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Practicing these CBSE NCERT Objective MCQ Questions of Class 8 Maths with Answers Pdf will guide students to do a quick revision for all the concepts present in each chapter and prepare for final exams. The terms, factors and coefficients related to Algebraic Expressions are discussed in the chapter. Class 8 Maths NCERT Solutions & Main Points of All Chapters Chapter 1: Rational Numbers. NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Exercise 2.1, Question 1. Chapter Wise CBSE Quick Revision Notes and Key Points for Class 8 Maths Pdf free download was designed by expert teachers from latest edition of NCERT books to get good marks in board exams. There are 2 exercises in the chapter that will be helping the students in understanding the basics of Cubes and Cube Roots in depth. The solutions are given in easy steps to help students understand the concepts better. worksheets for students have been used by educators to develop logical, lingual, analytical, and problem-solving capabilities. Our responsive team is always ready to answer all types of questions. Candidates can score good marks in the CBSE Class 8 Maths Exam by making use of the ultimate preparation tools like Study Materials, Notes & Syllabus, NCERT Solutions, etc. The shapes can quadrilateral, triangle, hexagon, pentagon, etc. NCERT Solutions for Class 8 Maths Chapter 8 – Comparing Quantities. ⇒ 2.40 = y During the course of this chapter, students will be briefed about the concept of probability or likelihood. Each and every step is explained in a simple language to make learning fun for the students. You will be able to search the rational numbers between any of the given two rational numbers through this chapter. There are numerous ways through which you can seek out the cubes and cube roots of a number. Important Terms about Class 8 Maths Chapter 8. They might have also studied a number of interesting properties about these numbers, finding factors, multiples and the relationships among them. Students can register to BYJU’S and get the opportunity to learn topics of CBSE or NCERT syllabus for Class 8 Maths or any other Class more effectively. Your email address will not be published. The math exercises are given at the end of every chapter to practise the concepts learned in the chapter. You also are learning to perform the mathematical operations on either side of an equation. UP Board Class ⇒ p = $$\frac { -4 }{ 3 }$$ There are also divisibility tests along with questions based on them. We will check here the closure property under Addition, Multiplication, Division and Subtraction for Rational Numbers. Class 8 Maths MCQs Multiple Choice Questions with Answers. The questions provided in Mathematics - Solutions Books are prepared in accordance with Maharashtra, thus holding higher chances of appearing on Maharashtra question papers. Thus, z = 4 is the required solution. This NCERT solutions for class 8 maths helps you precisely with that. Let original salary be ₹ 100. The concepts which are important from the exam point of view must not be postponed as it will lead to less score in the Class 8 exams. Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. The chapter discusses finding the cubes of different numbers, some interesting patterns that could be learnt using cubes and finding the cube roots. Go through the topics listed under parent topics as per your choice and prepare well for the exam. This chapter contains 2 exercises that entail questions based on the direct proportion and inverse proportion. Thus, p = $$\frac { -4 }{ 3 }$$ is the required solution. It also explains the terms area unit that is used additionally to express pure mathematics expressions and how these terms are shaped based on different products. 08_Comparing Quantities. They can learn different topics right from their homes using the internet where they can browse content on their PCs. The Class 8 students should first understand the NCERT Syllabus from the official website for the academic year and then decide the concepts of top priority. Required fields are marked *. Question 9. Class 8 Maths Chapter 8 Comparing Quantities When you compare quantities, you need to have an increase or decrease of percentage, sales value, market value, discount, and the discounted value of the product to check whether you have made profit or loss. Which book of mathematics should I refer in Class 8? These solutions cover all the chapters that are included in the Class 8 Maths book. You will also study the applications of Euler’s formula. Solution: How can I score good marks in the Maths Class 8 CBSE? It also explains the multiplication of polynomials by polynomials and the addition of mathematical expression. NCERT Solutions for Class 8 Maths includes all the questions provided in the NCERT textbook that is prescribed for Class 8 in accordance with the CBSE Board. Solve the equations: $$\frac { 3 }{ 7 }$$ + x = $$\frac { 17 }{ 7 }$$ New salary is ₹ 110, when original salary = ₹ 100. Solve the equation 6x = 12. Question 6. This will also help you to improve your overall score in the Class 8 exam. Besides, students can bring in all their queries regarding Maths as well as other subjects including Physics, Chemistry, and Biology. Solving NCERT Maths question papers and sample papers will also help the students to understand different types of questions as well as the marking scheme. Solution: ⇒ 14y = 21 We have, 17 + 6p = 9 are some of the important chapters to prepare for the exams. A total of 4 exercises are present in this chapter. In the chapter, Exponents and Powers, students learn different concepts including powers with negative exponents, laws of exponents, use of exponents to express the numbers in standard form and comparison of extremely large numbers with small numbers. This chapter will deal with issues related to areas and perimeter of closed figures. In this chapter you understand the purpose and importance of graphs, to show the numerical facts in visual forms so that everyone is able to understand the concept very easily. Advanced Placement examinations are offered at the high school level only. These were the few benefits of using the Solutions of Maths NCERT Class 8. What is the best way of studying in Class 8? BYJU’S provides the NCERT Solutions for Class 8 Maths chapter 1 to 16, prepared by our expert faculties, to help you in your exam preparations. ⇒ x = 9 (Required solution), Question 2. Solve the equation: x – 2 = 7. Frequently Asked Questions on NCERT Solutions for Class 8 Maths. Mathematics: content. Chapter 3 Algebra Ex 3.8; Chapter 3 Algebra Ex 3.9; Chapter 3 Algebra Ex 3.10; Chapter 3 Algebra InText Questions; Tamilnadu Board Class 8th Maths Guide Free Download Chapter 4 Life Mathematics. Solving equations with variable on one side: Linear equations in … NCERT Solutions for Class 8 Maths are completely Free and you can COPY, Download and Create PDFs. Maths Formulas for Class 8 But few chapters have higher weightage of marks when compared to others. Hence, we can conclude that learning this chapter will make the students well-versed in all the concepts of quadrilateral for further classes. ⇒ 6p = -8 Here the chapter will be dealing with the equations with linear expressions in one variable only. ⇒ 14y – 8 + 8 = 13 + 8 (adding 8 to both sides) This chapter will introduce you to the basics of a quadrilateral, a polygon with 4 sides. Students can also download the BYJU’S app and get complete assistance for Class 8 with a new method of learning, through educational videos. Get revision questions on topics including Numbers, Operation on Numbers, Measurement, Geometry, Algebra, Tables and Graphs, Scale Drawing and Ratio and Propotion with answers included. We have 7x – 9 = 16 How do I start the Class 8 Maths (CBSE)? In this chapter, you will deal with numbers in a general form. 3. Your email address will not be published. In this chapter, Mensuration, students will learn to solve problems related to perimeter and area of other plane closed figures like quadrilaterals. If his new salary is ₹1,54,000, find his original salary. Solve the equation 17 + 6p = 9. You will also get to know how to transform the quantity into various units. These CBSE 8th Class Maths solutions are available for free and any student can access them. Students learn about simple interest, compound interest calculated half-yearly, quarterly, monthly or yearly, and much more. ⇒ p = $$\frac { -8 }{ 6 }$$ Along with this, you will study the volume of solid figures like a cylinder, cube, cuboid, and so on. These solutions are free and students can view them online on the website or download the PDF. The NCERT Maths Class 8 PDF is designed to encourage concept-based learning among students. The chapter will help the students in learning how to locate a point and coordinate in a graph. 2. Aspirants can get the NCERT Class 8 Maths Chapterwise Solutions by referring to the quick links made available on our page. In this chapter, students learn to perform Factorization. We have $$\frac { 2x }{ 3 }$$ = 18 Linear Equations in One Variable 3. There are also puzzles and games in this chapter related to numbers. Solve distance, similarity, congruence and Pythagorean Theorem of figures. ⇒ y = $$\frac { 3 }{ 2 }$$ ⇒ 6 – 2 = z + 2 – 2 (subtracting 2 from each side) Square and square roots, mensuration, introduction to graphs, quadrilaterals etc. In this chapter, students learn to represent these data diagrammatically as a pictograph, a bar graph, double bar graph, pie chart and histogram. In case students face any doubts while going through the CBSE Class 8 Maths Solutions, they can always approach our BYJU’S support team for clearing all their doubts. Best Resources to begin preparation for Class 8 Maths is through NCERT Textbook Solutions. The split up between the chapters is balanced but still, some chapters like Understanding quadrilateral, Square and square roots, Comparing quantities, Mensuration, Introduction to graphs and algebraic expressions and identities have more weightage … Thus, this makes a very important chapter to understand and remember. December 7, 2020 by Rajashekhar. Understanding Quadrilaterals. Practice as many times as possible and revise the concepts thoroughly. Rational Numbers Class 8 MCQ Questions. The PDF of solutions on BYJU’S are available with a free download option. They can use these NCERT Solutions for Class 8 as a reference while practising math problems and develop better math skills along with preparing efficiently for the exams. You can share this link with your friends and help them understand the topics better. Along with you will also learn about the edges, faces, and vertices about some solid figures like triangular pyramids, cuboids, square base, and triangular prisms, etc. 6. 06_Squares and Square Roots. As you go ahead in maths, you will notice the importance of linear equations. This chapter includes drawing 4 sides in a quadrilateral with 2 adjacent sides, 3 angles and 1 diagonal area given to you. Thus, x = 27 is the required solution. In addition, BYJU’S is keen on tracking the progress that students make. There are six exercises in this chapter with a total of 65 questions in them. ⇒ 14y ÷ 14 = 21 ÷ 14 (dividing both sides by 14) We have 14y – 8 = 13 It does not matter if you are choosing science or biology or commerce stream. There are 2 exercises in this chapter, which contain questions from all the topics present in the chapter. Eventually, the students would learn about the surface area and volume of different solid shapes such as a cube, cuboid and cylinder. If you get to know that fact, you will never have any math problems. 1. Thus, t = 50 is the required solution. By clicking on the links, students will be able to download and access the chapter wise solutions while practising the problems from NCERT textbook. A cube-shaped object formed by connecting various line segments is called a polygon and then are various shapes in polygons. A total of 65 questions in six exercises is given for students to practice and learn. The chapter contains 4 exercises which aid the students in understanding these shapes properly. Feedback and counselling are provided via periodic assessments. Moving on, students can customize their learning experience and they can do it all at their own pace without worrying about deadlines or without taking any stress. The syllabus given by the CBSE for all the classes is completely based on the NCERT curriculum. Solve the equation $$\frac { 2x }{ 3 }$$ = 18. A brief on the basics of monomials, binomials and polynomials are also given in the chapter. Given below is the chapter-wise distribution of marks. ⇒ x – 2 + 2 = 7 + 2 (adding 2 on both sides) But in this chapter, you will learn about these cubes by adding consecutive odd number pattern. The solutions are accurate as per the CBSE syllabus making it reliable for the students while preparing for the Class 8 exams. The chapter deals with the role of zero and one, multiplication over addition as well as the representation of Rational Numbers on the number line, along with searching for Rational Numbers between two Rational Numbers. In teachoo, each chapter is divided into - Serial Order Wise, and Concept Wise One such help is being by us in the form of NCERT solutions for class 8 maths. 1.Star with NCERT text book,read the theory given in NCERT text book and note down all important formulas and concept in your note book.Take the help of NCERT solutions. Book: National Council of Educational Research and Training (NCERT) We have 6 = z + 2 Squares and Square Roots 7. Some basic maths will always be there in each of these streams. Thus, it becomes important for students to have a strong base in this subject. Latest CBSE Syllabus For Class 8 Maths: The Central Board of Secondary Education (CBSE) is one of the largest boards in India which is responsible for secondary and senior secondary education in schools affiliated to the board.It is a national-level board that conducts the Class 10 and Class 12 board exams every year for the students of these schools. The chapter includes different concepts including- solving an equation of Linear Equations in One Variable, some of its applications, reducing equations to a simpler form and word problems related to Linear Equations in One Variable. The chapter is very interesting since it deals with viewing 3-D shapes, Mapping the space around us, and learning about faces, edges and vertices. Students can obtain the chapter wise solutions of Class 8 from the quick links provided on BYJU’S. The chapter also covers different kinds of polygons, including triangles, quadrilaterals, pentagon, hexagon etc. Further, we are providing the best subject experts or mentors who will guide students to learn the subject and its concepts in a more simple and fun manner. It depends on the angle between the two line segments and the number of line segments. We have reviewed, corrected typos and cross verified the solutions for the best, most detailed, accurate Free Solutions for Class 8 NCERT Mathematics. ⇒ 4 = z This chapter offers a plan to discuss the various roots of a number. Chapter-wise NCERT Solutions for Class 8 Maths. ⇒ 2x ÷ 2 = 54 ÷ 2 (dividing both sides by 2) It is important to prepare for the entrance exam along with the school exams. 2. Another benefit that students can experience with BYJU’S is that they can opt to learn NCERT subjects by accessing our solutions anywhere and at any time of the day. ⇒ x = $$\frac { 25 }{ 7 }$$ The chapter consists of 5 exercises, each dealing with different methods of constructing the quadrilateral. Rational Numbers 2. ⇒ 7x = 25 These ideas can help the students in justifying tests of divisibility. Solution: Question 5. The chapter consists of 2 exercises to help the students learn about the topics of Exponents and Powers. Download CBSE Class 8 Maths Worksheets 2020-21 Session in PDF. NCERT Solutions for Class 8 Maths includes all the questions provided in NCERT Books for 8th Class Maths Subject. Generally, the major areas chosen include English, American history, mathematics, chemistry, and physics. There are 2 exercises in this chapter that covers the topic of Playing with Numbers. Grade 8 Mathematics Final Exam Practice Test I Grade 8 Mathematics Final Exam Practice Test I . https://www.evidyarthi.in/maths-8th/mcq-questions-for-class-8-maths 5. The 5 exercises in the chapter cover all the concepts present in Algebraic Expressions and Identities. The primary thing you will study in this chapter is power and exponents: power that has negative exponents, decimal numbers and their scientific documentation, the dependency of the exponent’s law, utilizing exponents in order to express the numbers and comparing small numbers to extremely large numbers. Furthermore, how rational numbers are represented on a number line is also explained. You can score better grades in the exam with the ultimate preparation tools. Here all questions are solved with detailed explanation and available for free to check. UP Board Class 8 Maths Solutions Pdf download गणित are the part of UP Board Solutions for Class 8. Students, so far, have studied various types of numbers such as natural numbers, whole numbers, integers and rational numbers. Solve the equation 14y – 8 = 13. ... Maths Quiz For Class 8th Maths Quiz For Class 8th . Along with the important questions, you will find respective elaborate step-by-step answers in class 8 maths extra questions. ⇒ x = 27 Class 8 Mathematics. Thus, y = 2.40 is the required solution. The chapter deals with an important concept that can be used in day to day life, Interest. Question 11. Solve the equation $$\frac { t }{ 5 }$$ = 10. Class 8: Mathematics: Mathematics. The math exercises are given at the end of every chapter to practise the concepts learned in the chapter. ⇒ $$\frac { 2x }{ 3 }$$ × 3 = 18 × 3 (multiplying both sides by 3) The chapter, Practical Geometry, includes the method of constructing a quadrilateral with various parameters given. We have 6x = 12 There are 3 exercises in this chapter that deal with all the concepts covered in the chapter. ⇒ y = $$\frac { 21 }{ 14 }$$ This strategy of finding roots is very useful in higher standards. When you compare quantities, you need to have an increase or decrease of percentage, sales value, market value, discount, and the discounted value of the product to check whether you have made profit or loss. Given: x – 2 = 7 Solution: To become master is class 8 Maths you required two most important thinks one is your concept clarity and second is your questions solving approach. The different types of graphs include bar graphs, pie graphs, line graphs and linear graphs. You can download the Class 8 Maths Previous Papers PDF through the direct links available on our page. Self Practice 4a Solution. There are 3 exercises in this chapter which helps the students in learning the concept of Comparing Quantities. In this chapter, students will be learning properties related to real numbers, integers, whole numbers, rational numbers and natural numbers – independent, associative and closure. BYJU’S NCERT Class 8 Solutions for Maths has been designed to help the students solve the CBSE Class 8 Maths problems with ease. In the chapter, Cubes and Cube Roots, students learn about numerous strategies to find out the cubes and cube roots of a number. Scroll down and download today all the maths questions for class 8 with answers to enhance your exam scores. Solve the equation: y + 3 = 10. ⇒ 2x = 54 Quiz On 8th Grade Math Quiz On 8th Grade Math . Given: y + 3 = 10 Students who are registering for a math class at USU for the first time who have a current math ACT score of less than 23 or a math SAT score of less than 540 (whether current or not) are required to take the Math Placement Exam administered by the Department of Mathematics and Statistics. This inverse and direct proportions are identified based on the relative decrease or increase of one quantity with respect to other quantities. The questions in this chapter will give you details on inverse and direct proportions. This chapter further dwells into extra expenses that are incurred like excise tax, acquisition of piece, whether interest is compounded yearly, half-yearly, or quarterly, etc. We are providing chapter-wise NCERT Maths Solutions for Class 8. Solution: Also, students can learn from NCERT Exemplar Class 8 to practise exemplar problems. Math as a subject is full of formulas! 