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## Rational And Irrational Numbers Worksheet 9th Grade

Learn vocabulary, terms, and more with flashcards, games, and other study tools. See more ideas about Real numbers, Irrational numbers and Real number system. Create New Sheet Share Select a Worksheet Version 1 Version 2 Version 3 Version 4 Version 5 Version 6 Version 7 Version 8 Version 9 Version 10 Grab 'em All Create New Sheet. The rules for. rational numbers and order of operations. 10 Questions. Rational and Irrational numbers powerpoint NS1 8th grade Math 2015 Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. This is the typically format of the practice tests we have seen going around. 3030030003… and 0. The difference between rational and irrational numbers can be drawn clearly on the following grounds Rational Number is defined as the number which can be written in a ratio of two integers. If the set of irrational numbers is denoted by H, then. The wholes are just the naturals with zero thrown in. Printable worksheets and online practice tests on Number System for Grade 9. Some of the worksheets for this concept are Work classifying numbers which, Concept 13 rational irrational numbers, Sets of real numbers date period, Numbers rational and irrational, Rational and irrational numbers 2, Irrational numbers, First published in 2013 by the university of utah in, Work 1 rational and irrational numbers. Difference between rational and irrational numbers Although rational numbers can go on and on with an infinite amount of numbers, they nonetheless have a pattern. A rational number is a number that can be written as a ratio of two integers. 9th Grade Math. 5 Identify. Comparison between Rational and Irrational Numbers. Whole numbers comprise of all natural numbers and zero. Rational number worksheets, 8th Grade Math TAKS Formula chart, math trivia algebra, simplifying algebraic expressions calculator. Other irrational numbers include the square root of 3, the square root of 5, pi, e, and the golden ratio. Whenever you have to have service with math and in particular with rational numbers calculator or algebra exam come pay a visit to us at Polymathlove. Showing top 8 worksheets in the category - Grade 9 Rational Numbers. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Ninth Grade (Grade 9) Rational and Irrational Numbers questions for your custom printable tests and worksheets. High school math for grade 10, 11 and 12 math questions and problems to test deep understanding of math concepts and computational procedures are presented. Compare and order rational numbers (positive and negative integers, fractions, decimals ). org is simply the excellent place to head to!. irrational numbers worksheet math grade worksheets rational awesome best vs s images and workshe. Rational Numbers A Multi-Part Lesson 12-1 PART B C Main Idea Compare and order fractions, decimals, and percents. Materials: Color by Classifying worksheet, blue, green, yellow, and black coloring utensils. Free 7th Grade Math Worksheets for Teachers, Parents, and Kids. Worksheets are Disputing irrational beliefs, 12 irrational beliefs <NAME>, Structured disputing of irrational beliefs, Techniques for disputing irrational beliefs, Rebt self help form, Activity reframing irrational thoughts purpose estimated time, Irrational distorted and pessimistic thinking patterns. Free Math Worksheets for Grade 7 - Homeschool Math. Whole numbers comprise of all natural numbers and zero. When we put together the rational numbers and the irrational numbers, we get the set of real numbers. You have solved polynomial equations and found that their roots are included in the set of complex numbers. √4 - rational because in standard form this number is 2 which is a natural, whole, integer. Rational Numbers, irrational Numbers, rationalize irrational numbres, operation on real numbers, laws of exponents, rules of indices and Real Numbers. 1 Know that the numbers that are not rational are called irrational. For example, -2, 7, 3/4, 0. Sep 18th, 2019. The Standards for Mathematical Practice describe the varieties of expertise, habits of minds, and productive dispositions that educators seek to develop in all students. org are unblocked. Questions on Rational Numbers. The set of integers does not include decimals or fractions. Learn what rational and irrational numbers are and how to tell them apart. If you're behind a web filter, please make sure that the domains *. Suppose that the sum of a and b is a rational number, c. Real Number Chart LSC-O Learning Center (409) 882-3373ℝ. Real Number Chart LSC-O Learning Center (409) 882-3373ℝ. The number 8 is a rational number because it can be written as the fraction 8/1. This question basically ASKS for indirect proof. New Online Test. Watch the video (Level 2: Rational & Irrational #s ) Complete the Notes & Basic Practice Check the Key and Correct Mistakes 2. 2: Use rational approximations of irrational numbers to compare the size of irrational numbers, plot them approximately on a number line, and estimate the value of expressions involving irrational numbers. 28) Find the rational number between: 1) 3 and 4 2) -7 and -6 29) Find three rational numbers between: 1) -5 and 8 2) ( -1/3 ) and (1/2) 30) State whether true or false: (practice worksheet on rational numbers) 1) Absolute value of a rational number is either positive or 0. The term is a whole number. Ninth Grade (Grade 9) Rational and Irrational Numbers questions for your custom printable tests and worksheets. org are unblocked. The rules for. So, 2, 5/11, -5. RATIONAL NUMBER- A number that can be written as a fraction, where the bottom is not equal to zero. 3010010001…, a rational will be 0. Descending Order of Rational Numbers Worksheet. An irrational number is a number which cannot be expressed in a ratio of two integers. 8th Grade Unit 2 1 Color by Classifying Objective: Students will classify numbers. On a number line, positive numbers are to the right of 0, and negative numbers are to the left of 0. Many people are surprised to know that a repeating decimal is a rational number. We offer a huge amount of good reference material on subject areas ranging from equations to geometry. com and read and learn about operations, mathematics and plenty additional math subject areas. 1 Express rational numbers as terminating or repeating decimals. 2) The sum of rational number and irrational number is an irrational-number. Eighth Grade (Grade 8) Rational and Irrational Numbers questions for your custom printable tests and worksheets. Irrational numbers-An irrational number is a number that cannot be expressed in the form of a/b, where "a" and "b" are integers and b ≠ 0. Rational Numbers Worksheet Grade 6. WORKSHEET - COMPARE AND ORDER RATIONAL NUMBERS www. Real numbers are mainly classified into rational and irrational numbers. Download Worksheets for Grade 8, Module 7, Lesson 11. Comparing irrational numbers worksheet - Questions. Find the width of a rectangle if its length is 5 more than the width and its perimeter is 90 cm. Rational Numbers are any real numbers that can be expressed as a simple fraction or ratio. These tools will help you. Displaying all worksheets related to - Irrational Beliefs. 22) 23) 24) 25). Lesson 16: Rational and Irrational Numbers. NCERT Grade 9 Maths Chapter 1, Number Systems, comes under the Unit of Number Systems. All of the numbers that we use in everyday life are real numbers. This is a comprehensive collection of free printable math worksheets for grade 7 and for pre-algebra, organized by topics such as expressions, integers, one-step equations, rational numbers, multi-step equations, inequalities, speed, time & distance, graphing, slope, ratios, proportions. Printable worksheets and online practice tests on Rational Numbers for Grade 8. Students will be expected to know relationships among fractions, decimals, and percents given a real-world context. com and discover graphing linear equations, practice and plenty of additional algebra subject areas. Problems on Irrational Numbers. Background Knowledge: Students should be familiar with various sets that numbers can be classified in (natural, whole, integer, rational, irrational, real, not real). Write a story that uses addition, subtraction, multiplication, or division of rational numbers. Identifying Rational And Irrational Numbers Worksheet - Switchconf Worksheets For All Download And Share Worksheets Free On. emathematics. NCERT Exemplar Class 8 Maths is very important resource for students preparing for VIII Board Examination. These Radical Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. Talking related with Rational Numbers Worksheets Grade 6, we've collected particular variation of photos to complete your references. Pre-Algebra Page 9 Integers and Rational Numbers 7. Irrational numbers-An irrational number is a number that cannot be expressed in the form of a/b, where “a” and “b” are integers and b ≠ 0. 8th Grade Rational Numbers. Which statement is false? A Some integers are irrational. In eighth grade, students are introduced to irrational numbers, rounding out their understanding of the real number system before learning about complex numbers in high. (iv) There are numbers which cannot be written in the form p/q , q ≠ 0 , p, q both are integers. The pre-algebra worksheets provide simple number sentences in the form of equations with missing values, and the students fill in the answer. 1) The student represents and uses rational numbers in a variety of equivalent forms. That is what a rational number is. Students learn that the following number sets represent rational numbers: natural numbers, whole numbers, integers, fractions, terminating decimals, and repeating decimals. Download Free Pre-Algebra > Rational Number Worksheets Below: All worksheets are free to download and use for practice or in your classroom. Number properties worksheet, Rational numbers worksheet, Irrational numbers worksheet, Math Reading Science Tests for Grades , Practice Sample Test, Free Online Worksheets. In other words, a fraction is formed by dividing one integer by another integer. Because the learning of these topics is integral to the learning. Identifying Rational And Irrational Numbers. Learn what rational and irrational numbers are and how to tell them apart. The rational number 1 is the multiplicative identity for rational number. Printable Worksheets And Lessons. Sample Grade 9 Number System worksheet : Printed. 3, -5/2, 3. For example, by truncating the decimal expansion of √2. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. 2) Product (Multiplication) formula of radicals with equal indices is given by. The Rational Number System Worksheet Solutions. All negative integers and whole numbers make up the set of integers. Common Core Math Worksheets - K-12. Shirleen Luttrell algebra course for a combined seventh and eighth grade class. Problems on Irrational Numbers. Rational numbers may seem like a tough subject to young mathematicians; this activity allows them to practice with multiple types of rationals and irrationals to become more familiar with this category. Example: 1 1. About "Comparing irrational numbers worksheet" Comparing irrational numbers worksheet : Worksheet on c omparing irrational numbers is much useful to the students who would like to practice problems on irrational numbers. − 10 40 = − 0. Examples of irrational numbers include and π. DA: 25 PA: 22 MOZ Rank: 75 Rational and Irrational Numbers - factmonster. Displaying all worksheets related to - Identify Numbers To 0. com is an online resource used every day by thousands of teachers, students and parents. The square root of is , also a rational number. 1 review before a quiz or test. Irrational means not Rational. Identifying Rational And Irrational Numbers. The number pi and square roots of non-perfect squares are examples of irrational numbers. The denominator in a Rational Number should not be 0 2. Grade 7 Learning Module in MATH from Rational And Irrational Numbers Worksheet, source: slideshare. Teacher Note about Entrance card question 1b: Students tend to define rational numbers as :”numbers that can be written as a fraction” The problem with this is that irrational numbers such as the square root of 3 are also fractions. Showing top 8 worksheets in the category - Identifying Rational And Irrational Numbers. Rational and irrational numbers. The focus is also on determining square roots of rational numbers. Some of the worksheets for this concept are , Grade 9 rational numbers and square roots, Fractions rational numbers, Summer package pre requisite algebra skills, Add subtract multiply divide rational numbers date period, Mathematics grade 9, Math 9 final, Grade 9 number system. This interactive game has 3 categories: Comparing Rational Numbers, Adding and Subtracting Rational Numbers, and Multiplying and Dividing Rational Numbers. Students of all levels will benefit. Rational Number Worksheets The following worksheets were found at WWW. These tools will help you. We carry a lot of really good reference materials on subject areas varying from long division to matrix. Number and Quantity > Key Concept:Real Numbers, Irrational Numbers and Decimal Expansion of Numbers. More Worksheet. Come to Emaths. Grade 8 - Mathematics Curriculum - Type of Numbers: Natural, Whole, Integers, Rational, Irrational & Real - Math & English Homeschool/Afterschool/Tutoring Educational Programs. Practice this lesson yourself on KhanAcademy. All negative integers and whole numbers make up the set of integers. The outside flaps cover the irrational and rational numbers. You can print off an unlimited number of worksheets and generate an unlimited number of questions related to each skill. The sum or product of rational numbers is rational. This video explains the difference between rational and irrational numbers and how to identify rational and irrational numbers. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Comparing and Ordering Rational Numbers Definitions. Problems on Irrational Numbers. Decimal Form of Rational Numbers - [worksheet] Model each of the following calculations with base ten blocks. mathematics number system rational and irrational numbers. All the Algebra help you need right here, and it'sl free. 7th Grade Worksheets & Other Resources. For example, by truncating the decimal expansion of √2. Prove that any irrational number multiplied by any non-zero rational number is equal to some irrational number. For example, by truncating the decimal expansion of √2. Rational numbers-A ration number is a number that can be expressed in the form a/b, where "a" and "b" are integers and "b" is not equal to 0. Search Search. 