be zero.
Or more realistically it is in the direction of the tiller, and its magnitude is the same as the paralell component of F3. So it should be sized according to the strength of the skipper:)
Where did I err this time?
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18. Feb 12, 2010
### nvn
magwas: Your first mistake is, your wire tensile force for alpha = 60 deg is incorrect. It should instead be Fw1 = 255.02 N.
L1 = 100 mm, L2 = 560 mm, M1 = 15 000 N*mm.
At alpha = 60 deg,
armend = (-86.60254*i - 50*j + 0*k) mm,
gamma = 6.02920 deg,
e_Fw1 = -0.994468*i + 0.105035*j + 0*k,
Fw1 = -M1/(armend X e_Fw1)3 = 255.02 N
Last edited: Feb 12, 2010
19. Feb 12, 2010
### magwas
Thank you again.
There had been some inconsistencies in my naming scheme. Fw1 refers to the force on the port wire 1.
You have given e_Fw1 and Fw1 as the direction and magnitude of starboard wire 1, which is the same as port wire 2.
Starboard wire 1 and port wire 2 have no tension wth this direction of M1.
(Wire 1 is the inner, wire 2 is the outer wire).
Here is the drawing in greater resolution.
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20. Feb 12, 2010
### nvn
magwas: In your diagram, alpha is drawn positive clockwise, where alpha = 0 deg means the steering system is in the straight-ahead position. To make a left-hand turn, you move the tiller at F3 toward the starboard side of the boat, correct? I.e. (that is), for positive alpha, you apply a force to the tiller at F3 opposite of the direction currently shown for F3. This causes starboard wire 1 and port wire 2 to be in tension, which rotates the rudder clockwise. Starboard wire 2 and port wire 1 have zero tension. Positive alpha causes the water to apply a counterclockwise moment M1 to the rudder, opposite of the direction currently shown for M1. For positive alpha, M1 is resisted by starboard wire 1 and port wire 2 tension. In other words, you have currently drawn M1 and F3 backwards. And you have currently drawn Fw1 and Fw2 on the wrong wires.
Another mistake you made in post 17 was saying, "F2 must be zero." That is incorrect. F2 = -F3, as mentioned in post 16.
21. Feb 12, 2010
### magwas
Thank you, I see my mistake with the directions now.
(I wonder if I ever be able to get this example right...)
However I do not understand why F2 = -F3.
Back to drawing...
22. Feb 12, 2010
### magwas
I have modified signs here and there, and now I have Fw1 = 255.016 N
However I still think that
- components of Fw1 and Fw2 paralell to the tiller cancel each other, and
- components of Fw1 and Fw2 orthogonal to the tiller are canceled by F3 by definition of F3.
What the problem with that?
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23. Feb 12, 2010
### nvn
Components of Fw1 and Fw2 parallel to the tiller cancel. Components of Fw1 and Fw2 perpendicular to the tiller also cancel (in a summation of perpendicular forces). Perform a summation of perpendicular forces on the tiller, and you will see that F2 = -F3. Answers are in posts 16 and 18, except make the following correction; F2 = 69.87 N, not -69.87.
Last edited: Feb 13, 2010
24. Feb 12, 2010
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# The number of defects in the first five cars to come through
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The number of defects in the first five cars to come through [#permalink]
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15 Nov 2010, 08:59
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The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
[Reveal] Spoiler: OA
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Re: defect problem kindly help [#permalink]
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15 Nov 2010, 09:16
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SoniaSaini wrote:
The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
not able to understand what question is asking for? kindly help me to solve this one.
cheers,
Sonia saini
Basically we have a set with 6 terms: {4, 6, 7, 9, 10, x}. The question asks if $$x$$ is either 3, 7, or 12 then for which values of $$x$$ the mean of the set equals to the median (note that $$mean=\frac{4+6+7+9+10+x}{6}=\frac{36+x}{6}$$ and the median will be the average of two middle terms, so it depends on the value of $$x$$).
If $$x=3$$ then $$mean=\frac{36+3}{6}=6.5$$ and $$median=\frac{6+7}{2}=6.5$$, so $$mean={median}$$;
If $$x=7$$ then $$mean=\frac{36+7}{6}=\frac{43}{6}$$ and $$median=\frac{7+7}{2}=7$$, so $$mean\neq{median}$$;
If $$x=12$$ then $$mean=\frac{36+12}{6}=8$$ and $$median=\frac{7+9}{2}=8$$, so $$mean={median}$$.
Answer: D (I and III only).
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Re: defect problem kindly help [#permalink]
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16 Nov 2010, 07:40
Hey Bunuel,
you're really an awesome person.
thank you very much.
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Re: defect problem kindly help [#permalink]
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25 May 2013, 07:33
The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
Intuitively each answer choice except for 7 , together with the given forms the union of 2 AP that has the same difference (d =3) and same number of terms.
3,4,6,7,9,10 = {3,6,9} U {4,7,10}
4,6,7,9,10,12 = { 4,7,10} U {6,9,12}
mean and median of such union is equal (symmetric distribution) and is equivalent to the average of both sets median (means)
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Re: The number of defects in the first five cars to come through [#permalink]
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23 Dec 2015, 19:20
let's arrange the numbers in ascending order:
4, 6, 7, 9, 10 = sum is 36.
which # if added will result mean=median?
ok, let's test 3:
so, the sum is 36+3=39. we have to divide this by 6 to find the mean, and we have 6.5
let's find the median
3, 4, 6, 7, 9, 10 = we can see that the median is (6+7)/2 so the median is 6.5
ok, so we see that the first one works, and thus we can eliminate B and C.
let's test second one:
new sum is 36+7=43. the average thus would be 43/6, and improper fraction.
new median
4, 6, 7, 7, 9, 10 - so the median is 7. we can see that the median is not equal to the mean. we can thus eliminate E, and we are left with A and D.
let's test the final one:
new sum is 36+12=48. divide by 6 = 8. 8 is the new average.
4, 6, 7, 9, 10, 12 - the new median is (7+9)/2 = 8.
we can see that median=mean, and we can cross A, and select D.
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Re: The number of defects in the first five cars to come through [#permalink]
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23 Dec 2015, 21:55
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yezz wrote:
The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
Intuitively each answer choice except for 7 , together with the given forms the union of 2 AP that has the same difference (d =3) and same number of terms.
3,4,6,7,9,10 = {3,6,9} U {4,7,10}
4,6,7,9,10,12 = { 4,7,10} U {6,9,12}
mean and median of such union is equal (symmetric distribution) and is equivalent to the average of both sets median (means)
Another intuitive way to see that mean will be equal to median is to imagine them on a number line. Both sets (with 3 and with 12) are symmetrical about the centre and hence mean = median.
------3-4--6-7--9-10-----
The centre is between 6 and 7 and the elements are symmetrical about it.
-------4--6-7--9-10--12-------
The centre is between 7 and 9 and the elements are symmetrical about it.
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Re: The number of defects in the first five cars to come through [#permalink]
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26 Jul 2017, 12:44
The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of these values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
Explanation:
Given the number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. Sixth car will have either of 3, 7 or 12 defects.
Let us assume sixth car has x defects
⇒ Mean number of defects = 9+7+10+4+6+x6=36+x6=6+x69+7+10+4+6+x6=36+x6=6+x6 .... (1)
Median of a data can be found out by arranging the terms in ascending order, then finding out the middle term if number of terms is odd and average of the two middle terms if number of terms is even.
Putting x = 3, we get:
Mean = 6.5
Terms arranged in ascending order are 3, 4, 6, 7, 9, 10.
⇒ Median = (6 + 7)/2 = 6.5
Since Mean = Median => x can be 3.
Putting x = 7, we get:
Mean = 6 + 7/6 = 43/6 = 7.16
Terms arranged in ascending order are 4, 6, 7, 7, 9, 10.
⇒ Median = (7 + 7)/2 = 7
Since mean is not equal to median => x cannot be 7.
Putting x = 12, we get:
Mean = 8
Terms arranged in ascending order are 4, 6, 7, 9, 10, 12.
⇒ Median = (7 + 9)/2 = 16/2 = 8
Since mean = median ⇒ x can be 8.
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Re: The number of defects in the first five cars to come through [#permalink] 26 Jul 2017, 12:44
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https://etiq.ai/research/how-fairness-metrics-can-be-misleading/
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# Etiq AI Blog
How fairness metrics can be misleading
# How fairness metrics can be misleading
What are fairness metrics and how you can use them.
Decision makers can rely upon machine learning models for guidance. However, sometimes these models can contain hidden bias, where certain people or groups are treated unfairly by the model due to individual features. To capture this discrimination, a variety of fairness metrics are used. Each of these measures can generally be classified as either a group or individual/counterfactual fairness metric, which is determined by what they are attempting to measure. For example, a group fairness metric will look at whether different demographic groups observe varied model behaviour i.e. are there more true positive model predictions for one gender group compared to another? In contrast, individual/counterfactual fairness measures will assess if similar individuals experience similar model treatment. Since these two metric types focus on different aspects of fairness, we expect that their results will be somewhat incompatible. Although, the amount of attention given to this topic in the literature is limited. Here, we begin with a review of the previous studies that do discuss this potential incompatibility between group and individual fairness metrics. Then, various measures are computed for an example dataset to explore the findings of the literature review. Moreover, we perform a dataset repair that optimizes group fairness. From these results, inconsistencies in the different metric types are apparent. Hence, fairness measures are useful approximations for highlighting bias in machine learning models, but caution should be used when applying these as stand-alone measures. In particular, optimising for one class of metric can lead to another being compromised.
Caption: Different fairness metrics grouped by gender demonstrates their incompatibility.
### Fairness metrics
Machine learning algorithms are widely used to construct prediction models that inform decision-making processes. For example, a bank may use a model to predict the likelihood of someone paying back a loan based upon certain individual characteristics. This likelihood estimate can then help the bank to decide who to approve for a loan. However, it is well-known that machine learning models can exhibit prejudice towards specific types of people due to, for instance, their race or gender. This discrimination can be the result of the machine learning algorithm, or the data used to train the model, or both. Recent studies have focussed upon ways to evaluate the bias that may exist within a model, as well as techniques that reduce the impact of biases in datasets and algorithms.
One method commonly used to assess the fairness of a prediction model is the computation of fairness metrics. These attempt to evaluate the discrimination that can occur at an individual level and group level. Individual fairness is upheld if similar individuals receive similar model outcomes. Conversely, group fairness examines whether distinct groups of individuals, such as males and females, experience consistent treatment. Moreover, these metrics are used for dataset repairs, where a dataset will be modified in some way, and the model retrained, so that a particular fairness metric is optimised.
Dwork et al. (2012) showed that when demographic parity (a group fairness measure) is achieved, large disparities amongst similar individuals can still exist, which means that group fairness does not necessarily correspond to individual fairness. In response to this, they proposed an individual fairness metric that measures whether individuals with similar features observe the same model responses. More specifically, the difference between two individuals, say a and b, is quantified by some distance measure d(a,b) – this can account for one or more features – then essentially individual fairness is satisfied when
$\sum_i|P(i|a)-P(i|b)|<=d(a,b), (1)$
where P(i|a) is the probability of outcome i for individual a. Another well-cited individual fairness measure is the consistency index formulated by Zemel et al. (2013). This evaluates the difference between each individual’s model classification and their k nearest neighbours, which are selected on the basis of individual commonalities. Again, this assesses whether a model behaves consistently for similar individuals, although only binary response models are considered. Written in full, consistency is expressed as
$consistency=1-\frac{1}{n}\large \sum_i|\hat{Y}_i-\frac{1}{k}\sum_{j \in kNN(x_i)}\hat{Y}_j|, (2)$
where n is the total number of individuals, Yiis the model prediction for individual i and xiis the feature vector for individual i.