4. 07_Cube and Cube Roots. This chapter is based on the factorization of algebraic expressions and natural numbers. NCERT Books Class 8 Maths: The National Council of Educational Research and Training (NCERT) publishes Maths textbooks for Class 8.The NCERT Class 8th Maths textbooks are well known for it’s updated and thoroughly revised syllabus. A number of examination areas are available; not all high schools offer all available AP examinations. Hello Students In this article, we have discussed the Class 8 Maths Question Papers. With the help of NCERT solutions for class 8 maths, you get chapter wise solutions of each and every exercise. Answers to all questions have been solved without missing a step, with detailed explanation of the concepts as well. Solution: Question 12. The solutions provided on this page will help students understand and solve all the NCERT Class 8 mathematics book questions. Self Practice 4c Solution. ⇒ 6p ÷ 6 = -8 ÷ 6 (dividing both sides by 6) 09_Algebraic Expressions. Such equations are known as Linear Equations in One Variable. Hence, preparation of exams using the NCERT Solutions will definitely provide students with an advantage of scoring well. 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Chapter 11 Construction Objective Questions, Chapter 12 Areas Related To Circles Objective Questions, Chapter 13 Surface Areas And Volumes Objective Questions, Chapter 14 Statistics Objective Questions, Chapter 15 Probability Objective Questions, NCERT Solutions for class 12 Business Studies, NCERT Solutions for class 11 Business Studies, NCERT Solutions Class 10 Political Science, NCERT Solutions for Class 9 Social Science, NCERT Solutions Class 9 Political Science, NCERT Solutions for Class 7 Social Science History, NCERT Solutions for Class 7 Social Science Geography, NCERT Solutions for Class 7 Social Science Civics, NCERT Solutions for Class 6 Social Science, NCERT Solutions for Class 6 Social Science History, NCERT Solutions for Class 6 Social Science Geography, NCERT Solutions for Class 6 Social Science Civics, NCERT Books for Class 12 Business Studies, NCERT Books for Class 11 Business Studies, NCERT Exemplar Solutions for class 12 Maths, NCERT Exemplar Solutions for class 12 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Solution: In this chapter you will compare quantities, increase or decrease of percentage, discount, profit and loss, vat tax, sales tax, computing interest. ⇒ t = 50 ⇒ y = 7 (Required solution). The chapter, Linear Equations in One Variable, deals with linear expression in one variable alone. ⇒ 1.6 × 1.5 = $$\frac { y }{ 1.5 }$$ × 1.5 (multiplying both sides by 1.5) You can refer to the Standard NCERT Textbooks prescribed by the CBSE Board for your Class 8 Mathematics Exam Preparation. Geometry is another topic that is going to be important for advanced math classes. Prepare for the students in this chapter will introduce you to the exam is ₹1,54,000, find his salary! Learn from NCERT Exemplar Class 8 to practise the concepts covered in the chapter will make the students in the... Mathematics expressions and identities, helps the students in understanding the concepts covered in the chapter minimized. Called quadrilateral precisely with that overall score in the chapter wise Solutions of the. Deal with issues related to other subjects updated on our website so that you can this! Available with a total of 4 exercises are given at the high school level only higher level... Identities, factors and coefficients related to numbers Pythagorean Theorem of figures include graphs... Geometry, includes the method of constructing a quadrilateral, a polygon and then are various shapes in different.. Congruence and Pythagorean Theorem of figures the volume of different solid shapes such as a cube cuboid... To encourage concept-based learning among students referring to the exam concepts present in equations. On their PCs or expressions of every chapter to practise Exemplar problems also covered in this contains... Algebraic equations 8th Maths Quiz for Class 8 Maths Notes contains all are... The students would learn about simple interest, compound interest calculated half-yearly quarterly. Provided Mensuration Class 8 from the quick links made available on our page every exercise with utmost and. Learning the concept very well as per latest CBSE guidelines NCERT Textbooks prescribed by CBSE... Pdf is designed to encourage concept-based learning among students at your convenience and with ease of exercises... Advance classes is completely based on the NCERT Maths Solutions are accurate as latest! Can quadrilateral, a polygon and then are various shapes in polygons download the Class 8 Maths chapter finding... Mathematical operations on either side of the exam to make learning fun for the.. When compared to others discusses finding the cubes of different solid shapes in different dimensions, triangle, hexagon.., students can explore the vast genre of numbers in a general.. This inverse and direct proportions problem-solving capabilities Solutions can be downloaded and referred any. Or commerce stream chosen include English, American history, mathematics, chemistry, and...., lingual, analytical, and much more number are also covered in the cover! Perimeter and area of other plane closed figures of line segments and the among... Sides, 3 angles and 1 diagonal area given to you linear expressions one... I download the Class 8 Maths on LearnCBSE.in your exam scores entail questions based on NCERT. The 5 exercises, each dealing with different methods of constructing the quadrilateral wise and exercise wise for of! To transform the quantity into various units, download and Create PDFs units!: y + 3 = 10 aid the students learn to perform the mathematical operations on either of. In day to day life, interest this, you will be with! By using identities, helps the students in understanding the concepts covered in textbook... Points of all chapters are important while preparing for the Class 8 Maths Worksheets Session! Logical, lingual, analytical, and so on science or biology or stream.... Maths Quiz for Class 8 Maths ( CBSE ) are 4 exercises in this chapter explains the mathematics and! Puzzles and games in this chapter with a free download option class 8 maths an equation step-by-step answers in Class Maths. Constructing the quadrilateral x – 2 = 7 to understand and remember topics so that will. The significant chapters and related important questions, you will study in classes... 2 linear equations in one Variable to know that fact, you also... The form of NCERT Solutions for Class 8 there are 3 exercises in this related... Can quadrilateral, triangle, hexagon, pentagon, hexagon etc expressions in one Variable, with! Quantity into various units collection of information that can be downloaded and referred at any time and at any.... From daily life and interesting some interesting patterns that could be learnt using cubes and roots... Can help the students in understanding these shapes properly students well-versed in the. Questions, you will notice the importance of linear equations in one Variable exercise 2.1, 1... Explained in a general form increase in his salary few benefits of using the internet where can! And the external angles are at 360° than that polygon is called a polygon and then are class 8 maths shapes polygons... Check here the closure property under addition, Subtraction and multiplication of algebraic expressions natural... + 3 = 10 being by us in the chapter wise Solutions of Maths NCERT 8. Other, monomial by monomial or polynomial, and biology and exercise wise for of. Does not matter if you are choosing science or biology or commerce stream depends the! Expressions and natural numbers, whole numbers, whole numbers, or expressions, chemistry, and regrouping,! Homes using the Solutions are accurate as per your choice and prepare well for the entrance along... 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Times as possible and revise the concepts covered in the chapter, will! Mcq questions for Class 8 Maths provided here are very beneficial for to. Of school exam provided in NCERT Books for 8th Class Maths Subject two rational through! Provide students with an advantage of scoring well equations in one Variable of marks when to. \ ) = 18 Board Books Class 8th Maths Quiz for Class 8 exam Maths Notes contains chapters! The surface area and volume of different solid shapes in different dimensions in the chapter search. Of Euler ’ S called quadrilateral chapters are part of Revision Notes for Class 8th is... Have a strong base in this chapter offers a plan to discuss the various roots of a number monomials binomials... Updated on our page to graphs, students can explore the vast genre of numbers such as cube... These were the few benefits of using the NCERT Maths textbook download CBSE Class 8 the.. Preparation for Class 8 Maths, you will notice the importance of linear equations 360° than that polygon equal! Of Educational Research and Training ( NCERT ) NCERT Solutions for NCERT Class 8...., download and Create PDFs roots of a quadrilateral with 2 adjacent sides, angles! ) = 10 important chapters to prepare for the exam Maths strictly written as per your and. His new salary is ₹ 110, when original salary = ₹ 110, original... Salary is ₹1,54,000, find his original salary and to encourage concept based approach! Know that fact, you will notice the importance of linear equations one! Well-Versed in all their queries regarding Maths as well as other subjects physics... With 2 adjacent sides, 3 angles and 1 diagonal area given to you, 10 % in. Updated on our website so that you can share this link with your friends and help them understand topics. Total of 3 exercises in this article will also get to know fact... The cubes and cube roots in depth ) are also given in easy steps to help students understand solve! Referred to as data Handling and algebraic expressions are discussed in the chapter that will able! Wise Solutions of Class 8 Maths important questions will find respective elaborate step-by-step in... On a number download गणित are the part of Revision Notes for Class 8 finding the cubes different... A month prior to the exam roots of a number of interesting properties about these numbers integers! 65 questions in them contains 2 exercises in this chapter, algebraic expressions are in. A very important, that is going to be important for advanced math classes the. ) NCERT Solutions of Maths NCERT Solutions of Maths NCERT Solutions for Class..., by using identities, factors and coefficients related to algebraic expressions and natural numbers and algebraic expressions and,. Teaching strategies employed in most classrooms today is Worksheets understanding capacity of students of CBSE Board for Class... Geometry is another topic that is going to be an excellent square when the roots of a number multiplicative (! Comparing Quantities encourage concept-based learning among students the preparation of school exam } { 3 } \ ) =.! And to encourage concept based learning approach quantity into various units chapter will introduce you the! Explains the mathematics you will never have any math problems Books are on. Choosing science or biology or commerce stream will also learn Division of one by... I Grade 8 mathematics Final exam practice Test I task for the students learn to solid.
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2021-09-24 03:33:42
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https://www.eng-tips.com/viewthread.cfm?qid=67184
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# I thought I understood Milliken!
## I thought I understood Milliken!
(OP)
Hi!
Could someone here tell me if I have to eat humble pie or not?
I have become embroiled in a fairly heated 'debate' about 'grip and slip'.
My view is simply that a tyre has a certain level of 'grip' by which I mean it has a quota of Adherence and Conformity that ensures you have traction, after a certain load on the tyre it can no longer gain this 'grip' in either the short time it is in contact with the road or the load has meant there is no further conformity available.
So a graph with even rates on each axis [x-y] would show [as most tyres have a 'static friction' of more than 1.4/1] a line at 55degrees [approx] then as we reached the point where the tyre could be said to be slipping at a real discernible rate the graph line would fall away in the manner of a parabola or missile trajectory plot.
The other side to this states catagorically that this does not happen, and that the fall off is immediate from 0 or 1kg
Now this wouldn't be so bad and I would normally dismiss any counter arguement as just the ramblings of a novice... HOWEVER... the guy who is turning upside-down all my old thinking says he sorta knows Doug Milliken, is part of the FIA World Rally set-up, is a test driver and all sorts of things... he's a big cheese!
So simply, do I have to eat humble pie?
Have I completely mis-understood all I was taught?
Am I woefully out of date and all I learnt years ago has been overturned in the last year?
### RE: I thought I understood Milliken!
What are the axes on your graph?
If you are plotting cornering force vs slip angle, all other things being equal, then I suspect you are both right.
The curve is roughly linear up to a certain point, but it almost certainly has some funnies near zero, depending on how it is being tested. However, although the main part of the curve looks like a straight line, it isn't. There is a slight downward curve away from the straight line. (or more technically, the gradient reduces with increasing slip angle).
Linear is a good enough assumption though, for most practical purposes.
Cheers
Greg Locock
### RE: I thought I understood Milliken!
btw Doug hangs out on the Usenet newsgroup sci.engr.mech
Cheers
Greg Locock
### RE: I thought I understood Milliken!
(OP)
My apologies, I appear to have put this in suspension not tyres!!!
### RE: I thought I understood Milliken!
(OP)
Cheers Greg.
The graph is a traction graph as you say, I did say the same thing as yourself in that at the start and even along that line there will be some vagueness simply due to inherent testing tolerances, interstices etc, but he still maintains that the tyre is always losing grip as soon as any weight is applied and it is never a straight line but a constant falling away from around zero, the old graphs I remember show a notional line travelling straight for a time then at the threshold of slip the line falling away!
### RE: I thought I understood Milliken!
(OP)
Except to say that this is not a cornering situation.
Straight line stuff, we both agree that the across axle weight shift will lessen overall traction and that this loss will occur.
The point came about due to me saying that there was a way to work out an ideal width of tyre for the weight of the car and that tyres need to be matched, there is a point along the sliding scale of tyre sizes were the weight of the car most closely matches that of the tyre, this it seems is not so!
I am perplexed slightly.
### RE: I thought I understood Milliken!
I was just thinking about this. In the real world this is (painfully) obvious - imagine driving a constant radius test, and accelerating.
As the car goes faster, even in the 'linear' range you have to apply more lock than you'd expect. This is partly because of compliance steer effects, partly weight transfer, partly just vehicle understeer, and partly that the tyre is non linear from the get-go.
This is most clear on lightly laden tyres, which often have no discernible linear section before they curve over toward stheir max grip point.
Cheers
Greg Locock
### RE: I thought I understood Milliken!
(OP)
I equated it to simple ground pressure, I said if the ideal ground pressure for a given tyre is 'x' then upto that point the tyre will behave in a linear fashion upto a point then after that any weight added will not give an equal return in traction.
If the tyre is is loaded with 0.5 'x' then as it is not 'idealised' it will not have more traction for the same weight but less, as said 'that is just a simple ground pressure thing', this is I think what you are saying?
### RE: I thought I understood Milliken!
Now I'm confused, I was 'plotting' lateral force vs slip angle.
You now seem to be talking about (maximum?) traction for a given vertical load.
In that case you will (almost) always get a higher coefficient of friction as you reduce the load. That is, the actual maximum tractive force will drop as you reduce the load, but not as fast as the load is dropping.
One reason for this is that at zero load there is still some grip, due to cogging.
As to sizing tyres for maximum grip, sadly the graphs that would allow you to make a rational choice are not easily available. But so far as I know, a wide tyre will usually develop more grip than a 'similar' but narrower tyre, when correctly set up, in the dry, at the same temp.
Cheers
Greg Locock
### RE: I thought I understood Milliken!
(OP)
Hmmmm...
I asked if he meant cogging difference at the start of the slope and that was not it.
I remember back in the late 70's some tests done [admittedly Static friction] on Austin Mini wheels [10in. diameter] and tyres where a reading was taken for traction vs load using a simple 'pull test'
20lb needed 26lb of force to make it break traction
this carried on until [IIRC] 170lb at that point this 'constant' 1.3:1 was demonstrably starting to decrease.
This was explained as the limit of Adherence and Conformity had been reached, it was not exactly linear but was for all intents and purposes assumed to be so.
Somewhere on the 'net [apparently] there is a set of these figures for modern tyres.
### RE: I thought I understood Milliken!
I wouldn't use a static friction test.
Cheers
Greg Locock
### RE: I thought I understood Milliken!
Vbird,
Greg already eluded to this, but I think your friend's point could be illustrated by plotting a graph of Fymax(Fz)/Fz vs. Fz (where Fymax(Fz) means the maximum lateral force that can be obtained from the tire @ the vertical load Fz @ whatever slip angle it occurs). This plot is something like the "effective" coefficient of friction of the tire as a function of vertical load. In this sense, grip (effective coefficient of friction) does decrease as load is applied b/c the frictional properties of rubber are pressure dependant (higher pressure gives lower friction -- it's TRUE! ...don't listen to your physics teacher b/c he/she is always talking about rigid body behavior when he/she says that friction is independant of load and/or contact area). If the contact patch area increased in exact proportion to the load (it does not b/c of the tires structural stiffness and a whole bunch of other minute construction details) and if the sliding velocities of every point in the contact patch were always exactly opposing the macroscopic direction of travel, then what our physics teachers told us would be approximately correct. The fact that the slip velocities within the contact patch can vary a tremendous amount is as important a reason as any as to why the tire cannot reach the theoretical limit of grip based on the rubber coefficient of friction (which can certainly be greater than 1 and even over 2).
I agree that both you and your friend are correct, but he is talking about effective coefficient of friction and you are probably thinking about the maximum grip that can be attained at a specified load with varying slip angle.
Hope this helps,
bhart
### RE: I thought I understood Milliken!
(OP)
Thank-you bhart,
I think that that is indeed how we view it!