22) 23) 24) 25). Solving problems with rational numbers in decimal form. You will need one for each student. 3 Solve real world and mathematical problems involving the four operations with rational numbers Glencoe Math Accelerated Chapter 3 Larson Pre Algebra Chapter 5 5 days Integers and Rational Numbers 8. RATIONAL NUMBER- A number that can be written as a fraction, where the bottom is not equal to zero. All the Algebra help you need right here, and it'sl free. V s hMdaqd oeM DwUiht aht wIVnrf8ipn mint beg APlJg Uexb irSa G i1H. Additive inverse of 0 is 0 itself; The multiplicative inverse of the rational number is a/b is b/a and vice versa. Problem Solving with Exponents and Scientific Notation 24 8. Common Core Math Worksheets - K-12. Home > Grade 8 > Rational and Irrational Numbers Rational and Irrational Numbers Directions: Using only numbers 1-8 (without repeating any number), fill in the boxes to create the following number types:. Below are the tests for each grade: When you enter the Perspectives site through the 3rd Grade link below, click on the appropriate grade and test and it will take you to the study guide you need. Sep 3, 2018- Explore ktfrmtn's board "Rational Numbers", followed by 382 people on Pinterest. A shopkeeper sells two quality of rice at rate of \$ 18 per kg. Rational Numbers also include decimals that repeat or terminate (since they can be written as fractions) Powers and Square roots may be rational numbers if their standard form is a rational number. MALATI materials: Rational numbers Rational Numbers for Grade 8 and 9 Some general remarks: • Research in Grades 8 and 9, locally and internationally, has shown that learners have a poor conception of rational numbers e. Rational and Irrational Numbers. Comparing irrational numbers worksheet - Questions. Number system involves exploring the following aspects: scientific notations (negative and positive powers of 10), exponents, approximation, ratios, roots, estimation, rational and irrational number operations, negative and positive exponents, add and. Rational and Irrational Numbers. net 6 First, write all the numbers as decimals. 9th Grade Math. The term is a whole number. Irrational Beliefs. rational numbers, we now know that not all numbers are rational. This step of introducing equations without variables can be a gentle first step into the world of finding missing values using algebraic manipulations. neither rational nor irrational number: New Worksheet. An Irrational Number is a real number that cannot be written as a simple fraction. Improve your math knowledge with free questions in "Identify rational and irrational numbers" and thousands of other math skills. Recognize that the decimal form of a rational number either terminates or repeats. org are unblocked. 9th grade Numbers Graphic Organizers Resources & Lesson Plans from Rational And Irrational Numbers Worksheet, source: teacherspayteachers. g-½=½ Compare and order rational numbers. Rational Numbers Worksheet Grade 6. Ninth Grade (Grade 9) Rational and Irrational Numbers questions for your custom printable tests and worksheets. Sample Grade 9 Number System worksheet : Printed. All the Algebra help you need right here, and it'sl free. How to find out if a radical is irrational There are a couple of ways to check if a number is rational: a. The next type of number is the "rational", or fractional, numbers, which are technically regarded as ratios (divisions) of integers. 3030030003… and 0. Worksheet #6 Fractions: Mixed Numbers Identify which of the following are improper fractions. Grade 9 math printable worksheets, online practice and online tests. What is the purpose of this document? To increase student achievement by ensuring educators understand specifically what the new standards mean a student must know, understand and be able to do. Important questions in Number systems with video lesson. By the time students enter eighth grade, students should have a strong grasp on operating with rational numbers, which will be an underlying skill in many algebraic concepts. Moving between different representations of rational and irrational numbers. For example, v2/3 is not a rational number, because 2 is not a perfect square. Rational numbers worksheet 6th grade. Rational & Irrational Numbers - ICSE Grade 9 MATHS Online Study Material - Get Free Sample Papers, Board Paper Solutions, Revision Quizzes, Video Lessons & Sample Tests on Brainnr. Paste your number strip on the board, or have a number line started on the overhead machine. Solving problems with rational numbers in fraction form. Chapter 3 Practice Test: Rational Numbers Multiple Choice Identify the choice that best completes the statement or answers the question. Decimal Form of Rational Numbers - [worksheet] Model each of the following calculations with base ten blocks. Rewrite expressions involving radicals and rational exponents using the properties of exponents. The number 8 is a rational number because it can be written as the fraction 8/1. Algebra 1 Here is a list of all of the skills students learn in Algebra 1! These skills are organized into categories, and you can move your mouse over any skill name to preview the skill. Rational & Irrational Numbers. Sixth grade unit 3 rational numbers integers resources include 6ns5 6ns6 6ns7 mighty math home. Seventh grade H. Compare (√3 + 5) and (3 + √5) and write <, >, or = in between them. I imagine I can lend you a hand. Unit 9: Square & Cube Roots; Irrational Numbers Clusters: Work with radicals and integer exponents. 1 Know that numbers that are not rational are called irrational. The sum of a rational and an irrational numbers is _____ A. When you need to have help on solution or maybe elementary algebra, Mathsite. In geometry, any. , irrational numbers cannot be rational numbers and vice-versa. Showing top 8 worksheets in the category - Ordering Rational And Irrational Numbers. Help: If students do not know how to estimate irrational numbers (squares of not perfect squares) have them review Estimating Square Roots. If your 8th grader needs extra practice with these concepts, you can create your own practice problems at home, using the samples below as examples. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14. Additive inverse of 0 is 0 itself; The multiplicative inverse of the rational number is a/b is b/a and vice versa. Rationalization. If you're behind a web filter, please make sure that the domains *. Rational And Irrational Numbers Class 9 Icse. Example: 1 1. , what is his gain or loss?. Zero is a rational number but it has no reciprocal as $$\frac{q}{0}$$ is not defined, where q is a rational number. Nevada Academic Content Standard What does this standard mean that a student will know and be able to do?. 75 You want to order numbers from greatest to least. Find the width of a rectangle if its length is 5 more than the width and its perimeter is 90 cm. Register free now. The sum or product of rational numbers is rational. A better definition is that rational numbers are "numbers that can be written as a fraction of integers". Sixth grade unit 3 rational numbers integers resources include 6ns5 6ns6 6ns7 mighty math home. a rational or an irrational number. 2, 5/11, -5. • If a real number can be written as a fraction, it is a rational number. Try our high school worksheets with your teen. 55? if a=7-4 , find the value of + 16/ in a 100 m race , A beats B by 20 m , or 4 sec. Rational numbers may seem like a tough subject to young mathematicians; this activity allows them to practice with multiple types of rationals and irrationals to become more familiar with this category. Showing top 8 worksheets in the category ordering rational numbers for 6th grade. Rational & Irrational Numbers. Problems on Rationalizing the Denominator. Solving problems with rational numbers in fraction form. Identify Numbers To 0. Math Antics has a brand new look! Find out why: ↓ Scroll down to check out our Video Lessons. How to find out if a radical is irrational There are a couple of ways to check if a number is rational: a. Zero is a rational number but it has no reciprocal as $$\frac{q}{0}$$ is not defined, where q is a rational number. Students of all levels will benefit. Standards: 8. g-½=½ Compare and order rational numbers. Working with Absolute Value. Difference between rational and irrational numbers Although rational numbers can go on and on with an infinite amount of numbers, they nonetheless have a pattern. What is the purpose of this document? To increase student achievement by ensuring educators understand specifically what the new standards mean a student must know, understand and be able to do. A better definition is that rational numbers are "numbers that can be written as a fraction of integers". Our Algebra worksheets are a great addition to any home school math curriculum. 0 Unported License. com is an online resource used every day by thousands of teachers, students and parents. Grade appropriate lessons, quizzes & printable worksheets. (Real, Irrational, Rational, Integer, Whole, Natural and/or Prime number) Example: Is both a Real and a Rational number. According to the Common Core Standards, 8th grade math games should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe. If the first three sides of a quadrilateral, taken in order are 14 cm, 13 cm and 12 cm respectively, and the angle between fourth side and the third side is a right angle, find the area of the quadrilateral. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. The Greeks first introduced Algebra in the third century and eventually it was also traced to the early Babylonians. Paste your number strip on the board, or have a number line started on the overhead machine. ) For example, 2 3, 355 113, and 7 4 are all rational numbers. Click on the free 7th grade math worksheet you would like to print or download. Converting and Ordering Rational Numbers Level: 6th Grade Pre-AP Stage 1 - Desired Results TEKS: (6. The venn diagram below shows examples of all the different types of rational, irrational nubmers including integers, whole numbers, repeating decimals and more. Download Free Pre-Algebra > Rational Number Worksheets Below: All worksheets are free to download and use for practice or in your classroom. Detailed solutions and answers to the questions are provided. Guided Lesson Explanation - Make sure students read the topic, it explains all of the problems at once. That is to. Detailed solutions and answers to the questions are provided. Real numbers include natural numbers, whole numbers, integers, rational numbers and irrational numbers. Sample Grade 9 Number System worksheet : Printed. Rational Numbers. Definition: The set of Irrational Numbers is defined by those numbers whose decimal representations never terminates or repeats. Estimate Rational Numbers. Class 9 math (India) In this chapter we'll be revisiting concepts of rational and irrational numbers and operations as well as concepts about real. Equivalent rational numbers are numbers with the same value, such as a positive 4 is Equal; to an negative 4. Irrational Numbers. irrational numbers, classifying real numbers, and comparing and ordering real numbers. This lesson is most appropriate for 9th-12th grade students. New Online Test. Guided Lesson Explanation - Make sure students read the topic, it explains all of the problems at once. Use the Rational, Irrational Numbers Lesson Plan to classify numbers and explore the difference between the decimal expansions of rational and irrational numbers. Students will be expected to know relationships among fractions, decimals, and percents given a real-world context. Cut and paste activity. Rational numbers may seem like a tough subject to young mathematicians; this activity allows them to practice with multiple types of rationals and irrationals to become more familiar with this category. You have solved polynomial equations and found that their roots are included in the set of complex numbers. 0 Unported License. org are unblocked. You can select different variables to customize these Exponents and Radicals Worksheets for your needs. A real number is a number that is somewhere on a number line, so any number on a number line that isn't a rational number is irrational. Compare the following rational numbers and tell whether they are greater than, less than, or equal to each other. The venn diagram below shows examples of all the different types of rational, irrational nubmers including integers, whole numbers, repeating decimals and more. 2: Use rational approximations of irrational numbers to compare the size of irrational numbers, plot them approximately on a number line, and estimate the value of expressions involving irrational numbers. In cases where you require assistance on a quadratic or perhaps algebra review, Roots-and-radicals. From fractions math worksheets year8 to linear inequalities, we have all the pieces included. building, rm. For more worksheet you can log on to www. 8th Grade Math Mrs. 251251251251 is a repeating decimal expansion because 251 keeps repeating in the same order. Printable Worksheets And Lessons. Irrational numbers can be found by squaring rational numbers. - <NAME>. DA: 25 PA: 22 MOZ Rank: 75 Rational and Irrational Numbers - factmonster. A number line can help you compare and order rational numbers. mathinthemedian Math TEKS 8th from Rational And Irrational Numbers Worksheet. Irrational numbers cannot be written as ratios of. All Real Numbers that are NOT Rational Numbers; cannot be expressed as fractions, only non -repeating, non. Flashcards. Arithmetic and Algebra Worksheets. Rationalization. By the time students enter eighth grade, students should have a strong grasp on operating with rational numbers, which will be an underlying skill in many algebraic concepts. Irrational numbers in decimal form are nonrepeating, nonterminating decimals. Instant scoring, progress tracking, & award certificates to keep your student motivated. Have students work with partners to sort the number cards into rational and irrational numbers. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Rational numbers are special because they can be written as a fraction. com and read and learn about operations, mathematics and plenty additional math subject areas. Find quality practice questions and worksheets for "Rational & Irrational Numbers" eTutorWorld's free worksheet is here to rack your brains and help you practice for your tests.