There are several group fairness measures, where metrics are computed for each group and then compared. For example, equal opportunity is a group level measure that examines the probability of a correctly predicted positive outcome for each group. If this probability is equal across all the groups then equal opportunity is satisfied. Equalised odds is an extension of this metric, which also considers the group probability of a correctly predicted negative outcome.
Another group metric is demographic parity, which uses the group probability of a predicted positive outcome, and is upheld if this probability is consistent over all the groups. Refer to Mehrabi et al. (2021) for a survey of other fairness measures. As suggested by the examples given here, each of the various group-level metrics focusses on a different aspect of fairness. These differences however do lead to inconsistencies, where it can be impossible to satisfy certain combinations of group fairness metrics simultaneously. For example, Garg et al. (2020) demonstrates that selected group measures are unable to be upheld at the same time, including equalised odds and demographic parity.
While the incompatibility of group-level metrics has been well-established in the literature, less attention has been given to the relationship between individual and group fairness measures. This relationship will be the focus of our article, in particular, we want to understand how performing a dataset repair that optimises group fairness will impact upon individual fairness, or vice versa. More specifically, we begin with a review of the relevant literature. Next, a repair method is applied to an example dataset to further explore the relationship between individual and group fairness. The fairness metrics computed before and after the repair are presented and compared to the findings from the literature.
### Previous work: Individual versus group fairness
Some studies have already considered a potential incompatibility between individual and group fairness measures. For instance, Binns (2020) discusses how often there will be a trade-off when trying to uphold both classes of metric. Firstly, they explain that if individual fairness is ignored in favour of group measures, then the issue of models classifying alike individuals very differently can persist. Secondly, if individual fairness is the only focus, they believe this can lead to notable differences in outcomes at the group level. Fleisher (2021) argues that individual fairness is an invalid choice of metric in isolation due to a number of factors, including its inability to ensure general fairness. An example Fleisher gives is a model that only predicts negative outcomes for every individual, which would satisfy individual fairness but is obviously an unfair model. He also concedes that all the group metrics fail to be stand-alone measures. Ultimately, Fleisher proposes that a variety of measures should be applied to fully assess discrimination in machine learning and that individual fairness should be viewed as “one kind of tool among many”.
Speicher et al. (2018) describe an index for overall unfairness, which measures model inequality by evaluating the level of beneficial treatment received by each individual. Moreover, when the data is partitioned into distinct groups, they show that this metric can be rewritten as the sum of two new measures referred to as between-group and within-group unfairness, which correspond respectively to the group-level and individual-level bias indicators discussed here. This suggests that the overall unfairness index assesses discrimination on both levels. The authors then use this decomposed expression to demonstrate the possible imbalance between group and individual fairness. Firstly, they consider having a small number of groups, which means that within the groups, both the number of people and the variation in model response will be considerable. Hence, in this situation, reducing group unfairness is relatively straightforward, although they claim that this could unintentionally affect the overall model unfairness and therefore increase the within-group unfairness. Alternatively, they look at when the number of groups grows significantly. As a result, the model response within the groups will be less varied, upholding individual fairness, and thus, the within-group unfairness is negligible. In order to now reduce the overall unfairness, group-level fairness must be improved, which they argue is a difficult task computation-wise due to the large number of groups. Thus, the behaviour described by Speicher et al. suggests that by obtaining group level fairness, it is impossible to fully uphold individual fairness, and vice versa.
In addition, Friedler et al. (2016) explain this group and individual incompatibility by firstly defining two opposing fairness perspectives, which they call WYSIWYG (what you see is what you get) and WAE (we’re all equal). They also define three information spaces, which they refer to as the unobserved, the observed and the decision spaces. From the WYSIWYG viewpoint, the unobserved and observed information spaces are the same. Whereas, WAE assumes that there are no discriminatory differences between groups in the unobserved space, however bias is introduced in the observed space outside an individual’s control. The authors discuss the example of Black students’ SAT verbal question scores being generally weaker (observed information), although unobserved qualities, such as intelligence, are the same amongst the groups.
They also define the different mappings between the observed space and the decision space for the two approaches, where the WYSIWYG view will have little distortion between the two spaces i.e. the distance between individuals in the observed space and the decision space is generally the same (upholds individual fairness), whilst WAE reduces the distance between the groups in the decision space (upholds group fairness). The authors encourage applying WAE when a decision is made using observed data with known group bias, whereas WYSIWYG is recommended when decisions need to be informed by individual performance. As well, they show that the WYSIWYG perspective ensures only individual fairness is met and group fairness is impossible since in this mindset, applying a group fairness mechanism, causing distortion, would be considered discriminatory. In contrast, the WAE approach only imposes group fairness and individual fairness is unattainable. This is because by applying an individual fairness measure here, groups that are a sizeable distance apart in the observed space will also be separated in the decision space, which is unfair according to WAE.
It should be noted that in the literature reviewed here, the focus upon individual and group incompatibility is not extended to difference measures that are often used to highlight group disparities i.e. Equal opportunity=(male group probability of a correctly predicted positive outcome) - (female group probability of a correctly predicted positive outcome). Moreover, counterfactual metrics are also not discussed by the publications mentioned, which are individual-level fairness measures that also consider the impact of a specific feature, such as gender, on the model behaviour. For example, they can be used to evaluate how the probability of a positive outcome changes if instead the individual was male and not female, whilst the remaining information about the individual stays the same. Refer to Pearl (2010) for more details.
This literature review suggests there is a potential imbalance between group and individual fairness in machine learning models. Failing to recognise individual-level bias and trying to maximise group fairness can result in unfair classification discrepancies amongst similar individuals. Conversely, using individual fairness as a stand-alone measure to assess and remove bias can lead to overt group discrimination. This issue of incompatibility is further examined with the application of a debiasing algorithm.
### “Debiasing”: Repairing the training dataset
We apply a repair method to an example dataset to demonstrate the inconsistencies of different fairness measures. The aim of this method is to improve group fairness, where the groupings are chosen based upon certain demographics, such as females, being vulnerable to discrimination. In this example, the groups considered are male and female, and the prejudice experienced by females in contrast to males is highlighted with the group True Positive Rate (TPR - the probability of a correctly predicted positive outcome). Furthermore, the consistency metric defined above (see (2)) is applied to assess individual fairness.
The Adult dataset is applied in this example to train an income prediction model. As well, a repair algorithm from the Etiq library is used, that has at its core resampling. A sample of the Python code needed to build the model and then perform the repair with the Etiq library is outlined in Figure . Essentially, running this code generates two models, where one is trained with the original dataset and the other with the repaired debiased dataset. As well, fairness metrics for each model are computed, which means measures for before and after the repair are obtained. Next, we compare these two sets of results to evaluate the impact of debiasing on fairness and determine whether they support the literature.
1from etiq_core import *
2
4
5# DatasetLoader transforms the data and splits it into training/validation/testing data.
7 label='income',
8 transforms=transforms,
9 bias_params=debias_param,
10 train_valid_test_splits=[0.8, 0.1, 0.1],
11 names_col = data.columns.values)
12metrics_initial= [accuracy, equal_opportunity, consistency]
13xgb = DefaultXGBoostClassifier()
14
15# DataPipeline computes metrics using the model provided.
17pipeline_initial.run()
18
19# Identify bias issues.
20identify_pipeline = IdentifyBiasSources(nr_groups=20, # nr_groups=number of segments
21 train_model_segment=True,
22 group_def=['unsupervised'],
23 fit_metrics=[accuracy, equal_opportunity],cutoff=0.2)
24# Apply the repair.
25repair_pipeline = RepairResamplePipeline(steps=[ResampleUnbiasedSegmentsStep(ratio_resample=1)], random_seed=4)
26
27# DebiasPipeline computes metrics for the repaired dataset using the model provided.
28debias_pipeline = DebiasPipeline(data_pipeline=pipeline_initial,
29 model=xgb,
30 metrics=metrics_initial,
31 identify_pipeline=identify_pipeline,
32 repair_pipeline=repair_pipeline)
33debias_pipeline.run()
34
35# Retrieve the calculated metrics
36debias_pipeline.get_protected_metrics()
37
38
### Results: Before and after the repair
The fairness results that correspond to the Adult dataset before (referred to as the baseline) and after the repair are shown in Figures 1-3. In Figure 1, the model accuracy (left) and equal opportunity measure (TPR males - TPR females) (right) are depicted. These two measures help to assess the effectiveness of the repair, where, if it is successful, accuracy is expected to remain relatively unchanged and equal opportunity should reflect the removal of group bias. Here, accuracy is shown to be generally unaffected by debiasing, as well, the baseline bias towards males changes to a slight bias towards females through repair. Hence, these plots suggest that the debiasing process has been effective. Although, the full impact of the repair should be further examined with other metric types, such as individual fairness measures.
In Figure 2, the TPR (top panel) and the consistency measure (bottom panel) are portrayed, which are group and individual fairness metrics respectively. The results for the original dataset and the repaired dataset are compared. The plots on the left and right correspond to the male group and the female group respectively. These figures reveal a sizable increase in the female TPR following repair, whilst the male TPR falls very slightly. In particular, the baseline male TPR was notably higher than the baseline female TPR, whereas after the repair, the female TPR is slightly higher than the male TPR. When the female TPR is low, the consistency measure is around 0.84, which suggests that individual fairness amongst females is relatively strong. However, after the repair is applied , when female TPR increases, the female consistency metric drops. This ‘seesaw effect’ between female TPR (group measure) and female consistency (individual measure) supports our findings from the literature. Note that male consistency has also decreased as a result of the repair, although the reduction is comparatively small. This behaviour also aligns with our previous discussion since individual fairness should decrease for all individuals if group fairness mechanisms are used to remove bias. Note that the gender specific consistency index is defined as written in (2) except that index i only refers to the females (males) in the dataset and n=No. of females (n=No. of males) for the female (male resp.) case. As well, it should be noted that here k=5, which is consistent with AI Fairness 360’s (https://aif360.mybluemix.net/) implementation of the consistency measure.
In Figure 3, the results for a counterfactual-type fairness metric are presented for males (left) and females (right), which looks at whether similar females and males according to their features are treated equally by the model. More precisely, it is defined as
$consistency=1-\frac{\text{No. neg. pred. males (females) with at least 1 female (male) pos. pred. nn}}{\text{No. neg. pred. males (females)}}, (3)$
where nn represents nearest neighbour and only the 5 closest neighbours are considered. This measure does evaluate individual fairness since it examines whether similar individuals have similar model treatment, although it specifically concentrates on similar males and females with opposing model predictions. From these plots, it appears that males have very strong individual fairness, although there is a sizable reduction following the repair. In contrast, the female group has a very weak individual fairness score, which also decreases after debiasing, although this reduction is smaller. These results portray a somewhat conflicting viewpoint to that conveyed by Figure 2, in particular, here female individual fairness is much lower than the male group and the repair seems to have more impact upon males than females. However, this fairness metric does decrease across the genders due to debiasing, which agrees with the consistency plots and the literature. This demonstrates that not only are there incompatibilities between group and individual fairness and between certain combinations of group metrics, but potentially there are inconsistencies between different types of individual fairness metrics, such as consistency and this counterfactual-type measure used here. It should be noted that the literature reviewed above did not specifically consider counterfactual fairness and its relationship with group fairness.
### Conclusion: Incompatibility of fairness metrics
The potential conflict between individual and group-level fairness has been investigated. Firstly, previous studies that highlighted this incompatibility were detailed in the literature review. Next, a repair method available from the Etiq library was applied to the Adult dataset, which is a repair algorithm designed to remove group bias. This example did support the literature findings such that inconsistencies between individual and group level metrics were identified. In particular, a ‘see-saw effect’ between TPR and consistency was observed before and after the repair. This behaviour did demonstrate that by optimising group fairness using the ‘debiased’ dataset, individual fairness was compromised. Additionally, an alternative individual fairness metric was considered that focussed upon gender. Similar to the inconsistency of certain group-level measures identified by Garg et al., a potential incompatibility of individual-level metrics was suggested due to the conflicting results of the consistency index and the counterfactual-type measure. Thus, when designing a machine learning model, it seems necessary to consider a variety of different metrics from individual and group-level so that a justifiable compromise between opposing metric types can be attained.