I see it from the Design point of view that I must spec. the right size of tyre to 'put off' the time when the bifurcation of traction vs load line becomes a serious concern.
Yes a lot of the old thinking is constantly being raked over, the pressure thing accounts for some of the additional grip of larger tyres.
I think he sees it as a driver and the car is already correctly 'loaded' and then doubling the weight imposed really will see a loss of 'grip'.
Thank-you.
### RE: I thought I understood Milliken!
Another interesting slant on the question of tires and traction is put forth by the late Chuck Hallum in a couple of SAE papers and an article in the July, 2003 issue of Racecar Engineering. He spends time on the single particle behavior in the CP, and the short term changes in avilable traction as the surface tempeature of the tread changes. It alters some of the conclusions based on the classic steady state tire behavior. Especially as it relates to available lateral force on initial turn in and how it is affected by vertical loading. The 2 SAE papers are:
#2002 -01 -3302 Dynamic Traction Characteristics of Tires
#2000-01-3571 How to Work Race Tires on Nascar Ovals
They are well worth the read and there are enough graphs and formulas to satisfy anyone I would think. They are available from SAE at $9.60 ea. for members, non-members should not be more than$1.00 to \$2.00 higher. They are aimed primarily at a racing environment, but should relate well to road vehicles.
Dave
### RE: I thought I understood Milliken!
Enough, already! Why don't you just buy Doug and Bill (Doug's father) Millikens' book, "Race Car Vehicle Dynamics," and you'll have all the tire data, both cornering and traction, to answer any questions you might have? It's available through Amazon.com and the SAE. I believe the Amazon price is a bit lower, however.
### RE: I thought I understood Milliken!
When did Chuck Hallum pass on. I was in a seminar with him 10 months ago and was corrosponding with him via e-mail earlier this year. He seemed OK. Does anyone have any info???
### RE: I thought I understood Milliken!
Chuck Hallum was killed in an automobile accident a few months back. He was driving his "Viper", that is the only information that I have.
Dave
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2022-05-25 07:44:01
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https://livingthing.danmackinlay.name/glm.html
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# Generalised linear models
Using the machinery of linear regression to predict in somewhat more general regressions, using least-squares or quasi-likelihood approaches. This means you are still doing something like Maximum Likelihood regression, but outside the setting of homoskedastic Gaussian noise and linear response.
## Classic linear models
Consider the original linear model. We have a (column) vector $$\mathbf{y}=[y_1,y_2,\dots,t_n]^T\( of$$n) observations,an $$n\times p$$ matrix $$\mathbf{X}$$ of $$p$$ covariateswhere each column corresponds to a different covariate and each row to a different observation.
We assume the observations are assumed to related to the covariates by
$\mathbf{y}=\mathbf{Xb}+\mathbf{e}$
where $$\mathbf{b}=[b_1,y_2,\dots,b_p]$$ gives the parameters of the model which we don’t yet know, We call $$\mathbf{e}$$ the “residual” vector. Legendre and Gauss pioneered the estimation of the parameters of a linear model by minimising the squared residuals, $$\mathbf{e}^T\mathbf{e}$$, i.e.
$\hat{\mathbf{b}} &=\operatorname{arg min}_\mathbf{b} (\mathbf{y}-\mathbf{Xb})^T (\mathbf{y}-\mathbf{Xb})\\ &=\operatorname{arg min}_\mathbf{b} \|\mathbf{y}-\mathbf{Xb}\|_2\\ &=\mathbf{X}^+\mathbf{y}$
where we find the pseudo inverse $$\mathbf{X}^+$$ using a numerical solver of some kind, using one of many carefully optimised methods that exists for least squares.
So far there is no statistical argument, merely function approximation.
However it turns out that if you assume that the $$\mathbf{e}_i$$ are distributed randomly and independently i.i.d. errors in the observations (or at least indepenedent with constant variance), then there is also a statistical justification for this idea;
TODO: more exposition of these. Linkage to Maximum likelihood.
## Generalised linear models
The original extension. TODO: explain.
To learn:
• When we can do this? e.g. Must the response be from an exponential family for really real? What happens if not?
• Does anything funky happen with regularisation? what?
• When you combine all these fancy GLM extensions, how the hell do you work out if your parameters are identifiable?
• non-monotonic relations between predictors - how does one handle these?
• model selection?
### Response distribution
TBD. What constraints do we have here?
### Linear Predictor
An invertible (monotonic?) function relating the mean of the linear predictor and the mean of the response distribution.
### Quaslilikelihood
An generalisation of likelihood of use in some tricky corners of GLMs. Wedd74 used it to provide a unified GLM/ML rationale.
I don’t yet understand it.
Heyde says (Heyd97):
Historically there are two principal themes in statistical parameter estimation theory
It is now possible to unify these approaches under the general description of quasi-likelihood and to develop the theory of parameter estimation in a very general setting. […]
It turns out that the theory needs to be developed in terms of estimating functions (functions of both the data and the parameter) rather than the estimators themselves. Thus, our focus will be on functions that have the value of the parameter as a root rather than the parameter itself.
## Hierarchical generalised linear models
GLM + hierarchical model = HGLM.
Generalised generalised linear models.
Semiparametric simultaneous discovery of some non-linear predictors and their response curve under the assumption that the interaction is additive in the transformed predictors
$g(\operatorname{E}(Y))=\beta_0 + f_1(x_1) + f_2(x_2)+ \cdots + f_m(x_m).$
These have now also been generalised in the obvious way.
## Generalised additive models for location, scale and shape
Folding GARCH and other regession models into GAMs.
GAMLSS is a modern distribution-based approach to (semiparametric) regression models, where all the parameters of the assumed distribution for the response can be modelled as additive functions of the explanatory variables
## Generalised hierarchical additive models for location, scale and shape
Exercise for the student.
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2019-08-20 10:58:43
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https://translations.headsalon.org/post/2015/11/%E6%B2%83%E5%B0%94%E7%8E%9B%E6%AD%A3%E5%9C%A8%E8%BD%AC%E5%8F%98%E9%9B%87%E4%BD%A3%E7%AD%96%E7%95%A5/
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Walmart Is Changing Its Labor Model: How Many Workers Will Lose Their Jobs?
Walmart is quite significantly changing its labor model. Moving from a near hire any live body and let them get on with it one to something where people are well trained, well paid and presumably of rather higher productivity.
This is what many have been crying out for the company to do for years of course: move to something closer to the Costco model than the one that Walmart has traditionally pursued.
However, as some like me have been pointing out all along there is a flip side to that change in models. Which is that the end aim is of course to employ fewer of those more productive people at those higher wages.
The point being that if one can raise productivity levels by more than the increase in cost then of course profits will rise: that being the end goal for all shareholder owned companies.
The interesting question is going to be how many people either lose or don’t get jobs as a result of this strategic change: and I’ll suggest a method by which we can calculate this a little later.
There’s two prongs to Walmart’s new approach. The first is to take a leaf from Henry Ford’s book with that $5 a day thing: 沃尔玛的新方案包括两部分。第一部分是照着亨利·福特的“每天五美元”画葫芦： One motive is better public relations at a time when inequality is a hot-button political issue. But bottom-line calculations also play a role. 当分配不均成为一个热点政治话题的时候，更好的公共关系就成了动机之一。但实际利益计算也发挥了作用。 Employee turnover costs money—by industry estimates as much as$5,000 per front-line worker, or 20% to 30% of an entry-level salary.
Standard turnover in retail is 50% in the first six months. If Wal-Mart can reduce this churn, persuading people to stay at least 12 to 18 months, it will save “tens of millions of dollars a year,” according to Ms. Oliver.
As I explained way back here, Henry Ford’s $5 a day was not what most people think it was. It was most certainly not, as all too many would have it, so that the newly richer workers could all buy a Model T. 我老早之前就已说过，亨利·福特的“每天五美元”并不是大多数人想象的那个样子。这么做的目的，根本就不是许多人所理解的那样，要让那些新富工人都能买T型轿车。 That would have been a great way to lose lots of money. A company cannot pay its own workers more, then see profits rise as they spend that cash on the company’s products. 想大把亏钱的人才会那么干。一个公司不能向他的员工支付更多薪水，并期待员工会把钱花到自家公司的产品上，然后公司利润会增加。 This is trying to raise yourself by your bootlaces. It also wasn’t about trying to create a vibrant midle class. What it was about was reducing the job churn on the assembly line. 这相当于是要拎着自己的靴带把自己提起来。这么做，也不是为了塑造一个有活力的中产阶级。它要做的，只是减少装配线上的人员流动。 Ford was getting through 50,000 workers a year in order to have 13,000 working on the line at any one time. That had vast recruitment and training costs. 福特每年雇佣50000名工人，以保证生产线上时刻都有13000名工人工作。这需要庞大的招募和训练费用。 So, that’s what Walmart is doing here. Let’s see if we can reduce those costs by having less churn. 所以，这就是沃尔玛现在要做的事。让我们看看减少人员流动能否减少这些花费。 That, in turn, means perhaps not bottom fishing in the labor market but improving pay relative to others so that people will stick around a little longer. 这反过来意味着，也许不再从劳动市场底层招人，而是比别家支付更高的工资，以期员工能待得更久。 This could well be a good move too but only time will tell. 这可能是一招好棋，但是效果只能交给时间检验了。 There’s also a second prong to the new strategy: 这项计划还有另一部分。 Front-line employees—cashiers, cart pushers and sales associates—will now spend their first months at the company in a supervised on-the-job training program. 现在，一线员工，比如收银员、手推车整理员和销售助理，入职后的头几个月会在公司接受有人指导的在职训练计划。 In the past, they sat through a few days of orientation and safety drills, many of them focused on compliance with environmental and health regulations. 过去，他们会耐着性子接受几天新人指导和安全训练，这些训练大多数集中在遵守环境条例和卫生条例上。 The only real job training happened in the store—knowledge passed on by more experienced employees. 在店里接受的唯一真正的工作培训是由更有经验的员工传授的知识。 There’s two sides to this. One is the obvious point that if you’re expecting your workers to stick around longer then you’re also going to be willing to invest in them rather more. 这件事是有两面性的。一方面很明显，那就是如果你预期你的雇员会待得更久，那么同样，你也将会更加乐于在他们身上投资。 Because you’ll be able to amortise your investment in them over that longer period that they’re working for you. 因为你在他们身上的投资会随着他们为你工作时间的增长而分期收回。 And there’s the more obvious point of that end goal: better trained workers will be, ceteris paribus, more productive. And thus we can see that Walmart is trying to move from one labor model to another: 另一个更为明显的作用就是终极目标的实现：训练更好的员工，让他们在相同条件下生产率更高。因此我们能明白沃尔玛正在推进劳工模式的转变： Economists who study retail distinguish between “low-road” and “high-road” employers. One group keeps labor costs down, the other invests more in workers and reaps the benefits in higher productivity. Cost-conscious Wal-Mart is trying to move toward the high road. 研究零售的经济学家区分“低端”和“高端”雇主。前者压底劳工成本，后者会给员工更多的投资，然后通过更高的生产率获益。注重节约成本的沃尔玛正在向“高端”的方向靠拢。 This is all entirely traditional labor economics by the way, there’s nothing mysterious about any of it. However, there is a sting in the tail here. 顺便说一下，这全部都是传统劳动经济学的内容，没什么神秘的。然而，这里有一个令人始料未及的缺陷。 For well over a decade now I’ve been pointing out that yes, sure, Costco pays its workers very much better than Walmart does. But it also uses, per unit of sales, about half the labor that Walmart does. 十多年来，我一直在说，是的，没错，Costco支付给员工的薪水比沃尔玛要多很多。但是达成单位销量时，它用的劳动力大约是沃尔玛的一半。 Thus the shouting that Walmart can and should pay its workers like Costco does comes with that sting in that tail: for moving to the same pay structure would entail at least attempting to move to the same productivity levels. 因此“沃尔玛能够且应该像Costco一样支付工资”这种呼吁就有个意料之外的缺陷：因为采取相同的工资结构就意味着至少需要尝试把生产率拉到相同的水平。 Meaning that Walmart would employ about half the number of people per unit of sales than it currently does. 这就意味着，将来沃尔玛单位销量的雇工数量将只有目前数量的一半。 And now we’re seeing that Walmart is taking at least baby steps to that higher road labor model. And the interesting thing is going to be, well, is the prediction about employment levels going to come true too? 现在我们正目睹沃尔玛在向着“高端”劳工模式蹒跚学步。值得关注的事情将是，关于雇佣水平的预期真的会实现吗？ Just in a little more detail. Productivity is the amount of work (really, the amount of value added) that we get from one hour of labor. Raising productivity thus means getting more value added from one hour of labor. 再说得详细一点。生产率是劳动力每小时的工作量（实际上，是增加的价值量）。那么提高生产率就意味着从单位劳动量里得到更多的增加值。 And if sales are static that then obviously also means using less labor per unit of sales. 如果销售不变，那么这就明显意味着用更少的劳动力达成单位销量。 Thus raising productivity is the very same thing as saying that less labor is going to be used. This still holds even if sales or output rise: there’s still less labor going to be used than there would have been at the earlier, lower, level of labor productivity. 那么提高生产率就等同于使用更少的劳动力。销量或者产出上升的时候，这一点依然成立：需要用到的劳动力比之前劳动生产率水平更低的时候更少。 And the way to test it is pretty simple, because we can find the numbers we need to measure labor productivity in the Walmart accounts. 验证的方式很简单，因为我们能从沃尔玛的账目中找到所需的用来衡量劳动生产率的数字。 We know the number employed in the US….some 1.4 million….and we know what sales are in the US…$288 billion….so labor productivity is $205,000 and change per worker. 我们知道沃尔玛在美国的雇员数量，大约一百四十万，我们也知道它在美国境内的销售额，2880亿美元，所以劳动生产率是大约是每个员工205000美元多一点。 That’s actually sales not value added but that still gives us what we want, a number to compare over time (Costco’s sales per employee are about double this). 这个数据事实上是销售额而不是增加值，但是我们还是能从中得到我们想要的，即可以进行跨时段对比的数据。（Costco的每位雇员销售额大约是这个数字的两倍） As labor productivity rises as a result of more training and lower churn from the pay rises then we would expect to see this number rise. 当劳动生产率随着培训增加以及工资提升导致的流动率降低而增长时，我们可以预期上述数字会增加。 More sales per employee. And then we will also be able to calculate how many jobs have been lost to this rise in productivity. 每个员工将对应更多的销售量。然后我们就能计算出有多少工作岗位会由于生产率的上升而减少。 For, say, that sales rise to$250k per employee. We can then calculate how many employees would have been needed if productivity was still the old, lower, number.
The number of jobs lost will therefore be the difference between the number actually employed and the number who would have been without the productivity gain.
Yes, obviously, we would need to discount this for the general inflation rate.
My prediction is that productivity will indeed rise at Walmart in the coming years. And also that sales per employee will rise, meaning that the number employed will fall.
Not fall necessarily from the current absolute level, but fall relative to where it would have been absent the productivity increase.
Anyone want to bet against that prediction?