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# Method of variation of parameters

Method of variation of parameters

In mathematics, variation of parameters also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations. It was developed by the Italian-French mathematician <NAME>.

For first-order inhomogeneous linear differential equations it's usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods are rather heuristics that involve guessing and don't work for all inhomogenous linear differential equations.

Given an ordinary non-homogeneous linear differential equation of order "n":$y^\left\{\left(n\right)\right\}\left(x\right) + sum_\left\{i=0\right\}^\left\{n-1\right\} a_i\left(x\right) y^\left\{\left(i\right)\right\}\left(x\right) = b\left(x\right)$. (i)let $y_1\left(x\right), ldots, y_n\left(x\right)$ be a fundamental system of the corresponding homogeneous equation:$y^\left\{\left(n\right)\right\}\left(x\right) + sum_\left\{i=0\right\}^\left\{n-1\right\} a_i\left(x\right) y^\left\{\left(i\right)\right\}\left(x\right) = 0.$ (ii)

Then a particular solution to the non-homogeneous equation is given by:$y_p\left(x\right) = sum_\left\{i=1\right\}^\left\{n\right\} c_i\left(x\right) y_i\left(x\right)$ (iii)where the $c_i\left(x\right)$ are continuous functions which satisfy the equations:$sum_\left\{i=1\right\}^\left\{n\right\} c_i^\text{'}\left(x\right) y_i^\left\{\left(j\right)\right\}\left(x\right) = 0 , mathrm\left\{,\right\} quad j = 0,ldots, n-2$ (iv)

(results from substitution of (iii) into the homogeneous case (ii); )
and:$sum_\left\{i=1\right\}^\left\{n\right\} c_i^\text{'}\left(x\right) y_i^\left\{\left(n-1\right)\right\}\left(x\right) = b\left(x\right).$. (v)
(results from substitution of (iii) into (i) and applying (iv);

$c_i\text{'}\left(x\right)=0$ for all x and i is the only way to satisfy the condition, since all $y_i\left(x\right)$ are linearly independent. It implies that all $c_i\left(x\right)$ are independent of x in the homogeneous case b(x)=0. )

This linear system of "n" equations can then be solved using Cramer's rule yielding:$c_i^\text{'}\left(x\right) = frac\left\{W_i\left(x\right)\right\}\left\{W\left(x\right)\right\} , mathrm\left\{,\right\} quad i=1,ldots,n$where $W\left(x\right)$ is the Wronskian determinant of the fundamental system and $W_i\left(x\right)$ is the Wronskian determinant of the fundamental system with the "i"-th column replaced by $\left(0, 0, ldots, b\left(x\right)\right).$

The particular solution to the non-homogeneous equation can then be written as:$sum_\left\{i=1\right\}^n int frac\left\{W_i\left(x\right)\right\}\left\{W\left(x\right)\right\} dx , y_i\left(x\right)$.