### References:
• Binns, R., 2020. On the apparent conflict between individual and group fairness. In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency (FAT* '20). ACM, New York, NY, USA, 514-524. https://doi.org/10.1145/3351095.3372864
• Dwork, C., Hardt, M., Pitassi, T., Reingold, O. and Zemel, R., 2012. Fairness through Awareness. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference (ITCS ’12). ACM, New York, NY, USA, 214-226. https://doi.org/10.1145/2090236.2090255
• Fleisher, W., 2021. What's Fair about Individual Fairness? In Proceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society (AIES '21). ACM, New York, NY, USA, 480-490. https://doi.org/10.1145/3461702.3462621
• Friedler, S., Scheidegger, C. and Venkatasubramanian, S., 2016. On the (Im)possibility of fairness. arXiv preprint arXiv:1609.07236 (2016). https://arxiv.org/pdf/1609.07236.pdf
• Garg, P., Villasenor, J. and Foggo, V., 2020. Fairness Metrics: A Comparative Analysis. arXiv preprint arXiv:2001.07864 (2020).https://arxiv.org/pdf/2001.07864.pdf
• Mehrabi, N., Morstatter, F., Saxena, N., Lerman, K. and Galstyan, A., 2021. A Survey on Bias and Fairness in Machine Learning. ACM Computing Surveys, 54(6), 1-35. Fleisher, W., 2021.https://dl.acm.org/doi/pdf/10.1145/3457607
• Pearl, J., 2010. An introduction to causal inference. Int J Biostat, 6(2):Article 7. https://doi.org/10.2202/1557-4679.1203
• Speicher, T., Heidari, H., Grgic-Hlaca, N., Gummadi, K., Singla, A., Weller, A. and Zafar, M.B., 2018. A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual & Group Unfairness via Inequality Indices. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD '18). ACM, New York, NY, USA, 2239-2248. https://doi.org/10.1145/3219819.3220046
• Zemel, R., Wu, Y., Swersky, K., Pitassi, T. and Dwork, C., 2013. Learning Fair Representations. In Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):325-333. https://proceedings.mlr.press/v28/zemel13.html
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2023-02-01 09:12:20
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https://www.tutorialspoint.com/recommended-way-to-embed-pdf-in-html
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# Recommended way to embed PDF in HTML?
To embed a PDF in HTML is an easy task and there are various ways. Let us see them one by one.
• Embed PDF in HTML using iframe.
• Embed PDF in HTML using the embed tag.
• Embed PDF in HTML using the object tag.
## Embed PDF in HTML using iframe
Set the src attribute of the iframe tag and add the link of the PDF to embed −
<iframe src="https://www.tutorialspoint.com/python3/python3_tutorial.pdf" width="700" height="500">
</iframe>
### Example
Let us now see an example to ember PDF using <iframe> −
<!DOCTYPE html>
<html>
<title>Embed PDF</title>
<body>
<center>
<h1>Python by Tutorialspoint</h1>
<p>Below is a preview of the Python Tutorial:</p>
<iframe src="https://www.tutorialspoint.com/python3/python3_tutorial.pdf" width="700" height="500">
</iframe>
</center>
</body>
</html>
## Embed PDF in HTML using the embed tag
We can also embed PDF using the <embed> tag −
<embed src="https://www.tutorialspoint.com/java/java_tutorial.pdf" width="700" height="500">
### Example
Let us now see an example to embed PDF using the embed tag −
<!DOCTYPE html>
<html>
<title>Embed PDF</title>
<body>
<center>
<h1>Java by Tutorialspoint</h1>
<p>Below is a preview of the Java Tutorial:</p>
<embed src="https://www.tutorialspoint.com/java/java_tutorial.pdf" width="700" height="500">
</center>
</body>
</html>
## Embed PDF in HTML using the object tag
We can embed PDF using the <object> tag. The data attribute of the object data is where you need to place the link of the PDF file to be embedded −
<object data="https://www.tutorialspoint.com/android/android_tutorial.pdf" width="700" height="500">
### Example
Let us now see an example to embed PDF using the object tag −
<!DOCTYPE html>
<html>
<title>Embed PDF</title>
<body>
<center>
<h1>Android by Tutorialspoint</h1>
<p>Below is a preview of the Android Tutorial:</p>
<object data="https://www.tutorialspoint.com/android/android_tutorial.pdf" width="700" height="500">
</center>
</body>
</html>
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2023-02-05 09:01:08
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https://space.stackexchange.com/questions/14452/density-impulse-of-monopropellant-hydrazine
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# Density impulse of monopropellant hydrazine?
I only found sources (like this ) giving impulse density of hydrazine used as a bipropellant in conjunction with various oxidizers, but I was unable to find any that would give me density impulse of monopropellant hydrazine... does anyone know?
Well, the density of hydrazine is $1.021 \frac{kg}{L}$, and its $I_{sp}$ is $220 s$ as a mono propellant. (Both values from the Wiki page).
That is a total of $224.6 \frac{kg \cdot s}{L}$, using the same units as your source.
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2019-11-15 02:09:27
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https://proofwiki.org/wiki/Category:Definitions/Normed_Vector_Spaces
|
# Category:Definitions/Normed Vector Spaces
Let $\struct {K, +, \circ}$ be a normed division ring.
Let $V$ be a vector space over $K$.
Let $\norm {\,\cdot\,}$ be a norm on $V$.
Then $\struct {V, \norm {\,\cdot\,} }$ is a normed vector space.
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2021-09-21 19:24:48
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https://cugojujynycijekoq.atholmoraleephotography.com/studies-on-collision-processes-of-complex-molecules-in-the-gas-phase-book-5579ae.php
|
Last edited by Tunris
Thursday, May 14, 2020 | History
2 edition of Studies on collision processes of complex molecules in the gas phase. found in the catalog.
Studies on collision processes of complex molecules in the gas phase.
Edward McLaughlin
# Studies on collision processes of complex molecules in the gas phase.
## by Edward McLaughlin
Published .
Written in English
Edition Notes
Thesis (M. Sc.)--The Queen"s University of Belfast, 1954.
The Physical Object
Pagination1 v
ID Numbers
Open LibraryOL20335396M
2, are made only through industrial processes. Pressure A key measure of gas-phase molecules is their pressure. For a gas in a container, the pressure of the gas is the force exerted by the gas particles hitting the surface of the container. There isn't really a container for our atmosphere so we need to think of pressure in a slightly File Size: KB. The gas-phase reaction occurs too rapidly to isolate any such chemical compound. Collision theory explains why most reaction rates increase as concentrations increase. With an increase in the concentration of any reacting substance, the chances for collisions between molecules are increased because there are more molecules per unit of : OpenStax.
1. Kinetic Theory of Gases This is a statistical treatment of the large ensemble of molecules that make up a gas. We had expressed the ideal gas law as: pV = nRT (1) where nis the number of moles. We can also express it as: pV = NkT (2) where Nis the number of molecules and kis Boltzmann’s constant k= File Size: KB. In this and the two following chapters we present a perspective onto the world of electronic, atomic and molecular collision processes. It constitutes and active and productive field of modern physics, which is often neglected in academic education – in spite of a wealth Author: Ingolf V. Hertel, Claus-Peter Schulz.
the gas phase. From that time until , virtually every kinetics text and treatise used this reaction as the ideal example of a two-body collision mechanism. One gas molecule of collides with a molecule of 12, they reshuffle atoms, and two molecules of HI are the result. But in , J. Size: 8MB. As a first step, the molecules thermalize with a helium or neon buffer-gas in the cryogenic buffer-gas cell and get cooled down to 6 Kelvin (helium) and 17 Kelvin (neon) respectively.
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### Studies on collision processes of complex molecules in the gas phase by Edward McLaughlin Download PDF EPUB FB2
Phase also has a pronounced effect on the mobility of molecules. Molecules in the gas phase are free to move around, and they do so quickly. On the other hand, they are pretty well spread out. Nevertheless, collisions in the gas phase happen quite easily, which make gas-phase reactions happen more readily.
This study underscores the need for continued observational studies of trans-methyl formate and for the exploration of other gas-phase formation routes to complex organic molecules.
View Show abstract. @article{osti_, title = {Handbook of chemical lasers}, author = {Gross, R W.F. and Bott, J F}, abstractNote = {The available literature and research work in chemical lasers which was published and performed between and are collected and critically reviewed.
Basic reviews are presented on the chemical kinetics of nonequilibrium reactions, gas dynamics of reactive flows, and. Atoms and molecules make up a large fraction of the interstellar medium (ISM) and other astrophysical environments. Understanding how they are formed, destroyed, and altered via gas-phase.
gas particles are in continuous random motion undergoing collisions with other particles and walls 4. collisions between any two gas particles are elastic (conservation of momentum and KE) 5.
avg KE of gas particles is proportional to absolute temperature of gas and same for all gases at same temperature. The relationship of the information obtained to that derived from gas-phase photoelectron spectroscopic (p.e.s.) studies on metal oxides is discussed.
He (I) photoelectron spectra, recorded in the – eV ionization energy region for the Na + N 2 O and Na + O 3 gas-phase reactions are presented. Instead, it can take several minutes for us to detect an aroma because molecules are traveling in a medium with other gas molecules. Because gas molecules collide as often as 10 10 times per second, changing direction and speed with each collision, they do not diffuse across a.
Molecular Processes in Plasmas describes elementary collision processes in plasmas, particularly those involving molecules or molecular ions. Those collision processes (called molecular processes) maintain plasmas, produce reactive species and emissions, and play a key role in energy balance in plasmas or more specifically in determining the energy distribution of plasma by: @article{osti_, title = {Collisional Activation of Peptide Ions in FT-ICR Mass Spectrometry}, author = {Laskin, Julia and Futrell, Jean H}, abstractNote = {In the last decade characterization of complex molecules, particularly biomolecules became a focus of both fundamental and applied research in mass spectrometry.
Most of these studies utilize tandem mass spectrometry (MS/MS) for. Get this from a library. Collision processes in gases. [F L Arnot] -- "This book is based on a course of lectures which I gave to advanced students in physics and chemistry in the University of St.
Andrews during the winter of Its main object is to assist. Start studying Chemistry Ch review. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Search. reactants and products are in the same phase. To react, gas particles must.
collide. To be effective, a collision requires If a collision between molecules is oriented properly, the molecules are. more. The title compound 1-exo (with minor amounts of its C8 epimer 1-endo) was prepared by Wolff-Kishner reduction of the cycloadduct of 1,3-cyclohexadiene and [1,3]-migration product 2-endo was synthesized by efficient selective cyclopropanation of endovinylbicyclo[]octene at the exocyclic phase thermal reactions of 1-exo afforded C8 epimerization to 1.
manipulating these molecules, but producing samples of very large, cold molecules at rest in the laboratory frame has remained elusive. Here we report on the creation of gas-phase naphthalene at 6 K, created through a novel rapid helium gas cooling method. Prior to this work, it.
Reactive processes, taking place when sodium ions collide with neutral iso-C 3 H 7 Cl molecules in the – eV range of energies in the center of mass frame, have been studied using an octopole radiofrequency guided-ion-beam apparatus developed in our laboratory.
A dehydrohalogenation reaction channel leading to Na(C 3 H 6) + formation has been observed up to eV while another. Institute of Physics, ELI Beamlines, Czech Academy of Sciences, Prague, Czech Republic Interests: lipid polymorphism, lipid cubic phases, non-lamellar lipid phases, lipid nanoparticles, protein crystallization, kinetics of crystal growth, kinetics of phase transitions, liquid crystals, time resolved X-ray scattering (SAXS and WAXS), X-ray powder diffraction, pump-probe and stop-flow kinetics.