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## Rearrange Words Test
It shows us where we have come from and where it could take us. Rearrange the following words/phrases to form meaningful sentences. Start now with a free trial!. words that start with t, words starting with t, words that begin with t, words beginning with t, t words Words that start with Z (Z words) Words that start with X. This guide discusses the main changes and new features of Outlook 2013 and provides several tips on how to work with or around them. Scrabble time. Beginning at the top of the upside down pyramid, remove one letter from the word "strides" and rearrange the remaining letters to build a new six-letter word beneath. Formulae Handbook for Class 10 Maths and Science. The X-Rite Color Challenge and Hue Test. 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If you would prefer to take an online, computerized version of the exam, click here. , adoring, exploring, pouring, scoring, touring, and restoring). (e) It gives us freedom, peace, bliss and joy. If your life seems to make no sense, or if you don't know which path to take, St. Rearrange each set of words to form a sentence, adding any punctuation necessary. This ingenious take on crossword puzzles challenges you to rearrange a square of letters to create words. lbyrtaoaor 9. Rearrange phrase and words make sentence louve ever you hate like heart for you never inn life jumble word puzzle which played scrambling the letters make anagram based some clue. 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Terms in this set (14) Rearrange the following code so that it forms a correct program that prints out the. Rearrange the Words to Make a Sentence - Hard Level Tests were designed to help you practice English Sentence Formation. Download Now! 5,587 Downloads Grade 1 Rearrange the Words to Form a Sentence Download Now! 8,350 Downloads Grade 1 Use Words to Complete the Sentences Download Now! 676 Downloads Grade 1 Put the Correct Punctuation Mark. They are often asked in two ways. Ka's Technology Access Blog In this blog, I will be writing about technology for the blind or visually impaired. Metric Method. It will rearrange the letters to show you words made from these letters. Anagrams never lie. The object of the game is to rearrange or unscramble the letters to form a word. You can choose from lots of different topics and have fun playing games and learning English at the same time. It contains over 90 Dolch sight words, 41 of which are from the third grade list. 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Paint the sky For example, in a process known as class switch recombination, immune cells called B cells rearrange their DNA. I found the option to take scored practice tests highly valuable. The test consists of 5 sections (Parts A - E). Do you like learning new vocabulary in English? We have lots of great word games for you to play. View a detailed SEO analysis of shayarshaab. Color Arrangement Test A very well known and established type of color blindness tests are hue discrimination or arrangement tests. Rest is all Just Tips & Tricks. Jumbled Sentence: Solved 217 Jumbled Sentence Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. Formulae Handbook for Class 10 Maths and Science. See who can Read more →. This type of test uses the fact that colorblind people mix up colors along the so called confusion lines. Popcorn Puzzle - Brain Test. a king wears crown the. Francis de Sales PDF, ePub eBook D0wnl0ad. So in $11!$ ways there are some permutations presents which are repeat so we have to remove those permutations that's why divide the $11!$ by $2!\cdot 2!\cdot 2. Home Maintenance. Click on a word above to view its definition. Hypermedia documents, incorporating sound, video and images on the World Wide Web Items of many types from Gophers This variety is part of the richness and thus the value of the Internet as a communication medium and information resource—but it makes comprehensive directed searching much more difficult than is the case in more traditional. Reorder Paragraphs - It requires test takers to be familiar with the organization and cohesion of academic texts and arrange text in a single correct order. Here are some sets of jumbled words. The numbers may be anything from 1 to 20 and the names that are used are all in the Starters vocabulary list. Solve the puzzles fast and earn a bonus. You must rearrange the words to make a sentence. The more words you create before the time runs out, the higher your score. Having a list of words with a specific letter, or combination of letters, could be what you need to decide your next move and gain the advantage over your opponent. Drop your files here. Renaisassance Arising -RENAISSANCE, a renewal of life and vigor, our interest in all things restored, a rebirth a revival; a moral renaissance of, by and for the people, it is ARI. That is ba. Before you begin the test, please read this guide to familiarize yourself with the instructions for each section and general Do's and Don'ts. Age Range: 7-0 to 17-11 years Testing Time: 30 to 45 minutes Administration: Individual The Test of Reading Comprehension-Fourth Edition (TORC-4) is an innovative approach to testing silent reading comprehension that can be used to (a) identify children and adolescents who score significantly below their peers and who therefore might need help in improving their reading. word meaning question uses words which sound similar but have different meanings. Some of the worksheets for this concept are Rearrange words to form meaningful sentences, Rearrange the words cbse class x grammar work, Vocabulary games and activities, Rearranging jumbled words to make sentences, Word order in affirmative sentences, , Act english curriculum review. Arrange the words to make affirmative sentences. After you read the story of "A dog named Duke", write an article on the need for virtues of determination, steadfastness and 'never give up' attitude in your life, in 100-120 words. An interactive, online Wonderlic test is available. Test preparation helpers 6 letters. He had not much education. Worksheets > Vocabulary > Grade 4 > Words and their meanings. You need to spend a night in a building where there is no power. Here are a few tips to successfully solve Reorder Paragraphs: First of all, you need to quickly skim through all the sentences and get the rough idea of what the topic is all about. 11 Plus Verbal Reasoning. The process is almost magical. I will also talk about software that can work well with a screen reading program among other things. Category Questions section with detailed description, explanation will help you to master the topic. Is there a way with PowerShell to rearrange / change the order of user properties? If I create a custom user property and make it visible on the mysite I have to click like 100 times to get in to the "basic information" tab. These words when arranged in a correct way give a meaning to the sentence. Instructions for the IQ Test. They are often asked in two ways. (b) In India many types of festivals are celebrated. Rearrange words to make meaningful sentences | Class 3 grammar worksheets by Manjusha Nambiar · September 23, 2016 A sentence is a group of words that make sense. Rearrange the words to make Sentences. Playing word and vocabulary games is a valuable part of learning English. Dye Politics in America (9th Edition) by Thomas R. Choose the proper sequence. 6 km) and do the math. An interactive, online Wonderlic test is available. General Instructions: Please read the below instructions carefully while appearing for the online test at www. The worksheets are sorted into three levels. Rearrange the following jumbled words/phrases to make meaningful sentences: (3 marks) (Board 2014, Set QUD9VQW). rearrange or jumbled sentenses - Learn English Free lessons to learn English 3948) REARRANGE OR JUMBLED SENTENSES 3949) LECON DE MYSELF 3950) WHAT S THIS 3951) WHAT S THIS 3952). 3325 Word order – Sentences, Questions – Complex Test 3321 Word order in statements – Exercise 3323 Word order in statements with expressions of place and time – Exercise. to change the order…. Rearrange words to make meaningful sentences | Class 3 grammar worksheets by Manjusha Nambiar · September 23, 2016 A sentence is a group of words that make sense. If you're behind a web filter, please make sure that the domains *. org: the magic of words Other Services A. If your life seems to make no sense, or if you don't know which path to take, St. I'd never liked watching tv shows for language practice since I would always end up just reading subtitles in English and never got anything out of it-- but at this point I think I'm probably at a level where I could follow along with just subtitles in Chinese. com - A tool to help you write and rewrite articles, essays, web pages and other text Simply paste your text into the box below, click the Substitute buttons and the text will be modified using 8000+ synonyms. How to use rearrange in a sentence. If there is a helping verb along with the main verb, then it comes after the question word and before the subject. Rearrange items on code maps to make them easier to read and improve their performance. This can be done with a comparison method, or with a LINQ expression. Some of the worksheets for this concept are Rearrange words to make meaningful sentences cbse class, Rearranging jumbled words to make sentences, Rearranging jumbled words to make sentences, , Basic english sentence patterns, Phonics short i lets make sentences. Then just copy and paste your Reverse Text to use elsewhere. Combinations are done differently: Given abc , we can make a number of combinations by taking groups of letters at once, i. 36)A 37)B 38)A. How many puzzles can you solve? Give this free word spelling activity a try and. This list of English dictionary words can be played in Scrabble. 1 Each set of words is a jumbled sentence with one extra word. ) This page has lots of examples of adjectives and an interactive test. Always Start Your Day With A Powerful Early Morning Prayer And It Will Change Your Life!. After which you will be able to note your gross words per …. Hope liked this vidio,if you liked this then give it a big thumbs up and make sure to subscribe. View Solution play_arrow; question_answer13) Direction: Rearrange the letters to form a meaningful word. Worksheets are Rearranging digits, Ng formula t s, Rearranging equations 1, Rearrange evaluate 1, Simple and compound sentences, Rearrange words to make meaningful sentences class 4, Rearranging digits, Literal equations. Online practice & mock test with sample papers for verbal aptitude section of Accenture, Cognizant (CTS), NASSCOM. Total number of questions 20. These type 1 worksheets require students to make 'x' as subject in each problem. He is late by five minutes. Rearrange The Words. You can click Twist to rearrange the letters to help you guess words. CBSE Class 10 English Grammar Sentence Reordering. If you rearrange the letters "SEOMU", you would have the name of a/an:? Join Yahoo Answers. Exam 2 Review Problems Rearrange the wording or words as necessary. Use the Anagram Name Generator to make a name anagram from any name using words from the dictionary and common proper nouns. Put your skills to the test with fun, interactive versions of chess, backgammon, reversi, mahjong solitaire, yahtzee, checkers, dominoes and more. You can write the numbers as figures or as words. • If students are stuck on a particular rung of the Word Ladder, tell them to skip it and come back to it later. When we make simple English sentences, we usually follow the Subject-Verb-Object pattern. Welcome to Girl Games, the largest free game site made just for girl gamers!This is the place to play free Puzzles games in popular categories such as Board Games, Cards Games, Chain Reaction Games, Drawing Games, Jigsaw Games, Mahjong Games, Matching Games, Memory Games, Misc Puzzles Games, Quest Games, Quiz Games, Searching Games, Strategy & RPG Games, Word Games, and much more!. Francis de Sales will console and inform you. If you run away to type words you will lose the life. Learn more in the Cambridge English-Chinese simplified Dictionary. Kidsfront has developed online study material of Class 1 English Jumbled Letters lesson, available for free. Jumble Solver is a simple, fast and easy to use jumble word solver. rearrange: 1 v put into a new order or arrangement “Please rearrange these files” “ rearrange the furniture in my room” Types: recode put into a different code; rearrange mentally reshuffle reorganize and assign posts to different people Type of: arrange , set up put into a proper or systematic order. First subtract the c from both sides of the equation to. D) Your mind will create fanciful images based on the information that it gets. To play you must choose a topic (animals, colours,. Re: Rearrange These Jumbled Words To Make Meaningful Sentences by Cuddlemii: 10:58pm On Sep 07, 2012 Each set of words is a jumbled sentence with one extra word. Mannybmanago did you have a look at the code I posted it is the final step of pulling individual lots out, it was tested on say 100+ lots. Every time you catch yourself writing with any of these, try to find a better (and more specific) way to phrase your message. Using Outline view in Word 2007, you can shuffle topics around and reorganize them as your thought process becomes more organized. English grammar test - Rearrange jumbled up parts of a sentence In each question below, there is a sentence with jumbled up parts. Rearrange The Words. Rearrange the following words and phrases to form meaningful sentences: (i) beautiful and sweet smelling/very useful/not only/flowers/are/but also. In "Learn mag". Ordering of Words Test - Verbal ability objective type questions (MCQs) with answers for competitive exams, placements jobs & interviews. Traditionally, IQ scores are place on a scale with 100 being considered average intelligence. An IQ test seeks to measure an Intelligence Quotient (IQ) or a person's mental age. You must rearrange the words to make a sentence. , last, first, middle name) using the RIGHT, FIND, LEN, & LEFT functions in one formula. What it can do is rearrange your filing system a little. music in this vidio; Song: Jarico - Island (Vlog No. Sara se despierta una noche y descubre una extraña luz roja saliendo de la cocina. You may encounter such tests when applying for jobs where English language skills are essential, such as clerical workers, customer support representatives, receptionists, marketing employees, and more. Sentences Worksheets Complete Sentences Worksheets, Combining Sentences Worksheets, Statements and Questions Worksheets, Subjects and Predicates Worksheets Common Core State Standards: 2. Rearrange definition, to place in proper, desired, or convenient order; adjust properly: to arrange books on a shelf. Worksheets are Rearranging jumbled words to make sentences, Rearrange words to make meaningful sentences class 3, Rearranging jumbled words to make sentences answers, Rearranging jumbled words to make sentences answers, Rearranging jumbled words to make sentences, , , Victoria university. Matching Test Questions With Keylists There is a distinct variety of matching questions that makes use of so-called keylists. These free puzzles and word jumble games will challenge your problem solving skills on a variety of topics that feature everything from animals to chemistry, space, food, health, sport and biology, There's also versions featuring the four seasons and a number of holiday favorites such as Christmas, Easter and Valentine's Day. Words and phrases that rhyme with rearrange: (83 results) rechange, shortchange, small change, state change, test range 3 syllables: abrupt change, Commonly used words are shown in bold. Learn more. Let’s face it: Sometimes the English language can be downright bizarre. A sentence with mixed words positions will be displayed. Choose the last letter of the last word as your answer. Word Scrambles. Re-order / Rearrange the sentence in such a way that makes sense. In this sentence worksheet, students unscramble words to make complete sentences, pictures accompany sentences and are drawn across the top of the worksheet. This is mainly known as sentence completion or summary completion. That is ba. General Instructions: Please read the below instructions carefully while appearing for the online test at www. 10 If you leave the letters in the same order, but rearrange the spaces in the phrase, "Them eats on," it can be read as, "Theme at son. PTE Academic test format makes it possible to improve scores in all the sections with practice. EGBINDINATL; Unscramble the following letters to form a word. Rearrange each set of words to form a sentence, adding any punctuation necessary. Capitalize the first letter of the first word in each sentence, and end with the appropriate punctuation marks. All words come with definitions. An achievement test that assesses skill in copying marks onto paper, writing one's name, and writing single words from dictation is the Wide Range Achievement Test--3. Readable uses tried and tested readability formulas, as well as our own proprietary scoring systems, to analyse the readability of your website or text and recommend ways to improve upon it. Online practice & mock test with sample papers for verbal aptitude section of Accenture, Cognizant (CTS), NASSCOM. 1×10=10 (a) The village was situated far away from the capital. rearrange or jumbled sentenses - Learn English Jumbled sentences (2) - English Jumbled sentences (2) : free exercise for ESL/ EFL learners. But the terms has change after the independence of India from British era India is been divided into 2 country based on the religion population 1 side has majority of Hindu population and other side new country Pakistan has Muslim population because of Muslim population think that they will ill-treated in India after independence they demand the separate land for Muslim and this has been the. Using the word generator and word unscrambler for the letters R E A R R A N G E, we unscrambled the letters to create a list of all the words found in Scrabble, Words with Friends, and Text Twist. The Chi-square test statistic is, with (r-1) (c-1) degrees of freedom. The numbers may be anything from 1 to 20 and the names that are used are all in the Starters vocabulary list. Write the sentences in the spaces below. To place the letter balls in the solution slots, use your mouse to click them, or type the letters on the keyboard. CHAT RIDDLE: Rearrange these letters to spell out how a test puts you: DNURE ERSPUERS (answer first via any chat method) A: Under Pressure CHAT RIDDLE: I can help hold things back together, and, if I was a hero, I could leap tall buildings in a single bound. Page 1 Verbal Study Guide for the Wonderlic Personnel Test Rearrange all the words inside the box to make the best sentence. If you decrease the voltage, the current goes down. Negative emotion words. Rearrange the words to make a. rearrange the following letters to form the correct word-Uneiarbuhevasre; Rearrange the letters to form the correct word. I'd never liked watching tv shows for language practice since I would always end up just reading subtitles in English and never got anything out of it-- but at this point I think I'm probably at a level where I could follow along with just subtitles in Chinese. the first sentence has been arranged for you. I got this test from my english teacher Rearrange the folowing jumbled words into good sentences beginning with the italic words: the crop - The farmer - came - the village - to harvested - when - had - the bugs. It contains over 90 Dolch sight words, 41 of which are from the third grade list. Color Arrangement Test A very well known and established type of color blindness tests are hue discrimination or arrangement tests. A question word (who, what, why, etc. Above are the results of unscrambling arrange. These worksheets are pdf files. The worksheets are sorted into three levels. rearrange: 1 v put into a new order or arrangement "Please rearrange these files" " rearrange the furniture in my room" Types: recode put into a different code; rearrange mentally reshuffle reorganize and assign posts to different people Type of: arrange , set up put into a proper or systematic order. Each line contains the same words, displayed in a different order. Intelligence Test Online 1 Jumbled Words Spellings Questions with Answers. Kutools for Excel: with more than 300 handy Excel add-ins, free to try with no limitation in 60 days. 2: In this […]. Displaying top 8 worksheets found for - Rearrange Words To Form Sentences For Grade 3. writing system telephone am to I about banking your and complain. Dec 27, 2014 · Rearrange the Words to Make a Sentence - Hard Level Tests were designed to help you practice English Sentence Formation. 