Examples

Specific second order equation

Let us solve : $y"+4y\text{'}+4y=cosh\left\{x\right\}.;!$

We want to find the general solution to the differential equation, that is, we want to find solutions to the homogeneous differential equation: $y"+4y\text{'}+4y=0.;!$Form the characteristic equation: $lambda^2+4lambda+4=\left(lambda+2\right)^2=0;!$: $lambda=-2,-2.;!$Since we have a repeated root, we have to introduce a factor of "x" for one solution to ensure linear independence. So, we obtain "u"1="e"-2"x", and "u"2="xe"-2"x". The Wronskian of these two functions is : :$= -e^\left\{-4x\right\}\left(2x-1\right)+2xe^\left\{-4x\right\}= \left(-2x+1+2x\right)e^\left\{-4x\right\} = e^\left\{-4x\right\}.;!$

Because the Wronskian is non-zero, the two functions are linearly independent, so this is in fact the general solution for the homogeneous differential equation (and not a mere subset of it).

We seek functions "A"("x") and "B"("x") so "A"("x")"u"1+"B"("x")"u"2 is a general solution of the inhomogeneous equation. We need only calculate the integrals:$A\left(x\right) = - int \left\{1over W\right\} u_2\left(x\right) f\left(x\right),dx,; B\left(x\right) = int \left\{1 over W\right\} u_1\left(x\right)f\left(x\right),dx$that is,:$A\left(x\right) = - int \left\{1over e^\left\{-4x xe^\left\{-2x\right\} cosh\left\{x\right\},dx = - int xe^\left\{2x\right\}cosh\left\{x\right\},dx = -\left\{1over 18\right\}e^x\left(9\left(x-1\right)+e^\left\{2x\right\}\left(3x-1\right)\right)+C_1$:$B\left(x\right) = int \left\{1 over e^\left\{-4x e^\left\{-2x\right\} cosh\left\{x\right\},dx = int e^\left\{2x\right\}cosh\left\{x\right\},dx =\left\{1over 6\right\}e^\left\{x\right\}\left(3+e^\left\{2x\right\}\right)+C_2$where $C_1$ and $C_2$ are constants of integration.

General second order equation

We have a differential equation of the form:$u"+p\left(x\right)u\text{'}+q\left(x\right)u=f\left(x\right),$and we define the linear operator :$L=D^2+p\left(x\right)D+q\left(x\right),$where "D" represents the differential operator. We therefore have to solve the equation $L u\left(x\right)=f\left(x\right)$ for $u\left(x\right)$, where $L$ and $f\left(x\right)$ are known.

We must solve first the corresponding homogeneous equation::$u"+p\left(x\right)u\text{'}+q\left(x\right)u=0,$by the technique of our choice. Once we've obtained two linearly independent solutions to this homogeneous differential equation (because this ODE is second-order) — call them "u"1 and "u"2 — we can proceed with variation of parameters.

Now, we seek the general solution to the differential equation $u_G\left(x\right)$ which we assume to be of the form:$u_G\left(x\right)=A\left(x\right)u_1\left(x\right)+B\left(x\right)u_2\left(x\right).,$

Here, $A\left(x\right)$ and $B\left(x\right)$ are unknown and $u_1\left(x\right)$ and $u_2\left(x\right)$ are the solutions to the homogeneous equation. Observe that if $A\left(x\right)$ and $B\left(x\right)$ are constants, then $Lu_G\left(x\right)=0$. We desire "A"="A"("x") and "B"="B"("x") to be of the form :$A\text{'}\left(x\right)u_1\left(x\right)+B\text{'}\left(x\right)u_2\left(x\right)=0.,$

Now,:$u_G\text{'}\left(x\right)=\left(A\left(x\right)u_1\left(x\right)+B\left(x\right)u_2\left(x\right)\right)\text{'}=\left(A\left(x\right)u_1\left(x\right)\right)\text{'}+\left(B\left(x\right)u_2\left(x\right)\right)\text{'},$:$=A\text{'}\left(x\right)u_1\left(x\right)+A\left(x\right)u_1\text{'}\left(x\right)+B\text{'}\left(x\right)u_2\left(x\right)+B\left(x\right)u_2\text{'}\left(x\right),$:$=A\text{'}\left(x\right)u_1\left(x\right)+B\text{'}\left(x\right)u_2\left(x\right)+A\left(x\right)u_1\text{'}\left(x\right)+B\left(x\right)u_2\text{'}\left(x\right),$and since we have required the above condition, then we have :$u_G\text{'}\left(x\right)=A\left(x\right)u_1\text{'}\left(x\right)+B\left(x\right)u_2\text{'}\left(x\right).,$Differentiating again (omitting intermediary steps):$u_G"\left(x\right)=A\left(x\right)u_1"\left(x\right)+B\left(x\right)u_2"\left(x\right)+A\text{'}\left(x\right)u_1\text{'}\left(x\right)+B\text{'}\left(x\right)u_2\text{'}\left(x\right).,$

Now we can write the action of "L" upon "u""G" as:$Lu_G=A\left(x\right)Lu_1\left(x\right)+B\left(x\right)Lu_2\left(x\right)+A\text{'}\left(x\right)u_1\text{'}\left(x\right)+B\text{'}\left(x\right)u_2\text{'}\left(x\right).,$Since "u"1 and "u"2 are solutions, then:$Lu_G=A\text{'}\left(x\right)u_1\text{'}\left(x\right)+B\text{'}\left(x\right)u_2\text{'}\left(x\right).,$

We have the system of equations:Expanding, :So the above system determines precisely the conditions:$A\text{'}\left(x\right)u_1\left(x\right)+B\text{'}\left(x\right)u_2\left(x\right)=0,$:$A\text{'}\left(x\right)u_1\text{'}\left(x\right)+B\text{'}\left(x\right)u_2\text{'}\left(x\right)=Lu_G=f.,$

We seek "A"("x") and "B"("x") from these conditions, so, given:we can solve for ("A"′("x"), "B"′("x"))"T", so::where "W" denotes the Wronskian of "u"1 and "u"2. (We know that "W" is nonzero, from the assumption that "u"1 and "u"2 are linearly independent.)

So,:$A\text{'}\left(x\right) = - \left\{1over W\right\} u_2\left(x\right) f\left(x\right),; B\text{'}\left(x\right) = \left\{1 over W\right\} u_1\left(x\right)f\left(x\right)$:$A\left(x\right) = - int \left\{1over W\right\} u_2\left(x\right) f\left(x\right),dx,; B\left(x\right) = int \left\{1 over W\right\} u_1\left(x\right)f\left(x\right),dx.$

Whilst homogeneous equations are relatively easy to solve, this method allows the calculation of the coefficients of the general solution of the "in"homogeneous equation, and thus the complete general solution of the inhomogeneous equation can be determined.

Note that $A\left(x\right)$ and $B\left(x\right)$ are each determined only up to an arbitrary additive constant (the constant of integration); one would expect two constants of integration because the original equation was second order. Adding a constant to $A\left(x\right)$ or $B\left(x\right)$ does not change the value of $Lu_G\left(x\right)$ because $L$ is linear.

=Literature="Elementary Differntial Equations and Boundary Value problems ", <NAME> and <NAME>, Wiley Interscience, 1965

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### Look at other dictionaries:

• Variation of parameters — In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations. It was developed by <NAME>[citation needed]. For first order… …   Wikipedia

• variation of parameters — a method for solving a differential equation by first solving a simpler equation and then generalizing this solution properly so as to satisfy the original equation by treating the arbitrary constants not as constants but as variables …   Useful english dictionary

• Method of undetermined coefficients — In mathematics, the method of undetermined coefficients, also known as the lucky guess method, is an approach to finding a particular solution to certain inhomogeneous ordinary differential equations and recurrence relations. It is closely… …   Wikipedia

• parameters, variation of — ▪ mathematics       general method for finding a particular solution of a differential equation by replacing the constants in the solution of a related (homogeneous) equation by functions and determining these functions so that the original… …   Universalium

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• Method of moments (statistics) — See method of moments (probability theory) for an account of a technique for proving convergence in distribution. In statistics, the method of moments is a method of estimation of population parameters such as mean, variance, median, etc. (which… …   Wikipedia

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text:
Why does the following proof of the Nested Interval Property require the Axiom of Completeness?

The proof in my text is as such:

Let $a_1,a_2,a_3,\ldots$ and $b_1, b_2, b_3,\ldots$ be the labels of the left- and right- hand endpoints respectively.