New studies of electronically nonadiabatic processes of oxygen atoms and oxygen molecules have also been begun. When ZPE effects play a major role, traditional mixed quantum-classical methods may need to be improved and we have recently made progress on including the effect of these adjustments on simulation results.
Download figure: Standard image High-resolution image Export PowerPoint slide We can work out the collision frequency by looking at figure in a little more detail. Within a time interval, the particle on the left will move a distance through the gas, represented by the length of the cylinder (as defined previously, is the average velocity of the particle).
Collision Process in Gases: An electrical discharge is normally created from unionised gas by Collision Process in Gases. These processes are mainly gas processes which occur due to the collision between the charged particles and gas atoms or molecules.
These are of the following two types. Elastic collisions. Radiative Association: bond formation Timescales: s - vibrational transition, s - electronic transition, s - collisional timescale (or lifetime of collisional complex) => molecule formation only after ~ collisions ( if electronic transitions are available).
Slow for small reactants, but can be rapid for complex radicals. Three inelastic processes that can occur during collisions of high-velocity gas-phase ions with gas molecules are considered.
These are: charge exchange (sometimes called electron transfer), in which, typically, one or more electrons from the gas are transferred to the ion; charge stripping, in which one or more free electrons leave the ion; and excitation, in which the ion and/or the gas.
Abstract. The gas phase reactions that produce polyatomic molecules in dense interstellar clouds are reviewed. The production of complex molecules and the extent of deuterium fractionation in dense clouds are discussed in the context of detailed : Eric Herbst, Eric Herbst.The average relative velocity of gas molecules can be obtained by the Maxwell-Boltzmann distribution and is equal to $$\langle v \rangle = \sqrt{\frac{8kT}{\pi m}}$$ The mean free path and the average relative velocity are related to the mean collision time $\tau$ (average time between two collisions) by $$\langle v \rangle = \frac \lambda \tau$$.The scope of chemical kinetics spans the area from nuclear processes up to the behavior of large molecules.
Current practice in chemical kinetics tries to identify the one particular elementary step that has a very large effect on the overall reaction rate. This elementary process is known as the rate-determining step of the reaction.
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2021-04-15 23:00:57
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https://encyclopediaofmath.org/wiki/Newton_interpolation_formula
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# Newton interpolation formula
A form of writing the Lagrange interpolation formula by using divided differences:
$$\tag{1 } L _ {n} ( x) = \ f ( x _ {0} ) + ( x - x _ {0} ) f ( x _ {0} ; x _ {1} ) + \dots +$$
$$+ ( x - x _ {0} ) \dots ( x - x _ {n - 1 } ) f ( x _ {0} ; \dots ; x _ {n} ),$$
where $f ( x _ {0} ; \dots ; x _ {k} )$ are the divided differences of order $k$; it was treated by I. Newton in 1687. Formula (1) is called Newton's interpolation formula for unequal differences. When the $x _ {i}$ are equidistant, that is, if
$$x _ {1} - x _ {0} = \dots = x _ {n} - x _ {n - 1 } = h,$$
then by introducing the notation $( x - x _ {0} )/h = t$ and expressing the divided differences $f ( x _ {0} ; \dots ; x _ {k} )$ in terms of the finite differences $f _ {k/2} ^ { k }$ according to the formula
$$f ( x _ {0} ; \dots ; x _ {k} ) = \ \frac{f _ {k/2} ^ { k } }{h ^ {k} k! } ,\ \ k = 0 \dots n,$$
one obtains a way of writing the polynomial $L _ {n} ( x)$ in the form
$$\tag{2 } L _ {n} ( x) = \ L _ {n} ( x _ {0} + th) =$$
$$= \ f _ {0} + tf _ {1/2} ^ { 1 } + \frac{t ( t - 1) }{2! } f _ {1} ^ { 2 } + \dots + \frac{t ( t - 1) \dots ( t - n + 1) }{n! } f _ {n/2} ^ { n } ,$$
which is called Newton's interpolation formula for forward interpolation. If the same change of variables is made in the interpolation polynomial $L _ {n}$ with nodes $x _ {0} , x _ {-} 1 \dots x _ {-} n$, where $x _ {-} k = x _ {0} - kh$,
$$L _ {n} ( x) = \ f ( x _ {0} ) + ( x - x _ {0} ) f ( x _ {0} ; x _ {-} 1 ) + \dots +$$
$$+ ( x - x _ {0} ) \dots ( x - x _ {- n + 1 } ) f ( x _ {0} ; \dots ; x _ {-} n ),$$
then one obtains Newton's interpolation formula for backward interpolation:
$$\tag{3 } L _ {n} ( x) = L _ {n} ( x _ {0} + th) =$$
$$= \ f _ {0} + tf _ {-} 1/2 ^ { 1 } + \frac{t ( t + 1) }{2! } f _ {-} 1 ^ { 2 } + \dots +$$
$$+ \frac{t ( t + 1) \dots ( t + n - 1) }{n! } f _ {-} n/2 ^ { n } .$$
Formulas (2) and (3) are convenient for computing tables of a given function $f ( x)$ if the point $x$ is at the beginning or the end of the table, since in this case the addition of one or several nodes caused by the wish to increase the accuracy of the approximation does not lead to a repetition of the whole work done as in computations with Lagrange's formula.
#### References
[1] I.S. Berezin, N.P. Zhidkov, "Computing methods" , 1 , Pergamon (1973) (Translated from Russian) [2] N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from Russian)
The divided differences $f ( x _ {0} ; x _ {1} ) \dots f ( x _ {0} ; \dots ; x _ {n} )$ are defined by:
$$f ( x _ {0} ; x _ {1} ) = \ \frac{f ( x _ {1} ) - f ( x _ {0} ) }{x _ {1} - x _ {0} } ,$$
$$f ( x _ {0} ; x _ {1} ; x _ {2} ) = \frac{1}{x _ {2} - x _ {1} } \left ( \frac{f ( x _ {2} ) - f ( x _ {0} ) }{x _ {2} - x _ {0} } - \frac{f ( x _ {1} ) - f ( x _ {0} ) }{x _ {1} - x _ {0} } \right ) ,$$
$${\dots \dots \dots \dots }$$
or
$$f ( x _ {0} ; \dots ; x _ {n} ) = \ \sum _ { i= } 0 ^ { n } \prod _ { j= } 0 ^ { n } {} ^ \prime \frac{f ( x _ {i} ) }{x _ {i} - x _ {j} } ,$$
where the prime in $\prod ^ \prime$ means that the factor $1/ ( x _ {i} - x _ {i} )$ is to be omitted. Formula (1) is also known as the finite Newton series for a function $f$.
#### References
[a1] K.E. Atkinson, "An introduction to numerical analysis" , Wiley (1978) [a2] P.J. Davis, "Interpolation and approximation" , Dover, reprint (1975) [a3] F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1974)
How to Cite This Entry:
Newton interpolation formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Newton_interpolation_formula&oldid=47967
This article was adapted from an original article by M.K. Samarin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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2022-10-01 23:18:58
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http://sciencewise.info/
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• Is cosmic acceleration proven by local cosmological probes?
Context: The cosmological concordance model ($\Lambda$CDM) matches the cosmological observations exceedingly well. This model has become the standard cosmological model with the evidence for an accelerated expansion provided by the type Ia supernovae (SNIa) Hubble diagram. However, the robustness of this evidence has been addressed recently with somewhat diverging conclusions. Aims: The purpose of this paper is to assess the robustness of the conclusion that the Universe is indeed accelerating if we rely only on low-redshift (z$\lesssim$2) observations, that is to say with SNIa, baryonic acoustic oscillations, measurements of the Hubble parameter at different redshifts, and measurements of the growth of matter perturbations. Methods: We used the standard statistical procedure of minimizing the $\chi^2$ function for the different probes to quantify the goodness of fit of a model for both $\Lambda$CDM and a simple nonaccelerated low-redshift power law model. In this analysis, we do not assume that supernovae intrinsic luminosity is independent of the redshift, which has been a fundamental assumption in most previous studies that cannot be tested. Results: We have found that, when SNIa intrinsic luminosity is not assumed to be redshift independent, a nonaccelerated low-redshift power law model is able to fit the low-redshift background data as well as, or even slightly better, than $\Lambda$CDM. When measurements of the growth of structures are added, a nonaccelerated low-redshift power law model still provides an excellent fit to the data for all the luminosity evolution models considered. Conclusions: Without the standard assumption that supernovae intrinsic luminosity is independent of the redshift, low-redshift probes are consistent with a nonaccelerated universe.
LuminosityBaryon acoustic oscillationsNuisance parameterLambda-CDM modelCosmologySupernovaCosmological parametersGoodness of fitCosmological modelAccelerated expansion of the Universe...
• New quantum effects in relativistic magnetohydrodynamics
Chiral anomaly induces a new kind of macroscopic quantum behavior in relativistic magnetohydrodynamics, including the chiral magnetic effect. In this talk we present two new quantum effects present in fluids that contain charged chiral fermions: 1) the turbulent inverse cascade driven by the chiral anomaly; 2) quantized chiral magnetic current induced by the reconnections of magnetic flux. We also discuss the implications for the evolution of the quark-gluon plasma produced in heavy ion collisions.
Chiral magnetic effectChiral anomalyRelativistic magnetohydrodynamicsInverse cascadeChiral fermionMagnetic helicityHelicityQuark-gluon plasmaChirality imbalanceChirality...
• Neutral Buckminsterfullerene in the diffuse interstellar medium
Emission of fullerenes in their infrared vibrational bands has been detected in space near hot stars. The proposed attribution of the diffuse interstellar bands at 9577 and 9632 \AA\ to electronic transitions of the buckminsterfullerene cation (i.e. C$_{60}^+$ ) was recently supported by new laboratory data, confirming the presence of this species in the diffuse interstellar medium (ISM). In this letter, we present the detection, also in the diffuse ISM, of the 17.4 and 18.9 $\mu$m emission bands commonly attributed to vibrational bands of neutral C$_{60}$. According to classical models that compute the charge state of large molecules in space, C$_{60}$ is expected to be mostly neutral in the diffuse ISM. This is in agreement with the abundances of diffuse C$_{60}$ we derive here from observations. We also find that C$_{60}$ is less abundant in the diffuse ISM than in star forming regions, supporting the proposal that C$_{60}$ can be formed in these regions.
Interstellar mediumLine of sightAbundanceFullereneBuckminsterfullereneStar-forming regionElectronic transitionDiffuse interstellar bandEvolved starsUltraviolet background...
• Science enabled by a Moon Village
A human-robotic "Moon Village" would offer significant scientific opportunities by providing an infrastructure on the lunar surface. An analogy would be the way in which human outposts in Antarctica facilitate research activities across multiple scientific disciplines on that continent. Scientific fields expected to benefit from a Moon Village will include: planetary science, astronomy, astrobiology, life sciences, and fundamental physics. In addition, a Moon Village will help develop the use of lunar resources, which will yield additional longer-term scientific benefits.
XenobiologyPlanetary scienceRoboticsAstronomyField...
• Simulating galaxies in the reionization era with FIRE-2: galaxy scaling relations, stellar mass functions, and luminosity functions
We present a suite of cosmological zoom-in simulations at z>5 from the Feedback In Realistic Environments project, spanning a halo mass range M_halo~10^8-10^12 M_sun at z=5. We predict the stellar mass-halo mass relation, stellar mass function, and luminosity function in several bands from z=5-12. The median stellar mass-halo mass relation does not evolve strongly at z=5-12. The faint-end slope of the luminosity function steepens with increasing redshift, as inherited from the halo mass function at these redshifts. Below z~6, the stellar mass function and ultraviolet (UV) luminosity function slightly flatten below M_star~10^4.5 M_sun (fainter than M_1500~-14), owing to the fact that star formation in low-mass halos is suppressed by the ionizing background by the end of reionization. Such flattening does not appear at higher redshifts. We provide redshift-dependent fitting functions for the SFR-M_halo, SFR-M_star, and broad-band magnitude-stellar mass relations. We derive the star formation rate density and stellar mass density at z=5-12 and show that the contribution from very faint galaxies becomes more important at z>8. Furthermore, we find that the decline in the z~6 UV luminosity function brighter than M_1500~-20 is largely due to dust attenuation. Approximately 37% (54%) of the UV luminosity from galaxies brighter than M_1500=-13 (-17) is obscured by dust at z~6. Our results broadly agree with current data and can be tested by future observations.