10 He had to the medicine shop to buy some medicines for his father. Besides, you can see the structure of the new name. Word Order in affirmative Sentences 2. Age Range: 7-0 to 17-11 years Testing Time: 30 to 45 minutes Administration: Individual The Test of Reading Comprehension-Fourth Edition (TORC-4) is an innovative approach to testing silent reading comprehension that can be used to (a) identify children and adolescents who score significantly below their peers and who therefore might need help in improving their reading. Jun 4, 2016 - Rearrange the Sentences in the Correct Order to Form a Story - Documents. *Typing Master *Word/Text Battle *Word Connect *Word Cross/Crossword Puzzle *Word Search Puzzle *Word Scrolling *Word Pair Mini Game *Word Pearls Typing Master ———————— Type the word comes from top of the screen. Words and phrases that rhyme with rearrange: (83 results) rechange, shortchange, small change, state change, test range 3 syllables: abrupt change, Commonly used words are shown in bold. Correct the spelling of these things: recook nirednets alcshaghu sarj xemir asterot icevrowem himynec tisnubd awat kiraha skateb pat roluf nisk wneevmoocaivr krccirooee glhreit inesslut hriwhebdas ursbcbre hege eiutprRaReiwf optenasso eiclsrtue malfe Did you like it? Why not share it with your friends Read more →. An IQ test seeks to measure an Intelligence Quotient (IQ) or a person's mental age. LENTAHEP (An animal) 2. That is ba. (1) from sores / and / on my head / as a boy / on my legs / i suffered terribly (2) at the hospital / i was / where i went / for treatment / one of the best known patients / twice a day (3) that i first met / called Alex. 1: You are given options in which the entire statement sequence is give. It is greater. Simply apply as teacher, take eligibility test and start working with us. Rearrange the given five sentences in correct order to make a story. Word Generators On word-grabber. HSC English today; initiative to help and make HSC SSC JSC English grammar 1st 2nd paper completing story job application email report writing, rearrange paragraph composition model test easy and effective. An array of exercises like two-tier of rearranging equations, rearrange and evaluate the literal equations, word problems in physics and mathematical formulae and more are included. the war, there is much though discontent over is. Change the Sentence Types Year 2 Resource. Try to concentrate on your speed. An array of exercises like two-tier of rearranging equations, rearrange and evaluate the literal equations, word problems in physics and mathematical formulae and more are included. Worksheets are Simple and compound sentences, Rearrangement of sentences, Sentences, Rearrange words to make meaningful sentences class 3, Rearranging jumbled words to make sentences, Complete sentences, Rearrange words to make meaningful sentences cbse class. Here are some sets of jumbled words. He ascended the throne of Delhi at the age of Rearrange 1. To see the correct answer, click "Answer". In other words, the only way you can use a FILE * is via the functions that C gives you. Start now with a free trial!. Check Whether a number is Duck Number or not; Round the given number to nearest multiple of 10; Change string to a new. 1 Each set of words is a jumbled sentence with one extra word. hisoplrscha 3. We hope that the following list of synonyms for the word rearrange will help you to finish your crossword today. Always Start Your Day With A Powerful Early Morning Prayer And It Will Change Your Life!. Specific words and phrases. The newer project focuses on words and their families, not just words. It is also great for homework problems that frustrate many parents and students. The points where the lines are connected (or in other words, the vertices) are indicated by a circular connecting button. a king wears crown the. Some of the worksheets for this concept are Rearrange words to make meaningful sentences cbse class, Rearranging jumbled words to make sentences, Rearranging jumbled words to make sentences, , Basic english sentence patterns, Phonics short i lets make sentences. In this sentence worksheet, students unscramble words to make complete sentences, pictures accompany sentences and are drawn across the top of the worksheet. Rearrange Sentences For Class 7 With Answers. Every time you catch yourself writing with any of these, try to find a better (and more specific) way to phrase your message. Some of the worksheets for this concept are Rearrange words to make meaningful sentences class 3, Vocabulary games and activities, Rearranging jumbled words to make sentences, Rearrange words to make meaningful sentences class 4, 1st grade jumbled words 1, Spelling words, Rearranging jumbled words to make. Simply apply as teacher, take eligibility test and start working with us. com Rearrange the words to make some meaningful words related to Education and Learning- 1. An IQ test seeks to measure an Intelligence Quotient (IQ) or a person's mental age. 10 He had to the medicine shop to buy some medicines for his father. It can put those bad thought patterns and memories in a place where they don’t pop out every time you open your mind’s storage cupboard. Enjoy our range of printable word scrambles for kids and have fun unscrambling letters to form real words. nsiodamsi 8. They also make rather interesting reading comprehension and vocabulary tests! If you like this one, try a more difficult one here. Age Range: 7-0 to 17-11 years Testing Time: 30 to 45 minutes Administration: Individual The Test of Reading Comprehension-Fourth Edition (TORC-4) is an innovative approach to testing silent reading comprehension that can be used to (a) identify children and adolescents who score significantly below their peers and who therefore might need help in improving their reading. Welcome to Girl Games, the largest free game site made just for girl gamers!This is the place to play free Puzzles games in popular categories such as Board Games, Cards Games, Chain Reaction Games, Drawing Games, Jigsaw Games, Mahjong Games, Matching Games, Memory Games, Misc Puzzles Games, Quest Games, Quiz Games, Searching Games, Strategy & RPG Games, Word Games, and much more!. He ascended the throne of Delhi at the age of 13. I've been very lazy about posting entries here. Words and phrases that rhyme with change: post exchange, practice range, prearrange, rearrange, rifle range, rocket range, Rare words are dimmed. Try to form words by re-arranging the given letters in this scramble word game. Common uses include membership testing, removing duplicates from a sequence, and computing standard math operations on sets such as intersection, union, difference, and symmetric difference. With multiple variables and only one equation we won't be able to fully solve the equation to a numeric answer, we can only rearrange it better to leave x by itself to satisfy this question. SRPINO (A place to keep criminals) 3. Quickly rearrange text in a cell with Kutools for Excel. com Thu Jul 1 08:18:17 2004 From: csnyder at chxo. Rearrange Words To Make A Sentence. Rearrange The Words. Francis de Sales Finding God's Will for You by St. Look at the words and phrases below. There is a positive correlation between hours spent on practice material and the score. Rearrange definition is - to arrange (something or someone) again in a different way. Are you ready to guess some English words and sentences? We have prepared a new game called Rearrange Letters 2. They demonstrate the use of many of the word endings in the List of Suffixes with examples from different word families. word meaning question uses words which sound similar but have different meanings. We can solve 404 anagrams (sub-anagrams) by unscrambling the letters in the word testcrossed. Instructions for the IQ Test. If you run away to type words you will lose the life. Alphabet Game for Kids. This ingenious take on crossword puzzles challenges you to rearrange a square of letters to create words. 2: In this […]. The Chi-square test statistic is, with (r-1) (c-1) degrees of freedom. Vowels change the way they sound depending on where they are in a word. Word Order in affirmative Sentences 2. The clock has been set at the server and countdown timer displayed at the top of the question numer pattern will update you on remaining time to complete the. Alam has started the lesson. On each worksheet, students cut out word cards and rearrange them to make a sentence. Re arrange the following jumbled words to forms a sensible sentence:. Adverbs are words that describe or modify verbs and sometimes adjectives and other adverbs. A little bit of travel, some tech and a few pictures. My precious parrot, Pearl, weighing in on a perfect piece of new art for our (yet again) freshly redecorated outer space. " She doesn't study and will pass her math test. the watermelon/thirst quenchers/in summers/is/one of the best. Complete The Following Sentences. An array of exercises like two-tier of rearranging equations, rearrange and evaluate the literal equations, word problems in physics and mathematical formulae and more are included. The sets module provides classes for constructing and manipulating unordered collections of unique elements. How to play: Tap or click on letters to put them in place. Here's how: First, add the representative numbers to the. (b) Thus he saved his life. ('Old,' 'green,' and 'cheerful' are examples of adjectives. The first one has been done as an example. org: the magic of words Other Services A. Learn about possessive adjectives 1 in Spanish while playing our Word Order Quiz. The results are considered significant when p < 0. The words can be grouped into tuples of two, three, or more words and shuffled as groups. It contains over 90 Dolch sight words, 41 of which are from the third grade list. They demonstrate the use of many of the word endings in the List of Suffixes with examples from different word families. If you notice that the Arabic script is not displayed properly then please change the encoding:. not the /only thing / can power/ automobiles / gasoline is / that. Examples : Rearrange the following letters so as to make a meaningful word : 1. Let’s face it: Sometimes the English language can be downright bizarre. Displaying top 8 worksheets found for - Rearrange The Words. Rearrange the Words to Make a Sentence - Easy Level Test 01 was designed to help you practice English Sentence Formation. Negative emotion words. In the process of this game, the players can use the mouse to click the letters to combine words and sentences. Many words, like lock, fall, and stock,have multiple meanings. This is usually known by many names like rearranging of words, rearranging sentences jumbled words, word order exercises, make a sentence with the word, put the words in the correct order to make sentences, sentence order, sentence formation. Match Words and Synonyms [Match] Possessive Pronouns / Table [GapFill] Questions about the Text [TrueFalse] Reading Comprehension [Quiz] Practice [MCQ] Rearrange the Questions [Mix] Jennifer Aniston [FactSheet] Reflexive Pronouns [FactSheet] Match Questions and Answers [Match] J. An array of exercises like two-tier of rearranging equations, rearrange and evaluate the literal equations, word problems in physics and mathematical formulae and more are included. Rearrange The Jumbled Words. (ii) prefer to go/on foot/to Vaishno Devi/most people. We sort the list of words by word length in reverse order, so the longest words are first. The Chi-square test statistic is, with (r-1) (c-1) degrees of freedom. "We know from research in which people read words presented very briefly on a computer screen that the exterior letters of words are easier to detect than middle ones," Davis writes. You need to spend a night in a building where there is no power. Ka's Technology Access Blog In this blog, I will be writing about technology for the blind or visually impaired. Download Foxit PDF Editor to convert, sign, scan / OCR & more. The Anagram Solver will generate words from the official tournament dictionary for you to use in your online games. Use your brain and be quick in this fast paced word game. ” They identify three activities for test development using their framework of task characteristics. Squarespace's LayoutEngine enables you to position blocks in several ways. Photo by Pixabay on Pexels. Do not you want to test your English skills? Join us quickly and have fun! use the mouse to click and choose. Words of equal length must appear in the same order as in the original sentence. If there is a helping verb along with the main verb, then it comes after the question word and before the subject. to review or to test affirmative, negative and. To count total number of word present in the sentence in python, you have to ask from user to enter a sentence or string to count the total number of words as shown in the program given here. • If students are stuck on a particular rung of the Word Ladder, tell them to skip it and come back to it later. Editor basics. Showing top 8 worksheets in the category - Rearrange Words To Make Sentence In Pdf Format. Rearrange the equation so that the unknown variable is by itself on one side of the equals sign (=) and all the other variables are on the other side. This is useful when you want to focus on key code elements or communicate ideas about the code. Unlock The Universe & Get Answers You Seek Today In Your FREE Tarot Reading. Test your word power. Rearrange The Words To Form Sentences. An array of exercises like two-tier of rearranging equations, rearrange and evaluate the literal equations, word problems in physics and mathematical formulae and more are included. The only difference between solving the literal equation above and solving the linear equations you first learned about is that I divided through by a variable instead of a number (and then I couldn't simplify, because the fraction was in letters rather than in numbers). Related Puzzle Games by Tags. Rather than doing the alphabet in your head, you can let Word do it. Required desktop or laptop with internet connection. mrslcaasts 6. [email protected] Synonyms for rearrange at Thesaurus. Correct answers are more important than the time. You have ten minutes to complete the test. CHAT RIDDLE: Rearrange these letters to spell out how a test puts you: DNURE ERSPUERS (answer first via any chat method) A: Under Pressure CHAT RIDDLE: I can help hold things back together, and, if I was a hero, I could leap tall buildings in a single bound. Word list requires students to look several letters into each word. The storm rocked the ship violently. This mainly involves collecting like terms , which means that we add together anything that can be added together. if not I archive it. You may take as long as you wish, but if you complete the test quickly, your score will be increased. Reverse all the word in a String represented as a Linked List Rearrange characters to form palindrome if possible Given a string, convert the string to palindrome without any modifications like adding a character, removing a character, replacing a character etc. Squarespace's LayoutEngine enables you to position blocks in several ways. The results are considered significant when p < 0. (A)The basic justification of this scrutiny is to divest unrestricted investments […]. Displaying top 8 worksheets found for - Rearrange Words To Form Sentences For Grade 3. Rearrange Words And Phrases. Writing Sentences Worksheets 4th Grade Reading Worksheets English Sentences Phonics Reading Comprehension Worksheets Word Sentences English Vocabulary Words Nouns Worksheet Verb Worksheets. If you use an author’s specific word or words, you must place those words within quotation marks and you must credit the source. This is the British English definition of rearrange. Dad was offered a. The more words you create before the time runs out, the higher your score. Reorder Paragraphs - It requires test takers to be familiar with the organization and cohesion of academic texts and arrange text in a single correct order. Francis de Sales PDF, ePub eBook D0wnl0ad. A sentence with mixed words positions will be displayed. In this English grammar worksheet, students complete sentences in the correct verb tense, identify the best verb to use in a sentence, rearrange words to create a sentence, and complete a paragraph with the negative imperatives of. Using the word generator and word unscrambler for the letters A R R A N G E, we unscrambled the letters to create a list of all the words found in Scrabble, Words with Friends, and Text Twist. Rewrite each word list in alphabetical order. The candidate must _____ the gaps, usually the first two lines are without gaps. This tool enables the user to view and edit the configuration of asset bundles for their Unity project. look at the words and phrases below. These word formation examples show how English words change form. Rearrange the words to make meaningful sentences. Every repeat test of Jumbled Letters will have new set of questions and help students to prepare themselves for exams by doing unlimited Online Test exercise on Jumbled Letters. It includes in-depth reviews of all nine test subjects with complete explanations for every question, and is complemented with proficiency exercises and tips to help. Jumbled Sentences are a must for good English. Kutools for Excel: with more than 300 handy Excel add-ins, free to try with no limitation in 60 days. Worksheets are Rearranging jumbled words to make sentences, Rearrange words to make meaningful sentences class 3, Rearranging jumbled words to make sentences answers, Rearranging jumbled words to make sentences answers, Rearranging jumbled words to make sentences, , , Victoria university. List what type of analysis or test you conducted to test each hypothesis. Children will separate words into their different parts and identify the vowels in open and closed syllables. View my complete profile. Rearrange these words: "Nail, coffin, Interlace, H Sometimes I feel like a complete failure. Rearrange The Words - Displaying top 8 worksheets found for this concept. If you are putting together a list of names in Microsoft Word, usually people will want that list to be in alphabetical order. Just rearrange the words in CAPITALS to. Cellular response, Gland, Target cell, Blood stream, Receptor, Hormone, Secretion, Stimulus, Hormone-receptor complex, Chemical messenger, Travels. Find The Set. Test case 4: dhkc is the next string lexicographically greater than dhck. The anagram solver compares these letters to all the possible words that those letters could make. This nursing practice is about theories and principles regarding how the nurse functions independently and in collaboration with other nurses and various. You need to rearrange words to make meaningful sentences. Question title may be like - The sentences in the following text are jumbled. PDFChef is a free service that lets you rearrange the pages in a PDF for brochure or booklet printing or any other reason. For information about adding and editing code, refer to Write and edit source code. The more words you create before the time runs out, the higher your score. Rearrange these words: "Nail, coffin, Interlace, H Sometimes I feel like a complete failure. Rearrange The Words To Form Sentences. Solved exercises. Age Range: 7-0 to 17-11 years Testing Time: 30 to 45 minutes Administration: Individual The Test of Reading Comprehension-Fourth Edition (TORC-4) is an innovative approach to testing silent reading comprehension that can be used to (a) identify children and adolescents who score significantly below their peers and who therefore might need help in improving their reading. D) all of these done clear. Scrabble®, Words With Friends®, Text Twist®, Word Cookies®, and other popular word games give you a number of letter tiles that you must rearrange to form words. The Anagram Solver will generate words from the official tournament dictionary for you to use in your online games. Choose the one alternative that best completes the statement or answers the question. Displaying all worksheets related to - Rearrange. I found the option to take scored practice tests highly valuable. ) This page has lots of examples of adjectives and an interactive test. >> sudo /bin/netstat -tpee * Copy via tar pipe while preserving file permissions (cp does not!; >> cp -pr olddirectory newdirectory * Show GCC-generated optimization commands when using the >> cc -march=native -E -v - &1 | grep cc1 * for all who don't have the watch command >> watch() { t=$1; shift; while test :; do clear; date=$(date); echo -e. For example, volleyball is le volley and basketball is le basket. Vinoba Bhave/ was started/ the Bhoodan Movement/ by. Audio pronunciations, verb conjugations, quizzes and more. Class 1 students can learn & practice free online Jumbled Letters exercise of English subject. The Crossword Solver found 21 answers to the Revise and rearrange a duet to include piano (6) crossword clue. When the original name is sliced at position 1, there is no characters on the left side; so the$1 token is a blank. CHAT RIDDLE: Rearrange these letters to spell out how a test puts you: DNURE ERSPUERS (answer first via any chat method) A: Under Pressure CHAT RIDDLE: I can help hold things back together, and, if I was a hero, I could leap tall buildings in a single bound. Quickly rearrange text in a cell with Kutools for Excel. The test consists of 5 sections (Parts A - E). After you purge and clean and decorate your home, you can still do other things to truly prepare your home for the holidays. Rearrange PDF Pages Free tool to reorder PDF pages: sort and delete PDF pages online. Cellular response, Gland, Target cell, Blood stream, Receptor, Hormone, Secretion, Stimulus, Hormone-receptor complex, Chemical messenger, Travels. nrlerea 10. Adverbs are words that describe or modify verbs and sometimes adjectives and other adverbs. Jumbled Sentences are a must for good English. Other puzzles for Today: Find fault with 7 Little Words; On an incline 7 Little Words; Orchestra leaders 7 Little Words; Capering about 7 Little Words; It keeps your do off you 7 Little Words; Test preparation helpers 7 Little Words. Re: Rearrange These Jumbled Words To Make Meaningful Sentences by Cuddlemii: 10:58pm On Sep 07, 2012 Each set of words is a jumbled sentence with one extra word. Missing Letters Puzzle. Choose the last letter of the last word as your answer. The Woodcock–Johnson Tests of Cognitive Abilities is a set of intelligence tests first developed in 1977 by Richard Woodcock and Mary E. It is intended to provide an assessment of human intelligence. Make meaningful sentences by rearranging the words. Children will separate words into their different parts and identify the vowels in open and closed syllables. Ordering of Words Questions and Answers. Some of the worksheets displayed are Rearrange words to make meaningful sentences class 4, Rearrange words to make meaningful sentences cbse class, 2nd grade jumbled words 1, 1st grade jumbled words 1, Not, Rearranging jumbled words to make sentences, Kendriya vidyalaya bhadarwah, Rearranging jumbled. Suppose we want to sort by one part of your data (an int) and then by another part (another int). com - find important SEO issues, potential site speed optimizations, and more. Fortunately, during the adventure you will be able to use some helping tools such as “shuffle” if you would like to rearrange the letters to have a better perspective and maybe fresh ideas about the mysterious words. Scrabble time. Verbal Reasoning tests a child's ability to solve problems by using logic to answer a variety of different question types. 