Consider the set A of the left-hand endpoints of the intervals, and let x = sup A. Since x is an upper bound for A, we have $a_n \leq x$. Since each $b_n$ is an upper bound for A, we have $x\leq b_n$. Then since $a_n\leq x \leq b_n$, we can conclude that $x\in I_n$ for every choice of $n\in \mathbb{N}$. Hence x is in the infinite intersection of nested intervals.

My question is.. could the proof work with $x = a_n$ instead? It seems that all the key properties would still hold -- $a_n \leq a_n \leq b_n$ for all n. This does not seem to require the AoC to be true.

-
$n$ is not a fixed number here, it is a variable for 1, 2, 3, ... When you say "$x=a_n$", what do you mean? $x=a_1$? Then maybe $x<a_2$. If you mean $x=a_2$, then maybe $x<a_3$, and so on. You need an $x$ that for sure is larger than or equal to each $a_n$. – <NAME> Feb 20 '11 at 3:03

Take some irrational number, e.g. $\sqrt{2}$. Consider its decimal expansion $$1.4142\ldots$$ Now construct a sequence of nested intervals: $$[1,2] \supset [1.4,1.5] \supset [1.41,1.42] \supset [1.414,1.415] \supset [1.4142,1.4143] \supset \cdots$$ These are nested intervals with rational endpoints, but their intersection contains no rational number. So without completeness the Nested Interval Property is false.


text:
# In a vernier calliper if the vernier is on the right side of the zero of the main scale and nth vernier scale division coincides with main scale division correct reading is

$(a)\;\text{observation reading - n$\times$least count} \\(b)\;\text {observation reading + n$\times$least count} \\(c)\;\text{observation reading$\times$least count} \\(d)\;\text{none}$

When zero of vernier is to the right of the zero of main scale the error is positive and is to be subtracted from the observed reading .
Zero error $=+n \times$ Least count
$\qquad$=Observed reading $- n \times$ least count
Hence a is the correct answer.
edited Apr 3, 2014 by meena.p


text:
Timezone: »

Oral
SAFFRON: an Adaptive Algorithm for Online Control of the False Discovery Rate
<NAME> · <NAME> · <NAME> · <NAME>

Thu Jul 12 08:00 AM -- 08:20 AM (PDT) @ A6
In the online false discovery rate (FDR) problem, one observes apossibly infinite sequence of $p$-values $P_1,P_2,\dots$, each testinga different null hypothesis, and an algorithm must pick a sequence ofrejection thresholds $\alpha_1,\alpha_2,\dots$ in an online fashion,effectively rejecting the $k$-th null hypothesis whenever $P_k \leq\alpha_k$. Importantly, $\alpha_k$ must be a function of the past, andcannot depend on $P_k$ or any of the later unseen $p$-values, and mustbe chosen to guarantee that for any time $t$, the FDR up to time $t$is less than some pre-determined quantity $\alpha \in (0,1)$. In thiswork, we present a powerful new framework for online FDR control thatwe refer to as SAFFRON''. Like older alpha-investing algorithms,SAFFRON starts off with an error budget (called alpha-wealth) that itintelligently allocates to different tests over time, earning backsome alpha-wealth whenever it makes a new discovery. However, unlikeolder methods, SAFFRON's threshold sequence is based on a novelestimate of the alpha fraction that it allocates to true nullhypotheses. In the offline setting, algorithms that employ an estimateof the proportion of true nulls are called adaptive'', henceSAFFRON can be seen as an online analogue of the offlineStorey-BH adaptive procedure. Just as Storey-BH is typically morepowerful than the Benjamini-Hochberg (BH) procedure underindependence, we demonstrate that SAFFRON is also more powerful thanits non-adaptive counterparts such as LORD.


text:
# hyperperfect number

A hyperperfect number $n$ for a given $k$ is an integer such that $k\sigma(n)=-1+k+(k+1)n$, where $\sigma(x)$ is the sum of divisors function. $n$ is then called $k$-hyperperfect. For example, 325 is 3-hyperperfect since its divisors (1, 5, 13, 25, 65, 325) add up to 434, and $3\times 434=-1+3+(3+1)325=1302$. Numbers that are 1-hyperperfect are by default called perfect numbers, since $1\sigma(n)=-1+1+(1+1)n=2n$.

The 2-hyperperfect numbers are listed in A007593 of Sloane’s OEIS. As of 2007, the only known 3-hyperperfect number is 325. The two known 4-hyperperfect numbers are 1950625 and 1220640625, a sequence too short to list in the OEIS, and no 5-hyperperfect numbers are known to exist. The 6-hyperperfect numbers are listed in A028499.

## References

• 1 <NAME>, “A Study of Hyperperfect Numbers” Journal of Integer Sequences 3 (2000): 00.1.3
Title hyperperfect number HyperperfectNumber 2013-03-22 17:49:38 2013-03-22 17:49:38 CompositeFan (12809) CompositeFan (12809) 4 CompositeFan (12809) Definition msc 11A05


text:
# cytoflow.utility.scale¶

class cytoflow.utility.scale.IScale[source]

An interface for various ways we could rescale flow data.

name

The name of this view (for serialization, UI, etc.)

Type: Str
experiment

The experiment this scale is to be applied to. Needed because some scales have parameters estimated from data.

Type: Instance(Experiment)
channel

Which channel to scale. Needed because some scales have parameters estimated from data.

Type: Str
condition

What condition to scale. Needed because some scales have parameters estimated from the a condition. Must be a numeric condition; else instantiating the scale should fail.

Type: Str
statistic

What statistic to scale. Needed because some scales have parameters estimated from a statistic. The statistic must be numeric or an iterable of numerics; else instantiating the scale should fail.

Type: Tuple(Str, Str)
data

What raw data to scale.

Type: array_like
inverse(data)[source]

Transforms ‘data’ using the inverse of this scale. Must know how to handle int, float, and list, tuple, numpy.ndarray and pandas.Series of int or float. Returns the same type as passed.

clip(data)[source]

Clips the data to the scale’s domain.

norm(vmin=None, vmax=None)[source]

Return an instance of matplotlib.colors.Normalize, which normalizes this scale to [0, 1]. Among other things, this is used to correctly scale a color bar.

class cytoflow.utility.scale.ScaleMixin(**kwargs)[source]
cytoflow.utility.scale.scale_factory(scale, experiment, **scale_params)[source]

Make a new instance of a named scale.

Parameters: scale (string) – The name of the scale to build experiment (Experiment) – The experiment to use to parameterize the new scale. **scale_params (kwargs) – Other parameters to pass to the scale constructor
cytoflow.utility.scale.register_scale(scale_class)[source]

Register a new scale for the scale_factory() and ScaleEnum.

cytoflow.utility.scale.set_default_scale(scale)[source]

Set a default scale for ScaleEnum

cytoflow.utility.scale.get_default_scale()[source]