GalaxyStellar massVirial massStellar mass functionLuminosity functionStar formationStarFIRE simulationsReionizationDust attenuation curve...
• A resolved and asymmetric ring of PAHs within the young circumstellar disk of IRS 48
For one decade, the spectral-type and age of the $\rho$ Oph object IRS-48 were subject to debates and mysteries. Modelling its disk with mid-infrared to millimeter observations led to various explanations to account for the complex intricacy of dust-holes and gas-depleted regions. We present multi-epoch high-angular-resolution interferometric near-infrared data of spatially-resolved emissions in its first 15AU, known to have very strong Polycyclic Aromatic Hydrocarbon (PAH) emissions within this dust-depleted region. We make use of new Sparse-Aperture-Masking data to instruct a revised radiative-transfer model where SED fluxes and interferometry are jointly fitted. Neutral and ionized PAH, Very Small Grains (VSG) and classical silicates are incorporated into the model; new stellar parameters and extinction laws are explored. A bright (42L$_{\odot}$) central-star with A$_v$=12.5mag and R$_v$=6.5 requires less near-infrared excess: the inner-most disk at $\approx$1AU is incompatible with the data. The revised stellar parameters place this system on a 4 Myr evolutionary track, 4 times younger than previous estimations, in better agreement with the surrounding $\rho$ Oph region and disk-lifetimes observations. The disk-structure converges to a classical-grains outer-disk from 55AU combined with a fully resolved VSG\&PAH-ring, at 11-26 AU. We find two over-luminosities in the PAH-ring at color-temperatures consistent with the radiative transfer simulations; one follows a Keplerian circular orbit at 14AU. We show a depletion of a factor $\approx$5 of classical dust grains compared to VSG\&PAH: the IRS-48 disk is nearly void of dust-grains in the first 55 AU. A 3.5M$_{Jup}$ planet on a 40AU orbit qualitatively explains the new disk-structure.
Astronomical UnitStarInfrared Spectrometer on SpitzerPoint sourceSpectral energy distributionNear-infraredSilicateExtinctionCompanionRadiative transfer...
• On some Rajchman measures and equivalent Salem's problem
We construct certain Rajchman measures by using integrability properties of the Fourier and Fourier-Stieltjes transforms. In particular, we state a problem and prove that it is equivalent to the known and still unsolved question posed by R. Salem (Trans. Amer. Math. Soc. 53 (3) (1943), p. 439) whether Fourier-Stieltjes coefficients of the Minkowski's question mark function vanish at infinity.
Minkowski's question mark functionModified Bessel FunctionRiemann-Lebesgue lemmaMonotonic functionMinkowski functionalElementary theoryRiemann-Stieltjes integralSingular measureFubini's theoremRegularization...
• 3D CFT Archipelago from Single Correlator Bootstrap
We show that the scaling dimensions of lowest operators in conformal field theories (CFTs) can be isolated in small and closed regions from single correlator bootstrap. We find the conserved currents play crucial roles in bootstrapping the crossing equation. By imposing a mild gap between the scaling dimensions of the conserved current and its next operator, the scaling dimensions of lowest operators are forced to lie in small isolated regions, i.e., these CFTs can be almost fixed by few lowest operators in certain channels. For CFTs with extended supersymmetry, the single correlator crossing equation involves several conserved or shorted operators and by imposing gaps in these sectors it is possible to isolate different CFTs. Specifically, we bootstrap the isolated regions corresponding to the 3D Ising model, $O(N)$ vector model, $N=1,2$ supersymmetric Ising models by introducing mild gaps in certain sectors with conserved or shorted operators.
Conformal field theorySupersymmetric CFTScaling dimensionConformal Bootstrap3D Ising modelGlobal symmetryOperator product expansionIsing modelExtended supersymmetryWess-Zumino model...
• The Reception of Newton's Principia
Newton's Principia, when it appeared in 1687, was received with the greatest admiration, not only by the foremost mathematicians and astronomers in Europe, but also by philosophers like Voltaire and Locke and by members of the educated public. In this account I describe some of the controversies that it provoked, and the impact it had during the next century on the development of celestial mechanics, and the theory of gravitation.
PlanetGravitational forceEarthSunNatural satelliteOrbital motionEllipticityCurvatureVorticityElliptical orbit...
• IRGAN: A Minimax Game for Unifying Generative and Discriminative Information Retrieval Models
This paper provides a unified account of two schools of thinking in information retrieval modelling: the generative retrieval focusing on predicting relevant documents given a query, and the discriminative retrieval focusing on predicting relevancy given a query-document pair. We propose a game theoretical minimax game to iteratively optimise both models. On one hand, the discriminative model, aiming to mine signals from labelled and unlabelled data, provides guidance to train the generative model towards fitting the underlying relevance distribution over documents given the query. On the other hand, the generative model, acting as an attacker to the current discriminative model, generates difficult examples for the discriminative model in an adversarial way by minimising its discrimination objective. With the competition between these two models, we show that the unified framework takes advantage of both schools of thinking: (i) the generative model learns to fit the relevance distribution over documents via the signals from the discriminative model, and (ii) the discriminative model is able to exploit the unlabelled data selected by the generative model to achieve a better estimation for document ranking. Our experimental results have demonstrated significant performance gains as much as 23.96% on Precision@5 and 15.50% on MAP over strong baselines in a variety of applications including web search, item recommendation, and question answering.
Information retrievalRankingGenerative modelDiscriminative modelGenerative Adversarial NetRankMinimaxLearning to rankConvolutional neural networkFactorisation...
• From Lorenz to Coulomb and other explicit gauge transformationsver. 2
The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and (ii) to show that, whatever propagation or non-propagation characteristics are exhibited by the potentials in a particular gauge, the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light. The example of the transformation from the Lorenz gauge (retarded solutions for both scalar and vector potential) to the Coulomb gauge (instantaneous, action-at-a-distance, scalar potential) is treated in detail. A transparent expression is obtained for the vector potential in the Coulomb gauge, with a finite nonlocality in time replacing the expected spatial nonlocality of the transverse current. A class of gauges (v-gauge) is described in which the scalar potential propagates at an arbitrary speed v relative to the speed of light. The Lorenz and Coulomb gauges are special cases of the v-gauge. The last examples of gauges and explicit gauge transformation functions are the Hamiltonian or temporal gauge, the nonrelativistic Poincare or multipolar gauge, and the relativistic Fock-Schwinger gauge.
Gauge transformationCoulomb gaugeSpeed of lightHamiltonianCausalityElectricity and magnetismPotentialScalarTransformationsVector...
• Dataset and Neural Recurrent Sequence Labeling Model for Open-Domain Factoid Question Answeringver. 2
While question answering (QA) with neural network, i.e. neural QA, has achieved promising results in recent years, lacking of large scale real-word QA dataset is still a challenge for developing and evaluating neural QA system. To alleviate this problem, we propose a large scale human annotated real-world QA dataset WebQA with more than 42k questions and 556k evidences. As existing neural QA methods resolve QA either as sequence generation or classification/ranking problem, they face challenges of expensive softmax computation, unseen answers handling or separate candidate answer generation component. In this work, we cast neural QA as a sequence labeling problem and propose an end-to-end sequence labeling model, which overcomes all the above challenges. Experimental results on WebQA show that our model outperforms the baselines significantly with an F1 score of 74.69% with word-based input, and the performance drops only 3.72 F1 points with more challenging character-based input.
Sequence labelingEmbeddingClassificationRankingF1 scoreNeural networkWord embeddingTraining setRankPart-of-speech...
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d >= 3.
HamiltonianNext-to-leading order computationRenormalizationQuantum field theoryVacuum energyConformal field theoryIsing modelPerturbation theoryMass gapRenormalization group...
• Pixel Color-Magnitude Diagram Analysis of the Brightest Cluster Galaxies in Dynamically Young and Old Clusters, Abell 1139 and Abell 2589
As a case study to understand the coevolution of Brightest Cluster Galaxies (BCGs) and their host clusters, we investigate the BCGs in dynamically young and old clusters, Abell 1139 (A1139) and Abell 2589 (A2589). We analyze the pixel color-magnitude diagrams (pCMDs) using deep g- and r-band images, obtained from the Canada-France-Hawaii Telescope observations. After masking foreground/background objects and smoothing pixels in consideration of the observational seeing size, detailed pCMD features are compared between the two BCGs. (1) While the overall shapes of the pCMDs are similar to those of typical early-type galaxies, the A2589-BCG tends to have redder mean pixel color and smaller pixel color deviation at given surface brightness than the A1139-BCG. (2) The mean pixel color distribution as a function of pixel surface brightness (pCMD backbone) indicates that the A2589-BCG formed a larger central body (~ 2.0 kpc in radius) by major dry mergers at an early epoch than the A1139-BCG (a central body ~ 1.3 kpc in radius), while they have grown commonly by subsequent minor mergers. (3) The spatial distributions of the pCMD outliers reveal that the A1139-BCG experienced considerable tidal events more recently than the A2589-BCG, whereas the A2589-BCG has an asymmetric compact core possibly resulting from major dry merger at an early epoch. (4) The A2589-BCG shows a very large faint-to-bright pixel number ratio compared to early-type non-BCGs, whereas the ratio for the A1139-BCG is not distinctively large. These results are consistent with the idea that the BCG in the dynamically older cluster (A2589) formed earlier and is relaxed better.
Brightest cluster galaxyGalaxyStellar populationsSurface brightnessHertzsprung-Russell diagramEarly-type galaxyMilky WayCanada-France-Hawaii TelescopeBright galaxiesElliptical galaxy...
• What does the Bullet Cluster tell us about self-interacting dark matter?ver. 2
We perform numerical simulations of the merging galaxy cluster 1E 0657-56 (the Bullet Cluster), including the effects of elastic dark matter scattering. In a similar manner to the stripping of gas by ram pressure, dark matter self-interactions would transfer momentum between the two galaxy cluster dark matter haloes, causing them to lag behind the collisionless galaxies. The absence of an observed separation between the dark matter and stellar components in the Bullet Cluster has been used to place upper limits on the cross-section for dark matter scattering. We emphasise the importance of analysing simulations in an observationally-motivated manner, finding that the way in which the positions of the various components are measured can have a larger impact on derived constraints on dark matter's self-interaction cross-section than reasonable changes to the initial conditions for the merger. In particular, we find that the methods used in previous studies to place some of the tightest constraints on this cross-section do not reflect what is done observationally, and overstate the Bullet Cluster's ability to constrain the particle properties of dark matter. We introduce the first simulations of the Bullet Cluster including both self-interacting dark matter and gas. We find that as the gas is stripped it introduces radially-dependent asymmetries into the stellar and dark matter distributions. As the techniques used to determine the positions of the dark matter and galaxies are sensitive to different radial scales, these asymmetries can lead to erroneously measured offsets between dark matter and galaxies even when they are spatially coincident.
Dark matterBullet ClusterSelf-interacting dark matterDark matter haloStarDark matter particleMerging galaxy clusterSoftening lengthWeak lensingNavarro-Frenk-White profile...
• Relativistic initial conditions for N-body simulationsver. 2
Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for LambdaCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code. This space-time coincides with a simple "N-body gauge" for z<50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable "forwards approach" for such cases.
N-body simulationCold dark matterBoltzmann codeDark matterCosmologyDecaying dark matterMetric perturbationSynchronous gaugeGauge conditionThe early Universe...