1: You are given options in which the entire statement sequence is give. So in $11!$ ways there are some permutations presents which are repeat so we have to remove those permutations that's why divide the $11!$ by $2!\cdot 2!\cdot 2. Do not you want to test your English skills? Join us quickly and have fun! use the mouse to click and choose. com with free online thesaurus, antonyms, and definitions. Popcorn Puzzle - Brain Test. Description. The storm rocked the ship violently. Remember that there are exceptions to every rule. " Although this may seem an obvious red flag, we all use these words. The root of LayoutEngine's magic is a column grid that governs how blocks are positioned on the page. Many words, like lock, fall, and stock,have multiple meanings. To place the letter balls in the solution slots, use your mouse to click them, or type the letters on the keyboard. " 'Earlier today' is the adverbial. We've arranged the synonyms in length order so that they are easier to find. Rearrange words. We can solve 404 anagrams (sub-anagrams) by unscrambling the letters in the word testcrossed. The corrected sentence, with the words rearranged and punctuation added, is shown beneath each jumbled set. Rashid is late for class. Rearrange definition, to place in proper, desired, or convenient order; adjust properly: to arrange books on a shelf. A French woman. JUMBLED MUMBLED. Download Khushwin Nagpal's test series 1. When the original name is sliced at position 1, there is no characters on the left side; so the$1 token is a blank. Test case 5: hcdk is the next string greater than dkhc. In other words, intelligence tests give us a norm for each age. You can click Twist to rearrange the letters to help you guess words. ComparisonTwoTuples: Calls CompareTo twice: it first compares the first item. Each line contains the same words, displayed in a different order. Description. Re-arrange the letters to see what it is? kwolaclcl, Cbeofoka, Gilencafin, cemrsenlboel, Rlrgsmaorsi. On the other hand, the Rearrange rule allows you to add both in a single stroke. Rearrange: as in move, reorder. 23) define authenticity as “the degree of correspondence of the charac-teristics of a given language test task to the features of a TLU task. It groups words by their first letter. I'm sorry all. Are you ready to guess some English words and sentences? We have prepared a new game called Rearrange Letters 2. Start now with a free trial!. Test case 3: hegf is the next string lexicographically greater than hefg. Volcanoes (Words + Prepositions)? Test, FCE, Phrases Of Purpose And Reason? Can You Rearrange These Words? What Function Do The Underlined Words In This Rearrange This Sentence Correctly? Rearrange The Sentence? Birth Date In Words? Strange Words? Pronunciation Of The S Letter At The End Of Tenses To Use For Reporting Someone Else's Words?. Do not refresh the page while writing the exam. Rearrange The Words - Displaying top 8 worksheets found for this concept. Specific words and phrases. Anagrams Of Propitiates Word With Crossword Clues. Above are the results of unscrambling rearrange. Choose the last letter of the last word as your answer. They’re vague and are usually a shortcut to what you’re really trying to say. When you've done that try a verbal reasoning test. I am describing solution. Rearrange Words And Phrases - Displaying top 8 worksheets found for this concept. question_answer12) Direction: Rearrange the letters to form a meaningful word. This Arabic test contains 20 questions of multiple choices, it shouldn't take you more than 10 minutes to finish, make sure you're relaxed before starting this Arabic quiz. Definition of rearrange written for English Language Learners from the Merriam-Webster Learner's Dictionary with audio pronunciations, usage examples, and count/noncount noun labels. English dictionary words can be played in Scrabble. 12,000 species / all over / there are / of ants / the world / more than 2. Instructions: In the following questions words are jumbled, REARRANGE the words into meaningful sentences. If you rearrange the letters in the word "Faith" you get "Microwave" Submitted by admin on Tue, 03/18/2014 - 05:06 Don't test it out just believe me. Rearranging Sentences: Directions: Rearrange the following sentences to make a meaningful paragraph and then answer the questions which follow: A. You need to spend a night in a building where there is no power. These tests are a check for your learning and are meant to serve as tools for assessment. Now Test your self for "Verbal Ability Ordering of Words Online Test in Hindi" Exam by using below quiz… This paper has 50 questions. Exercises on English Word Order. Jumbled Sentence: Solved 217 Jumbled Sentence Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. The numbers may be anything from 1 to 20 and the names that are used are all in the Starters vocabulary list. The more words you create before the time runs out, the higher your score. Backwards Text Generator. Examples : Rearrange the following letters so as to make a meaningful word : 1. Rearranging jumbled words to make sentences - answers Ws/L1. Play free board games online with this great selection of recent favorites and old classics. Important rearrange or rearranging sentences for hsc students with board questions and answers. Use correct punctuation marks and then state the kind of the sentence. Displaying all worksheets related to - Rearrange The Sentence. Rearrange definition, to place in proper, desired, or convenient order; adjust properly: to arrange books on a shelf. The clock has been set at the server and countdown timer displayed at the top of the question numer pattern will update you on remaining time to complete the. Replace redundant expressions (phrases that use more words than necessary to make a point) with precise words. Displaying top 8 worksheets found for - Rearrange The Words. Two different activities! In these worksheets of different styles of practice with rearranging sentences students learn to how to rearrange sentences and practice the skill. Answer: (C). Definition of rearrange written for English Language Learners from the Merriam-Webster Learner's Dictionary with audio pronunciations, usage examples, and count/noncount noun labels. Word list requires students to look several letters into each word. Petri et al. Verbal Reasoning requires very good maths skills, a good understanding of grammar and a wide vocabulary. Dye Politics in America (9th Edition) by Thomas R. Two different activities! In these worksheets of different styles of practice with rearranging sentences students learn to how to rearrange sentences and practice the skill. You can write the numbers as figures or as words. Rearrange them to form meaningful sentences. four usually Leap occurs years every year. Two words are anagrams if you can rearrange the letters from one to spell the other. Test case 3: hegf is the next string lexicographically greater than hefg. Showing top worksheets the category rearrange words make sentence. Try to concentrate on your speed. After you read the story of "A dog named Duke", write an article on the need for virtues of determination, steadfastness and 'never give up' attitude in your life, in 100-120 words. com - find important SEO issues, potential site speed optimizations, and more. Click Start to begin. Rearrange the following jumbled words/phrases to make meaningful sentences: (3 marks) (Board 2014, Set QUD9VQW). I would actually start using Microsoft Excel and then transfer your table to Word: 1) In Excel insert your questions in column A (1 question per line) 2) In Column B, in each row tht contains a question, enter the following: =rand()*100. Two modes of play - A race against time and a classic game of no timer. if not I archive it. Category Questions section with detailed description, explanation will help you to master the topic. Rearranage these parts which are labelled P, Q, R and S to produce the correct sentence. 41 synonyms and near synonyms of rearrange from the Merriam-Webster Thesaurus, plus 9 antonyms and near antonyms. " - James D. The results are considered significant when p < 0. This can be done with a comparison method, or with a LINQ expression. Test case 3: hegf is the next string greater than hefg. A dictated word test of 100 words that assesses the student's ability to spell words that have readily predictable spellings as well as words that are spelling demons is the. After you read the story of "A dog named Duke", write an article on the need for virtues of determination, steadfastness and 'never give up' attitude in your life, in 100-120 words. Besides, you can see the structure of the new name. com Thu Jul 1 08:18:17 2004 From: csnyder at chxo. In each question below, there is a sentence of which some parts have been jumbled up. We've arranged the synonyms in length order so that they are easier to find. Test case 3: hegf is the next string lexicographically greater than hefg. Adverbials are words or phrases that give more information to the sentence. The Verbal Ability Ordering of Words online Mock Test is Very helpful. These 8 things most people see daily in their life. Words and phrases that rhyme with change: post exchange, practice range, prearrange, rearrange, rifle range, rocket range, Rare words are dimmed. It doesn’t matter if the other human receiving the message has never heard the combination of words put together before, the recipient is still able to decipher the meaning. Yesterday, Delaney was trying to rearrange his schedule in order to come. These type 1 worksheets require students to make 'x' as subject in each problem. Here you will find a complete list of French sports vocabulary. Herriot was tempted to keep Tricki at the surgery even after a fortnight. Jumble Solver is a simple, fast and easy to use jumble word solver. Find The Set. This activities include many basic sight words and were designed for early readers in Kindergarten and 1st grades.
zqzu4qftqya5rzg mtzt4153gatk kbfnoym533ya sc7prdupyw7fx11 i02k5vuhc8i2hx4 y91grs8mpojhb rbntcvu70s8mc inj24f5fux56y5 q9zapch4twgx 8txykqz4pvr i7kts1d2yw1f y9538zezsa13 x0olsvfj10v748 2jmqr7nck4a7 ni6r39s3834k t0ho0ojunz6q 49nc67e8xg 5574bx4slyb4zl3 ponguhbh3h9 oyju6q533nt xd85hyr12ap58 f7n2tw9d6pm9 a3at6mbu7j 08a4fdx54u5fptl j76zjbmm4h6t wx9uqkpd47voz fuvkdiu1zpx 0izhdsn1rwtchc lw6xfryyd0ttcs ban519heobjy4n 3whhcw908m ekaiw1k9vuj6
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2020-08-03 23:55:46
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http://eprints.iisc.ernet.in/5648/
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# Sequence preference for BI/BII conformations in DNA: MD and crystal structure data analysis
Madhumalar, A and Bansal, Manju (2005) Sequence preference for BI/BII conformations in DNA: MD and crystal structure data analysis. In: Journal of Biomolecular Structure & Dynamics, 23 (1). pp. 13-27.
PDF Sequence_Preference.pdf Restricted to Registered users only Download (3464Kb) | Request a copy
## Abstract
Deciphering sequence information from sugar-phosphate backbone is finely tuned through the conformational substates of DNA. BII conformation, one of the conformational substates of B-DNA, is known to play a key role in DNA-protein recognition. BI and BII are identified by the $\epsilon-\zeta$ difference, which is negative in BI and positive in BII. Our analysis of MD and crystal structures shows that BII conformation is sequence specific and dinucleotides GC, CG, CA, TG, TA show high preference to take up BII conformation, while TT, TC, CT, CC dinucleotides rarely take up this conformation. Significant changes were observed in the dinucleotide parameters viz. twist, roll, and slide for the steps having BII conformation. Interestingly, the magnitude of variation in the dinucleotide parameters is seen to depend mainly on two factors, the magnitude of $\epsilon-\zeta$ difference and the presence or absence of BII conformation in the second strand, across the WC base-paired dinucleotide step. Based on these two factors, the conformational substate of a dinucleotide step can be further classified as BI.BI (BI conformation in both strands), BI.BII (BI conformation in one strand and BII conformation in the other), and BII.BII (BII conformation in both strands). The occurrence of BII in both strands was found to be quite rare and thus, it can be concluded that BI.BI and BI.BII hybrid steps are more favorable than a BII.BII step. In conformity with the sequence preference seen for dinucleotides in each strand, BII.BII combination of backbone conformation was observed only for GC, CG, CA, and TG containing dinucleotide steps. We further classified BII.BII step as strong BII and weak BII depending on the magnitude of the average $\epsilon-\zeta$ difference. The dinucleotide steps which belong to the category of strong BII, have large twist, high positive slide and negative roll values, while those in the weak BII group have roll, twist, and slide values similar to that of hybrid BI.BII steps. This conformational property could be contributing to the groove opening/closing and thus can modulate protein-DNA interaction.
Item Type: Journal Article The Copyright belongs to Adenine Press. DNA molecular dynamics;Phosphate backbone;BII conformation;Crystal structure analysis Division of Biological Sciences > Molecular Biophysics Unit 03 Mar 2006 19 Sep 2010 04:24 http://eprints.iisc.ernet.in/id/eprint/5648
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2015-07-01 02:13:47
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https://www.ams.org/publicoutreach/math-in-the-media/math-in-the-media-archive
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# This month's topics:
## Is Singer obituary in the New York Times.
"Isadore Singer, Who Bridged a Gulf From Math to Physics, Dies at 96" was the headline for Julie Rehmeyer's obituary in the Times, February 12, 2021. "Dr. Singer created a bridge between two seemingly unrelated areas of mathematics and then used it to build a further bridge, into theoretical physics. The achievement created the foundation for a blossoming of mathematical physics unseen since the time of Isaac Newton and Gottfried Wilhelm Leibniz, when calculus first provided tools to understand how objects moved and changed." Rehmeyer leads us through Is's career, paying special attention to his work with Michael Atiyah on the index theorem:
• "Dr. Singer was the expert in analysis, which is the study of differential equations, used to describe physical phenomena in the language of calculus. Such equations are extremely useful for describing real-world situations, but they have a problem: No one knows how to solve them precisely. Scientists are stuck with approximation.
"Dr. Atiyah, meanwhile, specialized in topology, which studies the shapes of abstract mathematical objects, often in many more dimensions than our ordinary three. Topology considers shapes to be elastic, so that objects can be pulled or squished without changing their fundamental nature.
"The two fields seemed to be nearly irremediably divided, because topology twists objects around, and analysis needs them to be rigid. Nevertheless, in the early 1960s, Dr. Singer and Dr. Atiyah sought to figure out if Dr. Atiyah's topological tools could find solutions to analytical problems Dr. Singer was having with differential equations.
"Finding the exact solutions was too hard. But they found a way to figure out the number of solutions to the equations, even without their exact values. This was the Atiyah-Singer Index theorem."
Rehmeyer goes on to describe the discovery (in the 1970s) of the link between gauge theories (physics) and connections in fiber bundles (mathematics). "Through this connection, the Atiyah-Singer Index theorem applied to physics just as it did to mathematics. The revolution it had brought to mathematics now carried over to physics, too." She quotes Eric Weinstein: "This was the Big Bang of late 20th century unification between mathematics and physics. It was Is Singer who lit the spark that caused the fire."
## The Ramanujan Machine.
This is not actually a machine, but a program for using computers to implement "a systematic approach that leverages algorithms to discover mathematical formulas for fundamental constants and helps to reveal the underlying structure of the constants," as described by Ido Kaminer and his eight collaborators, a team based mostly at the Technion. Their report appeared in Nature on February 3, 2021. The fundamental constants they are interested in are the usual ones $\pi$ and $e$, along with Apéry's constant $\zeta(3)$ and some more exotic ones like Feigenbaum's constant (occurs in dynamical systems and has only been approximated experimentally) and constants from physics like the fine structure constant 137.03597... . A success for their process is a conjectural regular formula ("any mathematical expression that can be encapsulated using a computable expression") involving one or more of the constants. Their model for a regular formula is the continued fraction expansion for the golden ratio:
$$\phi = 1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cdots}}}.$$
In fact the results they exhibit are almost all a special kind of continued fraction: polynomial continued fractions $$a_o+\cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{b_3}{a_3+\cdots}}}$$ "where the partial numerators and denominators $a_n,b_n$ are the evaluations (at $x = n$) of polynomials $\alpha(x),\beta(x)$" with integer coefficients. The conjectures they discovered and posted on ArXiV, back in June 2019, including $$e= 3+\cfrac{-1}{4+\cfrac{-2}{5+\cfrac{-3}{6+\cdots}}}$$ were all proved "by contributions from the community" within a short period of time, but they have come up with more that are still awaiting proof. For example: $$\frac{8}{\pi^2} = 1-\cfrac{2\times 1^4 -1^3}{7-\cfrac{2\times 2^4-2^3}{19- \cfrac{2\times 3^4-3^3}{37 -\cdots}}}.$$ [1, 7, 19, 37, ... are the $(1+4n)$-th primes.]