text: Simply put, film emulsions become less light-sensitive as they are exposed which requires adjusted exposure times based on the type of film and the duration of the metered exposure. At the same time, unintentional motion, specifically unwanted camera shake, can rob our images of sharpness and depth. Darktable: Is This Free Lightroom Alternative Right for You? In other words, if you are using a 50mm zoom position on your lens, you should not use a shutter speed below 1/50s without having the camera on a tripod. Let O be a point object on the principal axis. Using Nikon's File Naming and File Number Sequence in a Clever Way was the previous entry in this blog. Got it? What will be the focal length and power of the combination? Find recent content on the main index or look in the archives to find all content. Its S.I. At this point, I’m going to tell you how you can calculate a value for the focal length of a lens, based on the physical characteristics of the lens, before I even tell you what focal length means. (Don’t worry, though, we’ll get to the definition soon.) The refraction's through the two lenses are … There is an important principle in photography that we should discuss, especially if you are shooting with a DX sensor. Don’t freak out as yet. There is an important principle in photography that we should discuss, especially if you are shooting with a DX sensor. Reciprocity, or more specifically reciprocity failure, is a phenomenon photographers sometimes had to manage back in the pre-digital photography days of film. The reciprocal of the focal length is called the … This is much simpler than you think. However, there are times when autocorrect or well-meaning individuals sometimes confuse the Reciprocal Rule and reciprocity failure as being one and the same when they absolutely are not. Every photographer is different, and what works for one might very well not work for another. In today’s cameras there are various sensor sizes: from full frame (which is the approximate size of a frame of 35mm film from the old days) to 4/3rds (which is one of the smallest in a DSLR or ILC). What is Photography About, Anyway? And it is the major measurement of the reciprocal length unit. The defining characteristic of a lens is a quantity called the focal length of the lens. If you are going to handhold images at slower shutter speeds, you need to learn how to brace yourself properly. In order to reduce the appearance of inherent camera shake when hand-holding your camera, just don’t allow your shutter speed to dip below the reciprocal of your focal length. unit is Dioptre (D). Each of these 35mm frames is approximately the size of a modern full-frame digital sensor. Technology is improving our ability to shoot handheld shots at slower shutter speeds; however, it is still best to use a tripod for maximum quality at slow shutter speeds. Cameras versus Lenses – Which is More Important? If you engage your lens or camera’s image stabilization, you are effectively lengthening your allowable handheld shutter speed by ever how many stops the stabilization states it will compensate. Or Power = 9 diopter. Otherwise, you will be known for your well exposed, yet blurry images (from camera shake). However, if I were to mount that same 50mm to my cropped sensor 7D, it would instantly become approximately an 80mm lens (1.6 x 50mm) instead of 50mm. Add your answer and earn points. Feel free to adjust the shutter speed of the Reciprocal Rule and see if you can manage even longer shutters due to the stabilization. The Reciprocal Rule is useful because it takes into consideration the progressively decreasing angle of view produced as focal length increases. It is the reciprocal of the focal length of thelens taken in metres. There are very few absolutes when it comes to making photographs. Let me give you an example to put things in perspective. This results in a reciprocal of 1/80th of a second minimum shutter speed. See answers (1) Ask for details ; Follow Report In photography, motion is both our friend and enemy. p = $$\frac {1}{f}$$(m) Question 14. and check out his brand new video eCourse on Adobe Lightroom Classic! For example, Canon’s cropped sensor (APS-C) has a crop factor of 1.6x because a full-frame Canon sensor is approximately 1.6x larger than that of its cropped-sensor counterpart. It is called the reciprocal of focal length shutter speed rule and affects the sharpness of your images. If you enjoyed this article, you might also like... Back to Basics: Deciphering Shutter Speed and Motion, Back to Basics: Understanding the “Sunny 16 Rule” in Photography. The resulting “reverse crop factor” would be less than 1x. Let’s drill down a little further and examine how the Reciprocal Rule works. It is required to find the effective focal length of this combination. We won't share it with anyone, 11 Ways to Overcome Creative Blocks as a Photographer, The Best Black Friday Deals for Photographers in 2020, How to Shoot in Low Light - 9 Commonly Asked Questions, Two Nikon DSLRs Will Ship Next Year (Plus New F-Mount Lenses), Nikon Will Offer 27 Z Mount Lenses Before 2022 Is Out, Canon Has at Least 7 New RF-Mount Cameras in the Works, The Sony a7 IV Will Launch in 2021, With a 30+ MP Sensor and 4K/60p Recording, Lightroom Color Grading: An Easy Way to Supercharge Your Photos, How to Use Photoshop to Add Lightning to Your Stormy Photographs.


text:
# Does SLLN imply convergence in $L^1$?

Strong Law of Large Numbers demonstrates if $X_1,\,X_2,\,\ldots$ are i.i.d. random variables with $\mathbb{E}|X|<\infty$, $S_n:=\sum_{k=1}^n X_k$, then $$\frac{S_n}{n}\to \mathbb{E} X\quad\text{a.s.}$$ My question is can you give an example such that $\frac{S_n}{n}\not\to \mathbb{E} X$ in $L^1$?

No you cannot find such an example since $$\frac{S_n}{n}\to E[X]\quad \text{in }L^1.$$ It follows from the fact that it converges almost surely and that $$\left\{\frac{S_n}{n}\;\bigg|\; n\geq 1\right\}$$ is uniformly integrable.

Hint on how to show the uniform integrability property:

1. Using the iid assumption, show that $\{X_n\mid n\geq 1\}$ is uniform integrable.

2. Now show that $\left\{\frac{S_n}{n}\mid n\geq 1\right\}$ is uniformly integrable using for example the equivalent formulation of uniform integrability $(*)$.

$(*)$ A sequence $(X_n)_{n\geq 1}$ is uniformly integrable if and only if $$\sup_{n\geq 1}\int |X_n|\,\mathrm dP<\infty$$ and for all $\varepsilon>0$ there exists a $\delta>0$ such that if $P(A)\leq \delta$ then $$\sup_{n\geq 1}\int_A |X_n|\,\mathrm dP\leq \varepsilon.$$

• Perhaps you could add some hint how to prove the uniform integrability.
– saz
Feb 26, 2013 at 8:46
• @<NAME> Thanks indeed. I'm not sure if the second condition in your hint is easily applied. But perhaps a better way is to realize that $\frac{S_n}{n}$ is a backward martingale. Another way is to check directly by definition that $\frac{S_n}{n}$ is $U.I.$ Thank you a second time. Feb 28, 2013 at 2:55


text:
# Critical behavior for scalar nonlinear waves

@article{Masoero2013CriticalBF,
title={Critical behavior for scalar nonlinear waves},
author={<NAME> and <NAME> and <NAME>},
journal={Physica D: Nonlinear Phenomena},
year={2013},
volume={292},
pages={1-7}
}
• Published 13 December 2013
• Mathematics
• Physica D: Nonlinear Phenomena

## Tables from this paper

In this paper we characterize the Nazarov–Sklyanin hierarchy for the classical periodic Benjamin–Ono equation in two complementary degenerations: for the multiphase initial data (the periodic
We consider the zero-dispersion limit for the Benjamin-Ono equation on the torus for bell shaped initial data. Using the approximation by truncated Fourier series, we transform the eigenvalue

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We propose an extension of the Dubrovin–Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few
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• 2008
AbstractWe obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation $$u_t+6uu_x+\epsilon^{2}u_{xxx}=0,\quad u(x,t=0,\epsilon)=u_0(x),$$for
• <NAME>
• Environmental Science
Journal of Fluid Mechanics
• 1967
This paper presents a general theoretical treatment of a new class of long stationary waves with finite amplitude. As the property in common amongst physical systems capable of manifesting these
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Proceedings of the National Academy of Sciences of the United States of America
• 1998
This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way to small dispersion KdV (Korteweg-de Vries) equation and derives the hyperelliptic asymptotic solution of S. Venakides that describes the oscillations.
• Mathematics
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We introduce a deformation of the method of characteristics valid for Hamiltonian perturbations of a scalar conservation law in the small dispersion limit. Our method of analysis is based on the
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We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is
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In Part I the scattering transform method is used to study the weak limit of solutions to the initial value problem for the Korteweg-deVries (KdV) equation as the dispersion tends to zero. In that
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We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for
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A method for solving certain nonlinear ordinary and partial differential equations is developed. The central idea is to study monodromy preserving deformations of linear ordinary differential


text:
### How to extract gold from electronics | WIRED UK

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There are many ways to recover gold on your own Recovering gold by metal detecting, scrap computer and electronics components, and gold mining are three of the most popular ways Special equipment and knowledge are required for gold recovery With some basic equipment and education, anyone can learn to recover gold...

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text:
# Classify the main semantic relation of a sentence using keras

I tried to ask in SO, but they told me to ask here.

I have a big dataset like this:

RELATION<tab>SENTENCE
color<tab>The cat is black
color<tab>My dog is white
place<tab>Des Moines is in Iowa
place<tab>Des Moines is the capital of Iowa
is-a<tab>Des Moines is a city
is-a<tab>3D printer is a type of printer
is-a<tab>New Beetle was a car by Volkswagen
...

I need to build a classifier that, given a sentence, returns a relation as accurately as possible.

I have already programmed something with keras (python), but in this case I really don't know where to start from. For the moment I only realized that an important feature could be the order of the words in the sentence, but I don't know how to explot this.

Do you have some hint? E.g. about features, embeddings, hidden layers. May LSTM be a good NN? Why?

I hope this is not too broad, but I just need some hint.


text:
# Applying vertex normal vector in real-time, it reduces 60 to 1fps.

This topic is 2190 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Actually i don't have any problem in calculating the vexter normal vector.. I have done it by average adjucent faces normal approach.

But the issue is, I have a model that contains 119995 triangles, very large number of triangles, I need to change the vertices position of model in the real-time. for example I am rotating the model vertices. So, by changing the vertices position, face and vertex normal vector must be calculated again. When I enable the face normal, obtained FPS is 59 but when toggled to Vertex normal FPS goes down to 1 FPS,

in every single frame two loops are running, vertices position updating and vertex normal calculating, because of large number of trinagles, I think computer processor give up...

Is there any method to speed up the vertex normal calculations? by using GPU ? or any suggestions?

yea one more thing I am also using FBO but no results. I think the issue is loop running by vertex normal calculation. am i right?

At this stage I am running my simulation by using face normals but I wish I can use vertex normal in real-time. What to do ?

 void RotateMeshByComputingRotationMatrix(float XRotAngle) { for (int i=0; i<N_Vertices; i++) { Rotate_Model_Vertices(i, XRotAngle); } for (int i=0; i<N_Trinagles; i++) { ComputeFaceNormals(i); } for (int i=0; i<N_Trinagles; i++) { ComputeVerticeNormals(i); } }

Thanks.
Lucky

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What is the reason you're not just making a rotation matrix and letting OpenGL do the rotation? If you have to rotate manually, just rotate the normals with the same rotation instead of recalculating them.