• Phenomenology of ELDER Dark Matter
We explore the phenomenology of Elastically Decoupling Relic (ELDER) dark matter. ELDER is a thermal relic whose present density is determined primarily by the cross-section of its elastic scattering off Standard Model (SM) particles. Assuming that this scattering is mediated by a kinetically mixed dark photon, we argue that the ELDER scenario makes robust predictions for electron-recoil direct-detection experiments, as well as for dark photon searches. These predictions are independent of the details of interactions within the dark sector. Together with the closely related Strongly-Interacting Massive Particle (SIMP) scenario, the ELDER predictions provide a physically motivated, well-defined target region, which will be almost entirely accessible to the next generation of searches for sub-GeV dark matter and dark photons. We provide useful analytic approximations for various quantities of interest in the ELDER scenario, and discuss two simple renormalizable toy models which incorporate the required strong number-changing interactions among the ELDERs, as well as explicitly implement the coupling to electrons via the dark photon portal.
Standard ModelDark matterHidden photonDark sectorStrongly Interacting Massive ParticleElastic scatteringFreeze-outDark matter particleDegree of freedomKinetic decoupling...
• Sterile neutrino searches via displaced vertices at LHCb
We explore the sensitivity of displaced vertex searches at LHCb for testing sterile neutrino extensions of the Standard Model towards explaining the observed neutrino masses. We derive estimates for the constraints on sterile neutrino parameters from a recently published displaced vertex search at LHCb based on run 1 data. They yield the currently most stringent limit on active-sterile neutrino mixing in the sterile neutrino mass range between 4.5 GeV and 10 GeV. Furthermore, we present forecasts for the sensitivities that could be obtained from the run 2 data and also for the high-luminosity phase of the LHC.
Sterile neutrinoLHCbDisplaced verticesSterile neutrino massActive-sterile neutrino mixingLuminosityNeutrinoLarge Hadron ColliderStandard ModelExclusion limit...
• The nucleon spin explained using lattice QCD simulationsver. 2
We determine within lattice QCD, the nucleon spin carried by valence and sea quarks, and gluons. The calculation is performed using an ensemble of gauge configurations with two degenerate light quarks with mass fixed to approximately reproduce the physical pion mass. We find that the total spin carried by the quarks in the nucleon is $J_{u+d+s}{=}0.408(61)_{\rm stat.}(48)_{\rm syst.}$ and the gluon contribution is $J_g =0.133(11)_{\rm stat.}(14)_{\rm syst.}$ giving a total of $J_N=0.54(6)_{\rm stat.}(5)_{\rm syst.}$ consistent with the spin sum. For the quark intrinsic spin contribution we obtain $\frac{1}{2}\Delta\Sigma_{u+d+s}=0.201(17)_{\rm stat.}(5)_{\rm syst.}$. All quantities are given in the $\overline{\textrm{MS}}$ scheme at 2 GeV. The quark and gluon momentum fractions are also computed and add up to $\langle x\rangle_{u+d+s}+\langle x\rangle_g=0.804(121)_{\rm stat.}(95)_{\rm syst.}+0.267(12)_{\rm stat.}(10)_{\rm syst.}=1.07(12)_{\rm stat.}(10)_{\rm syst.}$ satisfying the momentum sum.
RenormalizationLattice QCDPion massStrange quarkExcited stateAxial chargeLight quarkDown quarkPropagatorQuark mass...
• Superconformal Symmetry and Correlation Functions
The N = 2, 4 superconformal symmetry constraints in d = 4 for four point functions of chiral primary 1/2-BPS operators are derived. The operators are described by symmetric traceless tensors of the internal R-symmetry group. A substantial simplification is achieved by introduction of null vectors. Two variable polynomials corresponding to different R-symmetry representations are constructed. The Ward identities for superconformal symmetry are obtained as simple differential equations. The general solution is presented in terms of a constant, a single variable function and a two variable function. An interpretation in terms of the operator product expansion is given for the case of fields of equal dimension and for the so called (next-to)extremal cases. The result is shown to accommodate long multiplets, semishort and short multiplets with protected dimension. Generically also non-unitary multiplets can appear. It is shown how to remove them to obtain a unitary theory. Implications of crossing symmetry for the four point functions studied are derived and discussed. It is shown that crossing symmetry fixes the single variable function in the general solution to be of free field form using singularity arguments. For a restricted set of next-to-extremal correlation functions with S3 symmetry amongst the first three fields it is shown that the amplitude is fixed up to normalization to free field form. We compute the conformal partial wave expansion of all representations in this amplitude and compute an averaged value of the anomalous dimensions for long multiplets given spin and twist in each relevant representation at first order in 1/N. Finally assuming the universal singularity structure we derive the general large N amplitude of four identical 1/2-BPS operators in the [0, p, 0] representation in terms of D functions. Explicit expressions for all coefficients are given.
Operator product expansionTwo-point correlation functionAnomalous dimensionScaling dimensionSuperconformal symmetrySupermultipletSupersymmetryEigenfunctionShort supermultipletUnitarity...
• gPhoton: The GALEX Photon Data Archive
gPhoton is a new database product and software package that enables analysis of GALEX ultraviolet data at the photon level. The project's stand-alone, pure-Python calibration pipeline reproduces the functionality of the original mission pipeline to reduce raw spacecraft data to lists of time-tagged, sky-projected photons, which are then hosted in a publicly available database by the Mikulski Archive at Space Telescope (MAST). This database contains approximately 130 terabytes of data describing approximately 1.1 trillion sky-projected events with a timestamp resolution of five milliseconds. A handful of Python and command line modules serve as a front-end to interact with the database and to generate calibrated light curves and images from the photon-level data at user-defined temporal and spatial scales. The gPhoton software and source code are in active development and publicly available under a permissive license. We describe the motivation, design, and implementation of the calibration pipeline, database, and tools, with emphasis on divergence from prior work, as well as challenges created by the large data volume. We summarize the astrometric and photometric performance of gPhoton relative to the original mission pipeline. For a brief example of short time domain science capabilities enabled by gPhoton, we show new flares from the known M dwarf flare star CR Draconis. The gPhoton software has permanent object identifiers with the ASCL (ascl:1603.004) and DOI (doi:10.17909/T9CC7G). This paper describes the software as of version v1.27.2.
Galaxy Evolution ExplorerCalibrationPhotometryEclipsesLight curvePythonCountingData archiveM dwarfsAstrometry...
• Improving neural networks by preventing co-adaptation of feature detectors
When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.
ArchitectureBackpropagationHyperparameterHidden Markov modelFilter bankNeural networkGeneMarketClassificationRegularization...
• An empirical analysis of dropout in piecewise linear networksver. 2
The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we empirically investigate several questions related to the efficacy of dropout, specifically as it concerns networks employing the popular rectified linear activation function. We investigate the quality of the test time weight-scaling inference procedure by evaluating the geometric average exactly in small models, as well as compare the performance of the geometric mean to the arithmetic mean more commonly employed by ensemble techniques. We explore the effect of tied weights on the ensemble interpretation by training ensembles of masked networks without tied weights. Finally, we investigate an alternative criterion based on a biased estimator of the maximum likelihood ensemble gradient.
ArithmeticHyperparameterRegularizationActivation functionTraining setNeural networkMaximum likelihoodStochastic gradient descentLearning ruleMonte Carlo method...
• Detection of virial shocks in stacked Fermi-LAT clustersver. 2
Galaxy clusters are thought to grow by accreting mass through large-scale, strong, structure-formation shocks. Such a shock is expected to accelerate relativistic electrons, thus generating a spectrally flat leptonic virial ring. However, until now, only the nearby Coma cluster has shown evidence for a $\gamma$-ray virial ring. We stack Fermi-LAT data for the 112 most massive, high latitude, extended clusters, enhancing the ring sensitivity by rescaling clusters to their virial radii and utilizing the expected flat spectrum. In addition to a central unresolved, hard signal (detected at the $\sim 6\sigma$ confidence level), probably dominated by AGN, we identify ($>4.5\sigma$ isolated; $5.9\sigma$ for our nominal model) a bright, spectrally flat $\gamma$-ray ring at the expected virial shock position. It implies that the shock deposits $\sim 0.5\%$ of the thermal energy in relativistic electrons over a Hubble time. This result, consistent with the Coma signal, supports and calibrates the virial shock model, and indicates that the cumulative emission from such shocks significantly contributes to the diffuse extragalactic $\gamma$-ray and low-frequency radio backgrounds.
Point sourceActive Galactic NucleiCluster of galaxiesPoint spread functionMock catalogCluster samplingTest statisticVERITASGalactic planeComa Cluster...
• First Steps Toward a Method for Estimating Cosmological Parameters using Strong Lensing, X-ray and Dynamics Total Mass Estimatesver. 3
In this thesis we want to introduce the first steps towards realising a new method to investigate the cosmological parameters and conduct a detailed analysis of the galaxy cluster MACS J0416. Toward this end, we use the current model from Grillo et al. (2015) as a template and the publicly available lensing code Lenstool. This code has previously been used by Jauzac et al. (2014), Richard et al. (2014), Jauzac et al. (2015) and Caminha et al. (2016) to model MACS J0416 (Grillo et al. (2015) used GLEE). We created $10$ different models to cover a reasonable set of different approaches. In addition to the replication of the Grillo et al. (2015) models, with two cluster scale halos and 175 circular cluster member mass-density profiles, we created models using elliptical mass-density profiles for the cluster members and models where we optimize the cluster member scaling relation slopes. In order to investigate the viability of using the projected total mass estimate from different cosmological models to estimate the cosmological parameter values, we created 49 models each representing a different set of cosmological parameters.
GalaxyStrong gravitational lensingCosmological parametersPhase space causticOptimizationVelocity dispersionMass distributionCluster Lensing And Supernova survey with HubbleDeflection angleCluster of galaxies...
• Revised Uncertainties in Big Bang Nucleosynthesis
Big Bang Nucleosynthesis (BBN) explores the first few minutes of nuclei formation after the Big Bang. We present updates that result in new constraints at the 2{\sigma} level for the abundances of the four primary light nuclides - D,3He,4He, and 7Li - in BBN. A modified standard BBN code was used in a Monte Carlo analysis of the nucleosynthesis uncertainty as a function of baryon-to-photon ratio. Reaction rates were updated to those of NACRE and REACLIB, and R-Matrix calculations. The results are then used to derive a new constraint on the effective number of neutrinos.
Big bang nucleosynthesisAbundanceMonte Carlo methodBig BangEffective number of neutrinosExpansion of the UniverseNucleosynthesisGaussian distributionNeutron lifetimeLight element abundances...
• On the time lags of the LIGO signals
To date, the LIGO collaboration has detected three gravitational wave (GW) events appearing in both its Hanford and Livingston detectors. In this article we reexamine the LIGO data with regard to correlations between the two detectors. With special focus on GW150914, we report correlations in the detector noise which, at the time of the event, happen to be maximized for the same time lag as that found for the event itself. Specifically, we analyze correlations in the calibration lines in the vicinity of 35\,Hz as well as the residual noise in the data after subtraction of the best-fit theoretical templates. The residual noise for the two more recent events, GW151226 and GW170104, exhibits equivalent behavior with respect to each of their time lags. A clear distinction between signal and noise therefore remains to be established in order to determine the contribution of gravitational waves to the detected signals.
Gravitational waveLaser Interferometer Gravitational-Wave ObservatoryLIGO GW150914 eventCalibrationTime delayCross-correlationLIGO GW151226 eventInterferenceTwo-point correlation functionFast Fourier transform...