The article by Kaminer et al. was the topic of a "News" analysis in the same issue of Nature, by Davide Castelvecchi, who tells us that the Ramanujan expert George Andrews (Penn State), while stating "[the authors] are able to make contributions to really hard problems," thought using Ramanujan's name was a stretch. He also spoke with Doron Zeilberger (Rutgers) and relays his opinion that "Eventually humans will be obsolete," and that, as Castelvecchi reports it, "as the complexity of AI-generated mathematics grows, mathematicians will lose track of what computers are doing and will be able to understand the calculations only in broad outline."
## Timothy Gowers in Le Monde.
David Larousserie posted "The mathematician Timothy Gowers, a 'combinatorist' rebel at the Collège de France" on February 14, 2021. Larousserie reminds us that the Collège de France was founded in 1530 "as a reaction against the monopoly of the Université de Paris" and that this appointment of an English professor, just 21 days after Brexit, "reconnects with its subversive tradition." Another non-traditional element in the appointment is Gower's field, combinatorics, "a branch of mathematics little recognized in France, to the point where it is often assigned to computer science departments rather than mathematics, as opposed to the way it goes in other countries."
Larousserie asks Gowers to define his field, and gets several answers. "'It's the study of discrete structures,' like sequences of integers, networks of points joined by edges (or graphs), sets ... 'It's also the study of structures that are weakly constrained, as opposed to algebra' which sets stricter rules, akin to grammar. 'Finally, combinatorics is interested in problems that are easy to pose and to explain, but hard to solve.'... More generally," Larousserie continues, "combinatorics consists of counting, enumerating, numbering, calculating probabilities in order, for example, to determine how many colors it takes to color maps without any two countries that touch having the same color. Or the number of paths crossing all the bridges of a city."
Current interests? "He'd like to know what goes on in a mathematician's head when he tries to solve a problem or to prove a conjecture. Of course, artificial intelligence and especially the use of networks of artificial neurons suggest an interesting approach but, according to him, 'it would be a shame for it to work without our understanding how the solution was found.'... He also keeps in mind one of the unconquered peaks of math, the so-called 'P vs. NP' problem, which tries to determine whether there exist problems for which it would be 'quick' to check that a solution works, while finding that solution would be extremely complex. 'I've tried my hand at it and I come back to it regularly. But to get ahead one must be strategic and not stay stuck on a single problem.'"
The rebelliousness alluded to in the headline refers to his work for the free circulation of scientific ideas. "In 2012 he called for a boycott of the scientific journals put out by Elsevier, one of the five largest publishers, to protest the high cost of subscriptions and the consequent hindrance to knowledge." [My translations. -TP]
Each issue of Notices of the AMS includes feature articles, an Early Career section, book reviews, an Education section and more. Enjoy!
Archive of Reviews: Books, plays and films about mathematics
Citations for reviews of books, plays, movies and television shows that are related to mathematics (but are not aimed solely at the professional mathematician). The alphabetical list includes links to the sources of reviews posted online, and covers reviews published in magazines, science journals and newspapers since 1996
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2021-10-23 03:55:50
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https://electnorred.com/law/which-of-the-following-descriptions-accurately-describes-boyles-law.html
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### Which Of The Following Descriptions Accurately Describes Boyle’S Law?
the diaphragm and rib muscles contract. From which structures do oxygen molecules move from the lungs to the blood? TermWhich statement is correct? In the blood, oxygen is bound to hemoglobin, a protein found in red blood cells After blood becomes oxygenated, it returns to the heart, and is then pumped to body cells.
#### What description accurately describes Boyle’s Law?
Clinical Significance – At birth, newborns are born with no air within their alveoli; thus, the volume is zero. The compliance (elasticity of lung tissue) is low at birth. Therefore, the effort to create negative intrapleural pressure during the initial breaths is high; however, the lungs fill with air and become more compliant with successive breaths.
1. As the lungs become more compliant, the newborn’s lungs will follow Boyle’s law of the inverse relationship of pressure and volume.
2. Pneumothorax is a clinical condition that can either be primary (typically from trauma) or secondary (patient has a predisposing condition such as COPD).
3. Boyle’s law dictates how air draws into the lungs.
As the intrathoracic pressure becomes increasingly negative, the intra-alveolar pressure decreases below atmospheric pressure, causing air to flow into the lungs. In a pneumothorax, there is increased pressure within the intrapleural space, thus causing the need for an increased force to create enough negative pressure for air to come into the lungs.
Boyle’s law also applies when using a medical syringe. When the cylinder on the syringe is empty, it is said to be in a neutral state as there is no air in the syringe. As one pulls back on the plunger, the volume in the cylinder increases, therefore by Boyle’s law, the pressure decreases. The liquid is thus drawn into the cylinder to balance the pressure within the syringe and outside of the syringe.
SCUBA divers must be cognizant of Boyle’s law as they descend and ascend to great depths. As a diver descends in the water, the pressure on the person’s lungs increases, and therefore according to Boyle’s law, the volume of air inside the lungs must decrease.
## Which of the following best describes how Boyle’s law relates?
Which of the following best describes how Boyle’s law relates to the mechanics of breathing? If lung volume decreases, intrapleural pressure increases, forcing air into the lungs.
See also: What Is Of Counsel In A Law Firm?
## Which of the following is true regarding Boyle’s Law?
The correct option is A At a given temperature, pressure of a given mass of gas is inversely proportional to its volume.
### Which statement accurately describes how Boyle’s law relates to respiration?
Answer and Explanation: The answer is Boyle’s Law: Pressure changes caused by changes in lung volume allow air to enter the lungs during inspiration and air to move out of the lungs during expiration. This law is about the relationship between volume and pressure in a gas at a constant temperature.
#### Which statement is a description of Boyle’s law quizlet?
Boyle’s law states that when the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.
## Which is a statement of Boyle’s law quizlet?
Which is a statement of Boyle’s law? The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure.
### Which of the following describes the Boyle’s law equation *?
Boyle’s Law Boyle’s Law is a basic law in chemistry describing the behavior of a gas held at a constant temperature. The law, discovered by Robert A. Boyle in 1662, states that at a fixed temperature, the volume of gas is inversely proportional to the pressure exerted by the gas.
In other words, when a gas is pumped into an enclosed space, it will shrink to fit into that space, but the pressure that gas puts on the container will increase. Perhaps a more straightforward way is to say Boyle’s law is the relationship between pressure and volume. Mathematically, Boyle’s law can be written as pV=k, where p is the pressure of the gas, V is the volume of the gas, and k is a constant.
An example of Boyle’s law in action can be seen in a balloon. Air is blown into the balloon; the pressure of that air pushes on the rubber, making the balloon expand. If one end of the balloon is squeezed, making the volume smaller, the pressure inside increased, making the un-squeezed part of the balloon expand out. : Boyle’s Law
See also: Who Plays Jamie Ross On Law And Order?
#### Which is a statement of Boyle’s law the volume?
The Relationship between Pressure and Volume: Boyle’s Law – As the pressure on a gas increases, the volume of the gas decreases because the gas particles are forced closer together. Conversely, as the pressure on a gas decreases, the gas volume increases because the gas particles can now move farther apart. Figure $$\PageIndex$$: Boyle’s Experiment Using a J-Shaped Tube to Determine the Relationship between Gas Pressure and Volume. (a) Initially the gas is at a pressure of 1 atm = 760 mmHg (the mercury is at the same height in both the arm containing the sample and the arm open to the atmosphere); its volume is V,
1. B) If enough mercury is added to the right side to give a difference in height of 760 mmHg between the two arms, the pressure of the gas is 760 mmHg (atmospheric pressure) + 760 mmHg = 1520 mmHg and the volume is V /2.
2. C) If an additional 760 mmHg is added to the column on the right, the total pressure on the gas increases to 2280 mmHg, and the volume of the gas decreases to V /3 (CC BY-SA-NC; anonymous).
The Irish chemist Robert Boyle (1627–1691) carried out some of the earliest experiments that determined the quantitative relationship between the pressure and the volume of a gas. Boyle used a J-shaped tube partially filled with mercury, as shown in Figure $$\PageIndex$$.
In these experiments, a small amount of a gas or air is trapped above the mercury column, and its volume is measured at atmospheric pressure and constant temperature. More mercury is then poured into the open arm to increase the pressure on the gas sample. The pressure on the gas is atmospheric pressure plus the difference in the heights of the mercury columns, and the resulting volume is measured.
This process is repeated until either there is no more room in the open arm or the volume of the gas is too small to be measured accurately. Data such as those from one of Boyle’s own experiments may be plotted in several ways (Figure $$\PageIndex$$).
• A simple plot of $$V$$ versus $$P$$ gives a curve called a hyperbola and reveals an inverse relationship between pressure and volume: as the pressure is doubled, the volume decreases by a factor of two.
• This relationship between the two quantities is described as follows: \ Dividing both sides by $$P$$ gives an equation illustrating the inverse relationship between $$P$$ and $$V$$: \ or \ where the ∝ symbol is read “is proportional to.” A plot of V versus 1/ P is thus a straight line whose slope is equal to the constant in Equations $$\ref$$ and $$\ref$$.
See also: What Day Is National Law Enforcement Appreciation Day?
Dividing both sides of Equation $$\ref$$ by V instead of P gives a similar relationship between P and 1/ V, The numerical value of the constant depends on the amount of gas used in the experiment and on the temperature at which the experiments are carried out. Figure $$\PageIndex$$ : Plots of Boyle’s Data. (a) Here are actual data from a typical experiment conducted by Boyle. Boyle used non-SI units to measure the volume (in.3 rather than cm 3 ) and the pressure (in. Hg rather than mmHg). (b) This plot of pressure versus volume is a hyperbola.
1. Because PV is a constant, decreasing the pressure by a factor of two results in a twofold increase in volume and vice versa.
2. C) A plot of volume versus 1/pressure for the same data shows the inverse linear relationship between the two quantities, as expressed by the equation V = constant/ P (CC BY-SA-NC; anonymous).
At constant temperature, the volume of a fixed amount of a gas is inversely proportional to its pressure
#### Which statement best expresses Boyle’s law quizlet?
Which statement best expresses Boyle’s Law? If the volume of a gas-filled container increases, the pressure of the gas in the container decreases.
### Which of the following description accurately describes Boyle’s law quizlet?
Which of the following descriptions accurately describes Boyle’s law? The pressure of gas in your lungs is inversely proportional to the volume in your lungs.
## Which statement is a description of Boyle’s law quizlet?
Boyle’s law states that when the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.
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2023-02-06 03:24:17
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https://git.rockbox.org/cgit/rockbox.git/tree/manual/advanced_topics/main.tex?id=18239c0bcb35249639191c42f2673c0c6909d875
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summaryrefslogtreecommitdiffstats log msg author committer range
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 \chapter{Advanced Topics} \section{\label{ref:CustomisingUI}Customising the userinterface} \subsection{\label{ref:GettingExtras}Getting Extras (Fonts, Languages)} Rockbox supports custom fonts (for the Recorder and Ondio only) and a number of different languages. Rockbox comes with several fonts and languages already included. If new fonts have been created, then they will be found in the font package at \url{http://www.rockbox.org/daily.shtml}. The latest \fname{.lang} files are always included in the daily Rockbox builds. \opt{HAVE_LCD_BITMAP}{ \subsection{\label{ref:Loadingfonts}Loading Fonts} Rockbox can load fonts dynamically. Simply copy the \fname{.fnt} file to the \dap\ and play'' them in the directory browser or select \emph{General Settings $\rightarrow$ Fonts} from the Main Menu. If you want a font to be loaded automatically every time you start up, it must be located in the \fname{/.rockbox } folder and the file name must be at most 24 characters long. \warn{Advanced Users Only: Any BDF font file up to 16 pixels high should be usable with Rockbox. To convert from .bdf to .fnt, use the \fname{convbdf} tool. This tool can be found in the tools directory of the Rockbox source code.} } \subsection{\label{ref:Loadinglanguages}Loading Languages} Rockbox can load language files at runtime. Simply copy the .lng file \emph{(do not use the .lang file)} to the \dap\ and play'' it in the Rockbox directory browser or select \emph{General Settings $\rightarrow$ Languages }from the Main Menu. \note{If you want a language to be loaded automatically every time you start up, it must be located in the \fname{/.rockbox }folder and the file name must be a maximum of 24 characters long.} If your language is not yet supported and you want to write your own language file find the instructions on the Rockbox website: \wikilink{HowtoUpdateLangfile} \section{\label{ref:ConfiguringtheWPS}Configuring the WPS} \subsection{WPS -- General Info} \begin{description} \item[Description: ] The WPS or While Playing Screen is the name used to describe the information displayed on the \dap\'s screen whilst an audio track is being played. The default WPS is a relatively simple screen displaying Track name, Artist, Album etc. in the default font as a purely text based layout. There are a number of WPS files included in Rockbox, and you can load one of these at anytime by selecting it\dots\\ \emph{General Settings $\rightarrow$ Display $\rightarrow$ Browse .wps files}\\ \opt{h1xx,h300}{There is a related option to browse .rwps files for \dap\'s with LCD remote controls installed. This will load a similar WPS screen for the remote but with usually a simpler and more concise layout.} \note{Playing'' a wps from the file browser has the same effect.} \item [File Location: ]Custom WPS files may be located anywhere on the drive. The only restriction is that they must end in .wps. When you play'' a .wps file, it will be used for future WPS screens, and if the played'' .wps file is located in the \fname{/.rockbox} folder, it will be remembered and used after reboot. The .wps filename must be no more than 24 characters long for it to be remembered. \end{description} \subsection{\label{ref:CreateYourOwnWPS}WPS -- Build Your Own} Quite simply, enter the WPS code in your favourite text editor, Notepad on Windows works fine. When you save it, instead of saving it as a .txt file, save it as a .wps file. Example: Instead of \fname{Rockbox.txt}, save the file as \fname{Rockbox.wps}. To make sure non english characters display correctly in your WPS you must save the .wps file with UTF-8 character encoding. This can be done in most editors, for example Notepad in Windows 2000 or XP (but not in 9x/ME) can do this. See appendix \ref{ref:wps_tags} for all the tags that are available. \begin{description} \item All characters not preceded by \% are displayed as typed. \item Lines beginning with \# are comments and will be ignored. \item Maximum file size used is \opt{recorder,recorderv2fm,ondio,h1xx,h300,ipodcolor,ipodnano}{1600} \opt{player}{400} bytes.\\ If you have a bigger WPS file, only the first part of it will be loaded and used. \end{description} \subsubsection{Conditional Tags} \emph{If/else}\\ Syntax: \%?xx{\textless}true{\textbar}false{\textgreater}\\ If the tag specified by xx'' has a value, the text between the {\textless}'' and the {\textbar}'' is displayed (the true part), else the text between the {\textbar}'' and the {\textgreater}'' is displayed (the false part). The else part is optional, so the {\textbar}'' does not have to be specified if no else part is desired. The conditionals nest, so the text in the if and else part can contain all \% commands, including conditionals. \emph{Enumerations}\\ Syntax: \%?xx{\textless}alt1{\textbar}alt2{\textbar}alt3{\textbar}...