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Realy Thanks...
Actually, in simulation, each vertex position must be updated at every single updated frame, so thats why, manual rotation is required instead of OpenGL rotation glRotatef().

yes its working.. I couldn't understand, why i didn't think of it.. to rotate the normals with the same rotation of the model vertices.

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Actually, in simulation, each vertex position must be updated at every single updated frame[/quote]

That sounds completely wrong. Give an idea of the simulation you are doing. If it is something with physics you can instead convert other objects into this ones frame by taking their final world position and then multiplying only all of those vertices of the smaller object by the big obejcts matrix. So the 110,000etc verts remain static and then the smaller things that interact with it that might be 100 vertices, you just put transform those objects. The fact that you posted this and it was a surpise that your fps dropped seems like maybe you are going by a bad approach, so give and idea of what you are doing and why you need those new verts stored.

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it sounds more like you need to do another approach to what your attempting to achieve.

modifying nearly 120,000 object's 60 times a second is a tremendous amount of work, since a vertex normal requires one to take the length of all adjacent faces to the vertex, then it requires a sqrt, doing a sqrt 100k times obviously has alot of overhead(hopefully your data structure means that your know the faces ahead of time that are connected to the vertice, if not, here's another huge bottleneck of lookup time).

in short, either try creating another thread to run the simulation in and separate the draw/update routines, use a shader to find the vertex normals on the gpu(this requires knowing the amount of rotation the vertex has done.), or attempt to approach w/e your trying to achieve in a diffrent direction. attempting to real-time the volume of data your attempting to manipulate doesn't work very easily, and your application is probably going to be locked to only very high-end machines.

to be fair, i can't imagine what beast of a machine your working on, that your haven't seen even more bottlenecks.

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OK this is my code... this code is working 100% perfectly in order to visualize the cutting section by a tool.. actually you can have an idea like a CNC machine. there is a tool that cut the surface of a model.

you can see in the below code I am rotating the model in X-direction and then I update the vertex normal by making another loop. that loop is a making a problem in FPS. and if I don't update the vertex normal vector after "rotating and cutting of the surface" then offcourse I can not see the good visualization of the cutting section.

so how can i update the vertex normal in this kind of situation.. ? thanks

 void RotateMeshByComputingRotationMatrix(float XRotAngle) // glutIdleFunc { float mat16[16]; float vec4[4]; for (int i=0; i<nb_Vertices; i++) { vec4[0] = getVertexPos(i).x; vec4[1] = getVertexPos(i).y; vec4[2] = getVertexPos(i).z; vec4[3] = 1; matrixRotateX(XRotAngle, mat16); // get rotation matrix along Y-axis VMatMult(mat16, vec4); p_VERTICES.set(vec4[0], vec4[1], vec4[2]); // rotation of vertex normal but this isn't working // when vertices change their position, vertex normal must be calculated again. With the rotation of vertices, vertex normals rotate too. //vec4[0] = VertNormals.x; //vec4[1] = VertNormals.y; //vec4[2] = VertNormals.z; //vec4[3] = 1; //VMatMult(mat16, vec4); //VertNormals.set(vec4[0], vec4[1], vec4[2]); } // when vertices change their position, face normal must be calculated again. for (int i=0; i<nb_Faces; i++) ComputeFaceNormal(&FaceNormals); // when vertices change their position, vertex normal must be calculated again. for (int ix = 0; ix<nb_Vertices; ix++) // compute the vertices normal of each vertex ComputeVerticeNormal(ix); } void UpdateVerticesPositionByBoundingBoxOfCuttingTOOL() // // glutDisplayFunc { for (int i=0; i<nb_Faces; i++) { if( IsCollision()) updatevertex(i); // update x , y, z } }

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The normal is a vector, not a point, so its W-component must be 0. Besides, don't calculate the rotation matrix for every loop iteration; it will be the same all the time.

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Thanks.. its works.


text:
# Maximizing $\dfrac{4 \sqrt{a} + 6 \sqrt{b} + 12 \sqrt{c}}{\sqrt{abc}}$ over $a+b+c=4abc$ and $a,b,c>0$

Let $$a,$$ $$b,$$ $$c$$ be positive real numbers such that $$a + b + c = 4abc.$$ Find the maximum value of $$\dfrac{4 \sqrt{a} + 6 \sqrt{b} + 12 \sqrt{c}}{\sqrt{abc}}.$$

First, I tried using $$\dfrac{4 \sqrt{a} + 6 \sqrt{b} + 12 \sqrt{c}}{\sqrt{abc}}=\dfrac{4}{\sqrt{bc}}+\dfrac{6}{\sqrt{ac}}+\dfrac{12}{\sqrt{ab}}$$. Then, I tried to apply some inequalities, but it didn't work.

I also tried just substituting $$abc=\dfrac{a+b+c}{4}$$ into the equation, but this also didn't do much. Could someone give me some guidance on how to proceed?

• One thing that should make it substantially easier: divide both sides of the constraint by $abc$ to get $\frac1{bc}+\frac1{ac}+\frac1{ab}=4$. Now you can do a change of variables $x=\frac1{\sqrt{bc}}$, $y=\frac1{\sqrt{ac}}$, $z=\frac1{\sqrt{ab}}$. (First prove that we can recover $a, b, c$ from $x, y, z$ so this is a one-to-one mapping!) What form does the constraint take in terms of this $x,y,z$? What does the function to optimize look like? Do you know how to optimize that sort of function subject to that constraint? Feb 28 at 17:41


text:
# Second-order differential equation and conditions

1. Mar 30, 2017

### Taylor_1989

1. The problem statement, all variables and given/known data
Hy guys I am have a problem with the last part of this question. part d), ii) I get the general formal which I have displayed below, but what I done understand is if I take the limits as show in ii) I get $0=\ \infty$ which obviously I am doing something wrong. Have I misinterpreted what they are say as y tends to 0 as x tends. Could anyone give me some advice it would be much appreciated, thanks in advance.

2. Relevant equations

3. The attempt at a solution
$y=c_1e^{2x}+c_2e^{-3x}-e^{-x}$

#### Attached Files:

• ###### upload_2017-3-30_16-35-3.png
File size:
23.4 KB
Views:
22
2. Mar 30, 2017

### Staff: Mentor

What equation did you get for question d) part i)? Part ii) is essentially saying that $\lim_{x \to \infty} c_1e^{2x} + c_2e^{-3x} - e^{-x} = 0$. What are the values of the two constants so that this can happen?

3. Mar 31, 2017

### Taylor_1989

@Mark44 I see now thank you as soo as u put in that form and do each lim seperatly I saw what was going on. Much apprectied.

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# Package inputenc Error: Unicode char - {U+2010)

I am encountering the following error and have no idea where to find the solution;

``````Package inputenc Error: Unicode char ‐ (U+2010)
(inputenc)                not set up for use with LaTeX.

See the inputenc package documentation for explanation.
Type  H <return>  for immediate help.
...

l.129   boundedness and actor‐
network theory.
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

[32] [33]) [34]
\openout2 = `chapters/abbreviations.aux'.
``````

Can anybody aid me in finding the solution? I am using ShareLatex if that is necessary information.

• Your character here (`‐`) is not a hyphen but a Unicode dash : replace it with a normal hyphen. – <NAME> Apr 18 '16 at 11:21
• Is it clear from this error message where this is? it refers to output.bbl, line 129 not to a page or lne in the coding – user103481 Apr 18 '16 at 11:23

## 1 Answer

Recent LaTeX versions declare the symbol U+2010 (DASH) in `utf8enc.dfu`, `t1enc.dfu`. The former is loaded by default. The declaration can be given explicitly for older LaTeX installations:

``````\usepackage[utf8]{inputenc}
\DeclareUnicodeCharacter{2010}{-}% support older LaTeX versions
``````

Versions with U+2010:

• `utf8enc.dfu`: 2016/02/28 v1.1s
• `t1enc.dfu`: 2016/02/28 v1.1s
• LaTeX 2016/03/31
• I'm having this problem, but my `pdflatex` is pretty current. At what version was this fixed? – ryanjdillon Sep 13 '17 at 18:16
• @ryanjdillon I have added the version numbers. The LaTeX version is relevant, but not the version number of pdfTeX. – <NAME> Sep 13 '17 at 18:26


text:
# Save MetaTrader Screenshots Directly To S3 From Windows VPS

I’m a big believer in learning from your trades. If you want to grow as a forex trader you need to be able to put in the time of personal reflection on your own trades.

MetaTrader makes this somewhat painless by taking screenshots of your open trades while you trade. While I’ve previously documented this before using Dropbox as the medium to transport your images off your Windows VPS you’ll find Dropbox can bloat your Windows box, and it needs resources to maintain it.