• A Study of High-redshift AGN Feedback in SZ Cluster Samples
We present a study of AGN feedback at higher redshifts ($0.3<z<1.2$) using Sunyaev-Zel'dovich (SZ) selected samples of clusters from the South-Pole Telescope and Atacama Cosmology Telescope surveys. In contrast to studies of nearby systems, we do not find a separation between cooling flow clusters and non-cooling flow clusters based on the radio luminosity of the central radio source. This lack may be due to the increased incidence of galaxy-galaxy mergers at higher redshift that triggers AGN activity. In support of this scenario, we find evidence for evolution in the radio luminosity function of the central radio source: while the lower-luminosity sources do not evolve much, the higher-luminosity sources show a strong increase in the frequency of their occurrence at higher redshifts. We interpret this evolution as an increase in high-excitation radio galaxies (HERGs) in massive clusters at $z>0.6$, implying a transition from HERG-mode accretion to lower-power low-excitation radio galaxy (LERG)-mode accretion at intermediate redshifts. Additionally, we use local radio-to-jet power scaling relations to estimate feedback power and find that half of the cooling flow systems in our sample probably have enough heating to balance cooling. However, we postulate that the local relations are likely not well suited to predict feedback power in high-luminosity HERGs, as they are derived from samples composed mainly of lower-luminosity LERGs.
• The origin of fast molecular outflows in quasars: molecule formation in AGN-driven galactic winds
We explore the origin of fast molecular outflows that have been observed in Active Galactic Nuclei (AGN). Previous numerical studies have shown that it is difficult to create such an outflow by accelerating existing molecular clouds in the host galaxy, as the clouds will be destroyed before they can reach the high velocities that are observed. In this work, we consider an alternative scenario where molecules form in-situ within the AGN outflow. We present a series of hydro-chemical simulations of an isotropic AGN wind interacting with a uniform medium. We follow the time-dependent chemistry of 157 species, including 20 molecules, to determine whether molecules can form rapidly enough to produce the observed molecular outflows. We find H$_2$ outflow rates up to 140 M$_\odot$ yr$^{-1}$, which is sensitive to density, AGN luminosity, and metallicity. We compute emission and absorption lines of CO, OH and warm (a few hundred to a few thousand K) H$_2$ from the simulations in post-processing. The CO-derived outflow rates and OH absorption strengths at solar metallicity agree with observations, although the maximum line of sight velocities from the model CO spectra are a factor $\approx$2 lower than is observed. We derive a CO (1-0) to H$_2$ conversion factor of $\alpha_{\rm{CO} (1-0)}$ = 0.15 M$_\odot$ (K km s$^{-1}$ pc$^2$)$^{-1}$, 5 times lower than is commonly assumed in observations of such systems. We find strong emission from the mid-infrared lines of H$_2$, which traces at least 70 per cent of the total H$_2$ mass. This H$_2$ emission may be observable by JWST.
Active Galactic NucleiMolecular outflowLuminosityMetallicityCoolingInterstellar mediumAbundanceDust grainUltraluminous infrared galaxyQuasar...
• Self-Normalizing Neural Networksver. 2
Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot exploit many levels of abstract representations. We introduce self-normalizing neural networks (SNNs) to enable high-level abstract representations. While batch normalization requires explicit normalization, neuron activations of SNNs automatically converge towards zero mean and unit variance. The activation function of SNNs are "scaled exponential linear units" (SELUs), which induce self-normalizing properties. Using the Banach fixed-point theorem, we prove that activations close to zero mean and unit variance that are propagated through many network layers will converge towards zero mean and unit variance -- even under the presence of noise and perturbations. This convergence property of SNNs allows to (1) train deep networks with many layers, (2) employ strong regularization, and (3) to make learning highly robust. Furthermore, for activations not close to unit variance, we prove an upper and lower bound on the variance, thus, vanishing and exploding gradients are impossible. We compared SNNs on (a) 121 tasks from the UCI machine learning repository, on (b) drug discovery benchmarks, and on (c) astronomy tasks with standard FNNs and other machine learning methods such as random forests and support vector machines. SNNs significantly outperformed all competing FNN methods at 121 UCI tasks, outperformed all competing methods at the Tox21 dataset, and set a new record at an astronomy data set. The winning SNN architectures are often very deep. Implementations are available at: github.com/bioinf-jku/SNNs.
Singular valueNeural networkContraction mappingArchitectureConvolutional neural networkRecurrent neural networkMachine learningDeep learningActivation functionHyperparameter...
• The Waning of the WIMP? A Review of Models, Searches, and Constraints
Weakly Interacting Massive Particles (WIMPs) are among the best-motivated dark matter candidates. In light of no conclusive detection signal yet despite an extensive search program that combines, often in a complementary way, direct, indirect, and collider probes, we find it timely to give a broad overview of the WIMP paradigm. In particular, we review here the theoretical foundations of the WIMP paradigm, discuss status and prospects of various detection strategies, and explore future experimental challenges and opportunities.
Dark matterWeakly interacting massive particleStandard ModelHiggs bosonStandard Model fermionDark matter particle massColliderSpin independentLaboratory dark matter searchPseudoscalar...
• NuSTEC White Paper: Status and Challenges of Neutrino-Nucleus Scatteringver. 2
The precise measurement of neutrino properties is among the highest priorities in fundamental particle physics, involving many experiments worldwide. Since the experiments rely on the interactions of neutrinos with bound nucleons inside atomic nuclei, the planned advances in the scope and precision of these experiments requires a commensurate effort in the understanding and modeling of the hadronic and nuclear physics of these interactions, which is incorporated as a nuclear model in neutrino event generators. This model is essential to every phase of experimental analyses and its theoretical uncertainties play an important role in interpreting every result. In this White Paper we discuss in detail the impact of neutrino-nucleus interactions, especially the nuclear effects, on the measurement of neutrino properties using the determination of oscillation parameters as a central example. After an Executive Summary and a concise Overview of the issues, we explain how the neutrino event generators work, what can be learned from electron-nucleus interactions and how each underlying physics process - from quasi-elastic to deep inelastic scattering - is understood today. We then emphasize how our understanding must improve to meet the demands of future experiments. With every topic we find that the challenges can be met only with the active support and collaboration among specialists in strong interactions and electroweak physics that include theorists and experimentalists from both the nuclear and high energy physics communities.
NeutrinoPionKinematicsForm factorDeep inelastic scatteringCharged currentFinal state interactionsWeak neutral current interactionElectron scatteringT2K experiment...
• Constraining Sterile Neutrinos from Precision Higgs Dataver. 2
We use the LHC Higgs data to derive updated constraints on electroweak-scale sterile neutrinos that naturally occur in many low-scale seesaw extensions of the Standard Model to explain the neutrino masses. We also analyze the signal sensitivity for a new final state involving a single charged lepton and two jets with missing energy, which arises from the decay of sterile neutrinos produced through the Higgs and $W,Z$ boson mediated processes at the LHC. Future prospects of these sterile neutrino signals in precision Higgs measurements, as well as at a future 100 TeV collider, are also discussed.
Sterile neutrinoHiggs bosonLarge Hadron ColliderStandard ModelColliderPrecision Higgs measurementsHiggs boson decaySterile neutrino massDecay widthYukawa coupling...
• No Ly$\alpha$ emitters detected around a QSO at z=6.4: Suppressed by the QSO?
Understanding how QSO's UV radiation affects galaxy formation is vital to our understanding of reionization era. Using a custom made narrow-band filter, $NB906$, on Subaru/Suprime-Cam, we investigated the number density of Ly$\alpha$ emitters (LAE) around a QSO at z=6.4. To date, this is the highest redshift narrow-band observation, where LAEs around a luminous QSO are investigated. Due to the large field-of-view of Suprime-Cam, our survey area is $\sim$5400~cMpc$^2$, much larger than previously studies at z=5.7 ($\sim$200 cMpc$^2$). In this field, we previously found a factor of 7 overdensity of Lyman break galaxies (LBGs). Based on this, we expected to detect $\sim$100 LAEs down to $NB906$=25 ABmag. However, our 6.4 hour exposure found none. The obtained upper limit on the number density of LAEs is more than an order lower than the blank fields. Furthermore, this lower density of LAEs spans a large scale of 10 $p$Mpc across. A simple argument suggests a strong UV radiation from the QSO can suppress star-formation in halos with $M_{vir}<10^{10}M_{\odot}$ within a $p$Mpc from the QSO, but the deficit at the edge of the field (5 $p$Mpc) remains to be explained.
QuasarLyman alpha emitterLyman break galaxySuprime-CamGalaxyStar formationSubaru telescopeField of viewFull width at half maximumCompleteness...
• Effective description of dark matter self-interactions in small dark matter haloes
Self-interacting dark matter may have striking astrophysical signatures, such as observable offsets between galaxies and dark matter in merging galaxy clusters. Numerical N-body simulations used to predict such observables typically treat the galaxies as collisionless test particles, a questionable assumption given that each galaxy is embedded in its own dark matter halo. To enable a more accurate treatment we develop an effective description of small dark matter haloes taking into account the two major effects due to dark matter self-scatterings: deceleration and evaporation. We point out that self-scatterings can have a sizeable impact on the trajectories of galaxies, diminishing the separation between galaxies and dark matter in merging clusters. This effect depends sensitively on the underlying particle physics, in particular the angular dependence of the self-scattering cross section, and cannot be predicted from the momentum transfer cross section alone.
GalaxySelf-interacting dark matterDark matter haloDark matterMilky WayEvaporationDark matter particleMerging galaxy clusterCluster of galaxiesEscape velocity...
• Attention Is All You Needver. 3
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.0 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
TransductionArchitectureRecurrent neural networkConvolutional neural networkHidden layerEmbeddingPath lengthHidden stateInferenceHyperparameter...
• On the origin of the hard X-Ray excess of high-synchrotron-peaked BL Lac object Mrk 421
For the first time, Kataoka \& Stawarz reported a clear detection of a hard X-ray excess, above $\gtrsim$20 keV, in the high-synchrotron-peaked BL Lac object Mrk 421. We find that this feature may not be produced by the low-energy part of the same electron population that produced the {\it Fermi}/LAT $\gamma$-ray. Because of that it is required that the power-law electron energy go down to $\gamma_{\rm min}\approx19$, which predicts a very strong radio emission (radio flux larger than the observed) even considering the synchrotron self-absorption effect. We investigate the possibility of this excess being produced from the spine/layer jet structure, which has been clearly detected in Mrk 421. We find that (1) similar to one-zone modeling, the spine emissions provide good modeling of the broadband spectral energy distribution, except for the hard X-ray excess; and (2) the hard X-ray excess can be well represented by the synchrotron photons (from the layer) being inverse Compton scattered by the spine electrons.
• Physical interpretation of the Planck's constant based on the Maxwell theory
The discovery of the Planck's relation is generally regarded as the starting point of quantum physics. The Planck's constant h is now regarded as one of the most important universal constants. The physical nature of h, however, has not been well understood. It was originally suggested as a fitting constant to explain the black-body radiation. Although Planck had proposed a theoretical justification of h, he was never satisfied with that. To solve this outstanding problem, we used the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet. We found the energy of the wave packet is indeed proportional to its oscillation frequency. This allows us to derive the value of the Planck's constant. Furthermore, we showed that the emission and transmission of a photon follows the principle of all-or-none. The "strength" of the wave packet can be characterized by zeta, which represents the integrated strength of the vector potential along a transverse axis. We reasoned that zeta should have a fixed cut-off value for all photons. Our results suggest that a wave packet can behave like a particle. This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by the Planck's law.
Planck's constantWave packetPlanck missionCosmic microwave backgroundPlanck lawTheoryPhotonEnergyBlack bodyParticles...
• emcee: The MCMC Hammerver. 4
We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to $\sim N^2$ for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.
Monte Carlo Markov chainAutocorrelationNuisance parameterBayesian posterior probabilityHyperparameterCovarianceMarkov chainStatisticsBayesianExpectation Value...