If you do happen to connect through your Dropbox successfully onto your Windows VPS, be careful to selectively sync your folders as every new folder will automatically be uploaded to your Windows box! I’ve destroyed a few Windows boxes because I had forgotten to not remove several large folders.

Surely though there has to be a better way. Dropbox wasn’t really intended for this type of work.

A better way would be where I could just push through the screenshot’s folder to some cloud storage space and then view it through the browser or an app on my computer.

And the software doing the pushing needs to be lightweight.

I don’t want a 1 tonne elephant sitting on my VPS.

Well, I do believe there is a solution.

## Store your images on Amazon’s S3

It is relatively cheap to store your photos on Amazon S3 with each GB costing around 2.5 cents! That’s correct, a whopping 2.5 cents to store all your forex images per gigabyte.

Here’s what you need to do to get set up:

### Create S3 Bucket

This is the easiest part. Simply create go to Amazon AWS and create an account.

Then click on Services and then on S3.

Take note of the short-name of the s3 region where the bucket has been created (eg. ap-southeast-2 for Sydney).

### Create IAM User

To interact with the S3 bucket from your Windows machine, create a specific user which will be granted the privileges to interact with your newly created S3 bucket.

Grant permission to the IAM user for it to be able to write to S3 buckets.

Copy the Access Key ID and Access Secret ID.

### Install AWS CLI in Windows VPS

Install the Windows MSI installer and follow through the prompts.

Once you have finished installing the AWS command-line tool, open Windows Run and enter cmd – this will open the Command Prompt.

Run aws configure and you will be prompted with some instructions on data to insert, namely:

• Access Key – from step 3B
• Access Secret – from step 3B
• Short name of the bucket’s location – from step 2A (ap-southeast-2 for my Sydney bucket)
• Output type – leave as json (unless you want some other format).

In Windows Explorer navigate to the location of your forex images. I found mine located in the folder like this:

C:UsersAdministratorAppDataRoamingMetaQuotesTerminal<YOUR_LONG_HASH_STRING>MQL4Files

Copy this long path string as text. I found right-clicking on the address bar in Windows Explorer and select Copy address as text.

Return to the Command Prompt and change directory to where the MetaTrader images have been stored:

C:UsersAdministrator> cd C:UsersAdministratorAppDataRoamingMetaQuotesTerminal<YOUR_LONG_HASH_STRING>MQL4Files

Once the current directory has been changed run the AWS S3 SYNC command:

aws s3 sync . s3://your-bucket-name

The . in the command above denotes the current directory and the s3:// address is the bucket you’ve created.

If everything has been configured correctly then you should see your files uploaded to s3 which would look like this:

### Create Batch File

The final step to begin the automation of processing the S3 sync automatically is to create a batch file which you can schedule to run on an automated schedule.

Create a file on your desktop using Notepad with the following code:

cd C:UsersAdministratorAppDataRoamingMetaQuotesTerminal<YOUR_LONG_HASH_STRING>MQL4Files
aws s3 sync . s3://your-bucket-name

Save the file somewhere meaningful, perhaps the Desktop and with an appropriate name.

You can test to see if this batch file works by double clicking on it in Windows. If you see the files in your new S3 bucket you’ve done well and can proceed to running the script based on a Task Schedule.

If however you’re having problems with the batch file doing anything see below for further ways you can diagnose issues.

Open up the Task Scheduler. If you’re comfortable creating a scheduled task using the command line, you can replace step 9 with the command line schtasks below, but you will still need to customise the settings.

From the UI, click Create Basic Task. On the window screen prompting you for when you want the task to start, set this to One time. Select the precise time during the day (if you selected daily). Select the action Start a program, then select the batch file created above.

On the final step, tick the box Open the Properties dialog for this task when I click Finish, then click Finish.

We need to apply some further edits to our basic task to make it recur.

On the Properties window you can write a more detailed description to help jog your memory on what the purpose of this task will be doing. In the Security Options section select the option to run the script without being logged in. While here, check the box to Run with highest privileges.

On the Triggers tab double-click the One time trigger item in the table, and set the following options to have the script run every 5 minutes:

Once you’ve clicked ok, click on the Conditions tab. Here we want to make sure we’ve got a Network available to enable you to connect and upload your files:

Finally, click on the Settings tab and set the following options:

You could apply further edits to the remaining settings if you wish.

To test if your task schedule works click on the Run option in the Actions pane.

### Check S3 Files

Go back to your Amazon S3 account and check to see if your files have been uploaded correctly.

If you are on a Mac you can use Trasmit or CyberDuck.

## Check Windows Batch File

If when you double-click on the .bat file you find the script doesn’t upload your png files to s3 then there are a couple of things we can add to our batch file to test what is wrong and then write additional code to get our script to work.

### Check 1: Output Errors

To diagnose if we are getting an error with our .bat file place at the end of the file the command pause. This will leave the command prompt window open after you have run it allowing you to read any errors before the command prompt window closes down.

Therefore, using my .bat file as an example, if I wanted to check if there were any errors simply have the following:

cd C:UsersAdministratorAppDataRoamingMetaQuotesTerminal<YOUR_LONG_HASH_STRING>MQL4Files
aws s3 sync . s3://your-bucket-name
pause

When you double-click on the .bat file again did you notice any errors?

### Check 2: AWS Credentials

To see if our AWS credentials are working correctly we are going to add a line to our .bat file to check if it correctly uses the right credentials to access our bucket.

Edit you .bat file so that it has aws s3 ls:

aws s3 ls
aws s3 sync . s3://your-bucket-name
pause

The command aws s3 ls simply lists all the buckets available for the credentials you have entered for the user. If you don’t see anything you should double check your configuration by running aws configure in another command prompt window.

Then check there has been a bucket created in the same location you see in the command prompt window.

If you don’t see any listings, and everything is correct with your bucket reference it may also be a credential issue, go to check #4 below.

### Check 3: Directory Reference

Let’s check to make sure there are files to be uploaded by inserted between the cd ... command and the aws s3 sync command a simple dir command to check the contents of the directory.

Your batch file should look something like this:

aws s3 ls
dir
aws s3 sync . s3://your-bucket-name
pause

With the batch file run you should see a listing of all the local files on your server that will be uploaded to s3. If you don’t see any files, check you have entered the correct directory address (check step 6 and 6A again).

### Check 4: Set AWS Configuration

There have been issues where the batch file will not run the correct AWS credentials, this is especially true when then task scheduler runs the file.

If you are currently logged in as the user which will run the batch file you can open a command prompt window to see if the AWS configuration settings are available, simply run:

C:> type "C:Users<USERNAME>.awsconfig"

Where <USERNAME> is the user running the script, eg. Administrator. If you see a listing of the bucket location and output type like so then you’ve got the credentials defined for the user.

[default]
region = ap-southeast-2
output = json

To explicitly set the type of user for the batch file to use, you can do so by adding the following lines:

set userprofile = C:Users%username%
set AWS_DEFAULT_PROFILE = userprofile
aws s3 ls
dir
aws s3 sync . s3://your-bucket-name
pause

Do you see the correct listing of your s3 buckets? And the correct contents of your files to upload?

### Check 5: S3 Reference

A simple check, but one which ended up getting me, was incorrectly referencing the s3 bucket url.

Instead of entering s3://your-bucket-name I had s3:\you-bucket-name.

## How do I delete files in the MQL4/Files folder?

Caution will be needed if you want to add a command to your .bat file to automatically delete the screenshots you’ve generated. However, the worst that can happen is that if you do delete a file you didn’t intend then it will be found in your Recycle Bin.

If you do want to exercise caution in deleting the files in your MQL4/Files directory then there are a couple of ways to minimise the risk of accidentally deleting files you didn’t intend:

1. Create another .bat script file with just the following contents:
cd C:UsersAdministratorAppDataRoamingMetaQuotesTerminal<YOUR_LONG_HASH_STRING>MQL4Files
del *.* /Q /S
RMDIR /S /Q .
• /Q flag runs the deletion in quiet mode, in other words it will not prompt you for every file if you are sure you really want to delete it.
• /S flag deletes all sub-folders.

Then when you feel it’s time to clean up your VPS you can log in to you account and run this batch file manually.

1. If you want some level of automation you could create the same batch file above with the same contents, but you would schedule to run the script over the weekend. Schedule the script to perform its clean on late Sunday night (the very end of the weekend), giving you enough time to check things have been properly uploaded.

If, though, you want to live on the bleeding edge then all you need to do to your current .bat file is to append at the end the following command to delete everything once it has uploaded everything to S3:

del *.* /Q /S
RMDIR /S /Q .

Still, I would only recommend you add this command once you’ve confirmed after a few days that everything is working as it should be.

## Conclusion

In this article we’ve learned how to use the AWS S3 sync command to upload a copy of our screenshots and performing this with a little footprint on our Windows VPS.

You’ve also learned how to diagnose issues that might creep up when running the script and have also learned how to clean up the folder, so it doesn’t bloat your MetaTrader directories.