• Some aspects of conformal ${\cal N}=4$ SYM four point function
The four point functions of chiral primary BPS operators in ${\cal N}=4$ superconformal Yang Mills are expressed in a form manifestly satisfying the superconformal Ward identities. They are subsequently expanded in terms of conformal partial waves. Correlation functions of two pairs of identical chiral primaries, one pair having the lowest possible scale dimension, are considered. Crossing symmetries determine their free field value up to numeric constants. The contributions from different supermultiplets to the partial wave expansion is analysed, and determined in the case of the free fields and compared with established results at strong and weak coupling. In the large $N$, strong coupling limit, non-trivial cancellations are found between the free field values and results from supergravity. In the perturbative case values are obtained for the anomalous dimensions of lowest twist operators and the correction to the coupling by analysing the conformal wave expansions of certain hypergeometric and logarithmic functions. Next, we attempt to count shortened ${\cal N}=4$ SYM operators, beginning by constructing from fundamental fields the most general operators belonging to certain $SU(4)_R$ representations at low twists. The number of independent solutions to the conditions imposed on such operators is found via a combinatoric approach. Generating functions for the number of operators with spin $\ell=0,1,2,\dotsc$ are derived. Explicit values are obtained for specific $R$-symmetry representations at low twist in various sectors of the theory. The asymptotic behaviour at large twist is also considered. Finally the conformal field theory operator product expansion is analysed. Solutions in terms of series expansions are found, initially for scalar operators in two dimensions, and then more generally.
Super Yang-Mills theoryFree fieldAnomalous dimensionScaling dimensionSupermultipletOperator product expansionTwo-point correlation functionConformal field theorySupergravitySymmetry...
• Fast unfolding of communities in large networksver. 2
We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. .
ModularityCommunity detectionOptimizationCommunity structureSocial networkMobile phone networksWeighted networkMobile phoneComplex networkGraph...
• Observing the very low-surface brightness dwarfs in a deep field in the VIRGO cluster: constraints on Dark Matter scenarios
We report the discovery of 11 very faint (r< 23), low surface brightness ({\mu}_r< 27 mag/arcsec^2) dwarf galaxies in one deep field in the Virgo cluster, obtained by the prime focus cameras (LBC) at the Large Binocular Telescope (LBT). These extend our previous sample to reach a total number of 27 galaxies in a field of just of 0.17 deg^2 located at a median distance of 390 kpc from the cluster center. Their association with the Virgo cluster is supported by their separate position in the central surface brightness - total magnitude plane with respect to the background galaxies of similar total magnitude. For a significant fraction (26\%) of the sample the association to the cluster is confirmed by spectroscopic follow-up. We show that the mere abundance of satellite galaxies corresponding to our observed number in the target field provides extremely tight constraints on Dark Matter models with suppressed power spectrum compared to the Cold Dark Matter case, independently of the galaxy luminosity distribution. In particular, requiring the observed number of satellite galaxies not to exceed the predicted abundance of Dark Matter sub-halos yields a limit m_X >3 keV at 1-{\sigma} and m_X > 2.3 keV at 2-{\sigma} confidence level for the mass of thermal Warm Dark Matter particles. Such a limit is competitive with other limits set by the abundance of ultra-faint satellite galaxies in the Milky Way, is completely independent of baryon physics involved in galaxy formation, and has the potentiality for appreciable improvements with next observations. We extend our analysis to Dark Matter models based on sterile neutrinos, showing that our observations set tight constraints on the combination of sterile neutrino mass m_{\nu} and mixing parameter sin^2(2{\theta}). We discuss the robustness of our results with respect to systematics.
GalaxyAbundanceDark matter modelDark matterVirgo ClusterCold dark matterMilky WayThermal WDMDwarf galaxyWarm dark matter...
• Implications of Strong Intergalactic Magnetic Fields for Ultra-High-Energy Cosmic-Ray Astronomyver. 2
We study the propagation of ultra-high-energy cosmic rays in the magnetised cosmic web. We focus on the particular case of highly magnetised voids ($B \sim \text{nG}$), using the upper bounds from the Planck satellite. The cosmic web was obtained from purely magnetohydrodynamical cosmological simulations of structure formation considering different power spectra for the seed magnetic field in order to account for theoretical uncertainties. We investigate the impact of these uncertainties on the propagation of cosmic rays, showing that they can affect the measured spectrum and composition by up to $\simeq 80\%$ and $\simeq 5\%$, respectivelly. In our scenarios, even if magnetic fields in voids are strong, deflections of 50 EeV protons from sources closer than $\sim\;$50 Mpc are less than $15^\circ$ in approximately 10-50% of the sky, depending on the distribution of sources and magnetic power spectrum. Therefore, UHECR astronomy might be possible in a significant portion of the sky depending on the primordial magnetic power spectrum, provided that protons constitute a sizeable fraction of the observed UHECR flux.
Ultra-high-energy cosmic rayVoidCosmic rayCosmic webHydrodynamical simulationsEarthCentaurus AFilling fractionIntergalactic magnetic fieldExtragalactic magnetic field...
• Current and Future Constraints on Primordial Magnetic Fieldsver. 2
We present new limits on the amplitude of potential primordial magnetic fields (PMFs) using temperature and polarization measurements of the cosmic microwave background (CMB) from Planck, BICEP2/Keck Array, Polarbear, and SPTpol. We reduce twofold the 95% CL upper limit on the CMB anisotropy power due to PMFs, from $A_{PMF}$ < 0.76 for Planck alone to $A_{PMF}$ < 0.36 for the combined dataset. We also forecast the expected limits from soon-to-deploy CMB experiments (like SPT-3G, Adv. ACTpol, or the Simons Array) and the proposed CMB-S4 experiment. Future CMB experiments should dramatically reduce the current uncertainties, by one order of magnitude for the near-term experiments and two orders of magnitude for the CMB-S4 experiment. The constraints from CMB-S4 have the potential to rule out much of the parameter space for PMFs.
Cosmological magnetic fieldCMB-S4B-modesCosmic microwave backgroundCosmological modelCosmic microwave background experimentFull width at half maximumCalibrationTelescopesInflationary gravitational wave...
• Shocks in relativistic transverse stratified jets, a new paradigm for radio-loud AGN
The transverse stratification of active galactic nuclei (AGN) jets is suggested by observations and theoretical arguments, as a consequence of intrinsic properties of the central engine (accretion disc + black hole) and external medium. On the other hand, the one-component jet approaches are heavily challenged by the various observed properties of plasmoids in radio jets (knots), often associated with internal shocks. Given that such a transverse stratification plays an important role on the jets acceleration, stability, and interaction with the external medium, it should also induce internal shocks with various strengths and configurations, able to describe the observed knots behaviours. By establishing a relation between the transverse stratification of the jets, the internal shock properties, and the multiple observed AGN jet morphologies and behaviours, our aim is to provide a consistent global scheme of the various AGN jet structures. Working on a large sample of AGN radio jets monitored in very long baseline interferometry (VLBI) by the MOJAVE collaboration, we determined the consistency of a systematic association of the multiple knots with successive re-collimation shocks. We then investigated the re-collimation shock formation and the influence of different transverse stratified structures by parametrically exploring the two relativistic outflow components with the specific relativistic hydrodynamic (SRHD) code AMRVAC. We were able to link the different spectral classes of AGN with specific stratified jet characteristics, in good accordance with their VLBI radio properties and their accretion regimes.
Astrophysical jetCollimationMach numberVery long baseline interferometryBlazarLorentz factorRarefaction waveAGN jetsShock waveActive Galactic Nuclei...
• Evidences against cuspy dark matter halos in large galaxiesver. 2
We develop and apply new techniques in order to uncover galaxy rotation curves (RC) systematics. Considering that an ideal dark matter (DM) profile should yield RCs that have no bias towards any particular radius, we find that the Burkert DM profile satisfies the test, while the Navarro-Frenk-While (NFW) profile has a tendency of better fitting the region between one and two disc scale lengths than the inner disc scale length region. Our sample indicates that this behaviour happens to more than 75% of the galaxies fitted with an NFW halo. Also, this tendency does not weaken by considering "large" galaxies, for instance those with $M_*\gtrsim 10^{10} M_\odot$. Besides the tests on the homogeneity of the fits, we also use a sample of 62 galaxies of diverse types to perform tests on the quality of the overall fit of each galaxy, and to search for correlations with stellar mass, gas mass and the disc scale length. In particular, we find that only 13 galaxies are better fitted by the NFW halo; and that even for the galaxies with $M_* \gtrsim 10^{10} M_\odot$ the Burkert profile either fits as good as, or better than, the NFW profile. This result is relevant since different baryonic effects important for the smaller galaxies, like supernova feedback and dynamical friction from baryonic clumps, indicate that at such large stellar masses the NFW profile should be preferred over the Burkert profile. Hence, our results either suggest a new baryonic effect or a change of the dark matter physics.
GalaxyNavarro-Frenk-White profileMilky WayRotation CurveBurkert profileDark matterDark Matter Density ProfileStellar massDark matter haloBaryonic Tully-Fisher relation...
• Simulations of Cold Electroweak Baryogenesis: Hypercharge U(1) and the creation of helical magnetic fieldsver. 2
We perform numerical simulations of Cold Electroweak Baryogenesis, including for the first time in the Bosonic sector the full electroweak gauge group SU(2)$\times$U(1) and CP-violation. We find that the maximum generated baryon asymmetry is reduced by a factor of three relative to the SU(2)-only model, but that the quench time dependence is very similar. In addition, we compute the magnitude of the helical magnetic fields, and find that it is proportional to the strength of CP-violation and dependent on quench time, but is not proportional to the magnitude of the baryon asymmetry as proposed in the literature. Astrophysical signatures of primordial magnetic helicity can therefore not in general be used as evidence that electroweak baryogenesis has taken place.
QuenchingChern-Simons numberCP violationCP-oddHiggs fieldBaryon asymmetry of the UniverseHyperchargeGauge fieldHiggs bosonHelical magnetic field...
• First Results from the Lyman Alpha Galaxies in the Epoch of Reionization (LAGER) Survey: Cosmological Reionization at z ~ 7ver. 3
We present the first results from the ongoing LAGER project (Lyman Alpha Galaxies in the Epoch of Reionization), which is the largest narrowband survey for $z \sim$ 7 galaxies to date. Using a specially built narrowband filter NB964 for the superb large-area Dark-Energy Camera (DECam) on the NOAO/CTIO 4m Blanco telescope, LAGER has collected 34 hours NB964 narrowband imaging data in the 3 deg$^2$ COSMOS field. We have identified 23 Lyman Alpha Emitter (LAE) candidates at $z$ = 6.9 in the central 2-deg$^2$ region, where DECam and public COSMOS multi-band images exist. The resulting luminosity function can be described as a Schechter function modified by a significant excess at the bright end (4 galaxies with $L_{Ly\alpha} \sim$ 10$^{43.4\pm0.2}$ erg s$^{-1}$). The number density at $L_{Ly\alpha}\sim$ 10$^{43.4\pm0.2}$ erg s$^{-1}$ is little changed from z= 6.6, while at fainter $L_{Ly\alpha}$ it is substantially reduced. Overall, we see a fourfold reduction in Ly$\alpha$ luminosity density from $z$ = 5.7 to 6.9. Combined with a more modest evolution of the continuum UV luminosity density, this suggests a factor of $\sim 3$ suppression of Ly$\alpha$ by radiative transfer through the $z \sim$ 7 intergalactic medium (IGM). It indicates an IGM neutral fraction $x_{HI}$ $\sim$ 0.4--0.6 (assuming Ly$\alpha$ velocity offsets of 100-200 km s$^{-1}$). The changing shape of the Ly$\alpha$ luminosity function between $z\lesssim 6.6$ and $z=6.9$ supports the hypothesis of ionized bubbles in a patchy reionization at $z\sim$ 7.
Lyman alpha emitterLuminosity functionLyman Alpha Galaxies in the Epoch of ReionizationLuminosityGalaxyIntergalactic mediumReionizationCOSMOS surveySchechter functionSubaru telescope...
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