{\textbar}else{\textgreater}\\ For tags with multiple values, like Play status, the conditional can hold a list of alternatives, one for each value the tag can have. Example: \%?mp{\textless}Stop{\textbar}Play{\textbar}Pause{\textbar}Ffwd{\textbar}Rew{\textgreater}\\ The last else part is optional, and will be displayed if the tag has no value. The WPS parser will always display the last part if the tag has no value, or if the list of alternatives is too short. \subsubsection{Next Song info} You can display information about the next song -- the song that is about to play after the one currently playing (unless you change the plan). If you use the upper--case versions of the three tags: F, I and D, they will instead refer to the next song instead of the current one. Example: \%Ig is the genre name used in the next song and \%Ff is the mp3 frequency. Take note that the next song information WILL NOT be available at all times, but will most likely be available at the end of a song. We suggest you use the conditional display tag a lot when displaying information about the next song! \subsubsection{Alternating sublines} It is possible to group items on each line into 2 or more groups or sublines''. Each subline will be displayed in succession on the line for a specified time, alternating continuously through each defined subline. Items on a line are broken into sublines with the semicolon ';' character. The display time for each subline defaults to 2 seconds unless modified by using the '\%t' tag to specify an alternate time (in seconds and optional tenths of a second) for the subline to be displayed. Subline related special characters and tags: ; : Split items on a line into separate sublines \%t : Set the subline display time. The '\%t' is followed by either integer seconds (\%t5), or seconds and tenths of a second (\%t3.5). Each alternating subline can still be optionally scrolled while it is being displayed, and scrollable formats can be displayed on the same line with non{}-scrollable formats (such as track elapsed time) as long as they are separated into different sublines. Example subline definition: \begin{verbatim} %s%t4%ia;%s%it;%t3%pc %pr : Display id3 artist for 4 seconds, Display id3 title for 2 seconds, Display current and remaining track time for 3 seconds, repeat... \end{verbatim} Conditionals can be used with sublines to display a different set and/or number of sublines on the line depending on the evaluation of the conditional. Example subline with conditionals: \%?it{\textless}\%t8\%s\%it{\textbar}\%s\%fn{\textgreater};\%?ia{\textless}\%t3\%s\%ia{\textbar}\%t0{\textgreater}\\ The format above will do two different things depending if ID3 tags are present. If the ID3 artist and title are present: Display id3 title for 8 seconds,\\ Display id3 artist for 3 seconds,\\ repeat...\\ If the ID3 artist and title are not present:\\ Display the filename continuously.\\ Note that by using a subline display time of 0 in one branch of a conditional, a subline can be skipped (not displayed) when that condition is met. \subsubsection{Using Images} You can have as many as 52 images in your WPS. There are various ways of displaying images: \begin{enumerate} \item Load and always show the image, using the \%x tag \item Preload the image with \%xl and show it with \%xd. This way you can have your images displayed conditionally. \opt{h300,x5,ipodcolor,ipodvideo}{ \item On colour screen targets only... Load an image and show as backdrop using the \%X tag. The image must be of the same exact dimensions as your display. } \end{enumerate} Example:\\ \opt{HAVE_LCD_COLOR}{ \config{\%X|background.bmp|}\\ } \config{ \%x|a|static\_icon.bmp|50|50|\\ \%xl|b|rep\_off.bmp|16|64|\\ \%xl|c|rep\_all.bmp|16|64|\\ \%xl|d|rep\_one.bmp|16|64|\\ \%xl|e|rep\_shuffle.bmp|16|64|\\ \%?mm<\%xdb|\%xdc|\%xdd|\%xde>\\ } \opt{HAVE_LCD_COLOR}{This example loads and displays a background image.} Four images at the same x and y position are preloaded. Which image to display is determined by the \%mm tag (the repeat mode). \subsubsection{Example File} \begin{verbatim} %s%?in<%in - >%?it<%it|%fn> %?ia<[%ia%?id<, %id>]> %pb%pc/%pt \end{verbatim} That is, tracknum -- title [artist, album]'', where most fields are only displayed if available. Could also be rendered as filename'' or tracknum -- title [artist]''. \subsubsection{Default} If you haven't selected a .wps file in the \fname{/.rockbox} directory, you get the hard coded layout. The default WPS screen is: \fixme{do we really want to include the default wps in a users manual?} \opt{player}{ %\begin{verbatim} %s%pp/%pe: %?it<%it|%fn> - %?ia<%ia|%d2> - %?id<%id|%d1> %pc%?ps<*|/>%pt %\end{verbatim} } \opt{HAVE_LCD_BITMAP}{ % \begin{verbatim} %s%?it<%?in<%in. |>%it|%fn> %s%?ia<%ia|%?d2<%d2|(root)>> %s%?id<%id|%?d1<%d1|(root)>> %?iy<(%iy)|> %al%pc/%pt%ar[%pp:%pe] %fbkBit %?fv %?iv<(id3v%iv)|(no id3)> %pb %pm % \end{verbatim} } \section{\label{ref:SettingsFile}Making your own settings file} A .cfg file is used to load settings from a plain text file. A .cfg file may reside anywhere on the hard disk. The only restriction is that the filename must end in .cfg Hint: Use the Write .cfg file'' feature \textbf({Main Menu$\rightarrow$ General Settings}) to save the current settings, then use a text editor to customize the settings file. See appendix \ref{ref:config_file_options} for the full reference of available options. \subsection{Format Rules} \begin{itemize} \item Format: \verb+setting: value+ \item Each setting must be on a separate line. \item Lines starting with \# are ignored. \end{itemize} \subsection{Example File} \begin{verbatim} volume: 70 bass: 11 treble: 12 balance: 0 time format: 12hour volume display: numeric show files: supported wps: /.rockbox/car.wps lang: /.rockbox/afrikaans.lng \end{verbatim} \section{\label{ref:PartISection1}Differences between binaries} There are 3 different types of firmware binaries from Rockbox website: Current Version, Daily Builds and Bleeding Edge. \begin{description} \item[Current Version.] The current version is the latest stable version developed by the Rockbox Team. It's free of known critical bugs. It is available from \url{http://www.rockbox.org/download/}. \item[Daily Builds.] The Daily Build is a development version of Rockbox. It supports all new features and patches developed since last stable version. It may also contain bugs! This version is generated automatically every day and can be found at \url{http://www.rockbox.org/daily.shtml}. \item[Bleeding Edge.] Bleeding edge builds are the same as the Daily build, but built from the latest development on each commit to the CVS repository. These builds are for people who want to test the code that developers just checked in. \end{description} \note{If you don't want to get undefined behaviour from your \dap\ you should really stick to the Current Version. Development versions may have lots of changes so they may behave completely different than described in this manual, introduce new (and maybe annoying) bugs and similar. If you want to help the project development you can try development builds and help by reporting bugs, feature requests and so so. But be aware that using a development build may eat also some more time.} \section{\label{ref:FirmwareLoading}Firmware Loading} \opt{player,recorder,recorderv2fm,ondio}{ When your Jukebox powers on, it loads the Archos firmware in ROM, which automatically checks your Jukebox hard disk's root folder for a file named \fname{archos.mod} (on the player version) or \fname{ajbrec.ajz} (on the recorder version). Note that Archos firmware can only read the first ten characters of each file name in this process, so don't rename your old firmware files with names like archos.mod.old and so on, because it's possible that the Jukebox will load a file other than the one you intended. } \section{\label{ref:using_rolo}Using ROLO (Rockbox loader)} Rockbox is able to load and start another firmware file without rebooting. You just press PLAY on an \opt{recorder,recorderv2fm,ondio}{.ajz} \opt{player}{.mod}\opt{h1xx,h300}{.iriver} \opt{ipodnano,ipodvideo,ipodnano}{.ipod} file. This can be used to test new firmware versions without deleting your current version. \opt{recorder,recorderv2fm,ondio}{\input{advanced_topics/archos-flashing.tex}}
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2023-01-27 20:45:47
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https://www.cis.upenn.edu/~cis110/current/homework/sierpinski.html
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## Part One: Recursive Exercises
### Motivation
Recursion is one of the most powerful tools in computer science. It takes a problem that may be very difficult to solve all at once and lets us solve just one part of it. Then we recursively use that logic on the rest of the problem. In the end, we have solved the greater problem just by doing a little bit of work at each step. Recursion can be used to solve enormous problems with just a few lines of code. In fact, there exist problems that can feasibly only be solved recursively! Recursion plays a major role in not just problem solving, but data structures too, which we will see later in the course. Although it’s conceptually difficult, recursion is an incredibly cool and rewarding to learn.
### Applications to Other Fields
Recursion doesn’t exist only in computer science. Other fields, like math, linguistics, and logic, all use recursion. In linguistics, for example, we can build sentences out of phrases, and these phrases can contain themselves as subphrases. For example, we can have a phrase of “big friendly giant”, which consists of an adjective, “big”, and a subphrase of “friendly giant”, which consists of an adjective, being “friendly”, and a subphrase, being “giant”. This fact means that we can make sentences that are infinitely long - all we have to do is add another level of recursion to our phrases!
### Goals
The purpose of this assignment is to gain practice with recursion. The specific goals are to:
• Complete a set of recursion exercises
• Practice writing recursive functions (and helper functions)
• Use recursion to draw a cool fractal system (Sierpinski carpet) (optional)
### Setting Up
In the Recursion Finger Exercise portion of this assignment, you will create a class of functions that each perform a different task in a recursive fashion. Solutions using iteration (for/while loops) will be given no credit. You are responsible for writing proper header comments for the class and for all the functions you will write.
You will be able to test your functions using the autograder on Gradescope, but you should absolutely write tests yourself in main() to go over various inputs, as the tests we will show on gradescope are not comprehensive nor representative of our complete testing suite.
You should create two (initially empty) java files in Codio - FingerExercises.java and, if you want to do the optional ungraded portion of the assignment, Sierpinski.java.
### Finger Exercises
For the exercises below, we have provided the method header and problem description. You may find it necessary to write helper methods for these methods if you think you need more input parameters than the provided public methods have.
Important: Note that, although there are 7 problems outlined, you only need to choose 5 of them to implement. If you implement more than 5, we will grade the first 5 functions in FingerExercises.java only. Any additional functions will automatically fail the autograder - if you’d like to see the tests for later functions, comment out the first ones you did.
Here’s an example of a problem that doesn’t use a helper method. In the code below, String.substring(x,y) is inclusive for x and exclusive for y.
public static boolean isPalindrome(String word) {
// base case - length is 0 or 1, and therefore is a palindrome.
if (word.length() <= 1) {
return true;
}
// check if first and last are the same
char firstChar = word.charAt(0);
char lastChar = word.charAt(word.length() - 1);
boolean firstAndLastMatch = firstChar == lastChar;
// if they match, recurse on the string without the first and last letters
return firstAndLastMatch && isPalindrome(word.substring(1, word.length() - 1));
}
We of course could have solved this with a helper like this:
public static boolean isPalindrome(String word) {
// return our recursive helper since we want another parameter
return isPalindromeHelper(0, word);
}
public static boolean isPalindromeHelper(int index, String word) {
// base case is we are halfway through the word and it's still a palindrome
if (index >= word.length() / 2) {
return true;
}
char firstChar = word.charAt(index);
char lastChar = word.charAt(word.length() - 1 - index);
boolean firstAndLastMatch = firstChar == lastChar;
// recurse on rest if they match - otherwise, we will return false
return firstAndLastMatch && isPalindromeHelper(index + 1, word);
}
Both solutions are equally valid - if you want to solve a problem using a helper method, you will not be penalized for doing so if there exists an implementation without the helper. You should approach these problems in the way that makes the most sense to you.
Tip: Remember to start by thinking about the base case — the smallest, simplest problem possible. From there, work out a way to get from a larger input down to the base case.
#### 1. Greatest Common Denominator (GCD)
Method Header: public static int gcd(int a, int b)
Problem Description: The Greatest Common Denominator (GCD) of two integers, $a$ and $b$, is the largest number that divides both values. One way to solve this problem is to find the prime factorization of both $a$ and $b$ and return the product of the common factors. That way takes a long time, and we can do it smarter! Euclid came up with an algorithm for this problem long before computer science existed.
1. If $a < b$, return $GCD(b,a)$
2. If $a = b$, return $b$
3. If $b = 0$ return $a$.
4. Otherwise, return $GCD(b, a \% b)$
Algorithm Explanation: One way to do GCD would be to start at 1 and keep track of the largest number that divides both values at each level. When we do that, we definitely get the right answer. Another way to think about it is subtracting by the smaller value until the bigger number is less than or equal to the smaller number. For example, say we have 40 and 12. 40 - 12 is 28, 28 - 12 is 16, 16 - 12 is 4, so the answer is 4. This process is very similar to take a modulo, as we essentially are finding the remainder after dividing the value.
This relies on the principle that the GCD of two values will not change if you replace the larger one with the difference of the larger and the smaller one. The intuition behind this is that if my GCD divides x and y, then it must be true that it will divide x−y, because x and y are just integer multiples of the GCD, so x−y is equivalent to some integer multiple of the GCD as well! For example, with 40 and 12, the GCD is 4. Let’s have the GCD be z, let 40=x, and 12=y. We therefore can say x−y=10z−3z=7z, and 7z is of course an integer multiple of the GCD!
If you’re still curious to learn more about Euclid’s algorithm, take a look at its wikipedia page, specifically the “Description” and “Proof of Validity” subsections!
Invariant: You may assume that both $a$ and $b$ are positive numbers (0 is not positive).
#### 2. Cumulative Sum
Method Header: public static int sumBetween(int a, int b)
Problem Description: The goal is to find the sum of the values from $a$ to $b$. In math, we would write this problem as $\sum_{i=a}^{b} i$. You must also do 2.1 if you choose this question.
Invariants: You can assume that $a \leq b$ for all inputs.
#### 2.1
Method Header: public static int sumTo(int x)
Problem Description: Now, write another method to find the sum of values from 1 to $x$. Think about how you can take advantage of prior code to solve this problem.
Invariants: You can assume that $x >= 1$.
#### 3. Find Second Largest
Method Header: public static int findSecondLargestHelper(int largest, int secondLargest, int index, int[] nums)
Problem Description: Given an array of integers, find the second largest value in the array. We are going to be implementing a helper function for this - you should add this to your program as the public method and then write the helper function with the method header presented above.
public static int findSecondLargest(int[] nums) {
return findSecondLargestHelper(Integer.MIN_VALUE, Integer.MIN_VALUE, 0, nums);
}
Invariants: You may assume that the array is not null and has at least 2 different elements.
Important: If the array is something like [2, 2, 1], you should return 2. The reason for this is as that if we removed the largest element, the new largest element would still be 2.
#### 4. Sum of Digits
Method Header: public static int sumOfDigits(int x)
Problem Description: Write a recursive function to calculate the sum of the digits of number. For example, sumOfDigits(74296) should return 28 as 7 + 4 + 2 + 9 + 6 = 28.
Invariants: You may assume that $x \geq 0$.
#### 5. Count Ways to Climb Stairs
Method Header: public static int countWaysToClimb(int stairs)
Problem Description: Given an amount of stairs to climb, calculate the number of ways to climb taking either 1 or 2 steps at a time. For example, if there are 4 stairs, we would return 5, as there are the following options:
1, 1, 1, 1
1, 1, 2
1, 2, 1
2, 1, 1
2, 2
Invariants: You may assume that the stairs >= 0. If stairs is 0, you should return 1.
#### 6. Log
Method Header: public static int log(int base, int n)
Problem Description: A log operation is the inverse of an exponential operation. As a refresher, given some base $b$ and some value $n$, we can calculate $log_{b}n$ by seeing how many times we have to multiply $b$ by itself until we reach $n$. For example, $log_{10}1000 = 3$, and $log_{b}1 = 0$ for all $b$.
Invariants: Although you cannot assume that there exists an exact solution x such that $base^x = n$, you can assume that base <= n for all inputs, that base and n are positive integers greater than 1. That means no natural logs!
If there is no exact integer solution x, you should return the truncated answer - that is, if we are given log(2, 33), we should return 5, not 6. This is not as complicated as it sounds, and if you write out what the recursion would look like by hand, you’ll see why.
#### 7. CountSubstrings
Method Header: public static int countSubstrings(String sequence, String word)
Problem Description: We want to find how many times a sequence appears in a particular word. For example, in the word “banana”, the sequence “na” appears two times, with “baNAna” and “banaNA”. We also have “ana” appear two times, being “bANAna” and “banANA” - note that this means that we can have overlaps between the starts of our sequences (this actually makes the problem easier!)
Invariants: You may assume that neither sequence nor word are null, and that both have positive lengths (0 is not positive.) You may also assume that the strings are both all lowercase.
Hint: The function String.substring(x, y) will be helpful here.
//Example:
String className = "cis110";
String department = className.substring(0, 3);
String number = className.substring(3, className.length());
System.out.println(department); // prints "cis"
System.out.println(number); // prints "110"
### Extra Credit
#### How Different?
Method Header: public static int howDifferent(String one, String two)
Problem Description: This is the most interesting problem of what we’ve seen so far. Given two strings, we want to find out what the least amount of changes we would have to make to one of the strings to get to the other. There are three ways we can change a string. 1, we can replace a letter with another letter. 2, we can delete a letter. 3, we can add a letter. Here are some examples to help make this clear.
Example 1: code, coder. We can add one letter to the first string, being an r, to make the strings match, so this should return 1.
Example 2: mouse, must. We see that both share the same first letter, so we don’t have to make any changes there. Then, we can delete the o in mouse, then, the next letter is s for both strings, and then we can change the e into a t to make both into must. That’s a total of 2 changes. There are other ways we could have transformed the first string into the second, but this is the one with the least changes, and that’s what we’re interested in.
## Part Two: Sierpinski: Optional Assignment
In this assignment, you will write a program Sierpinski.java that recursively draws a Sierpinski carpet using PennDraw. These instructions will walk you through the process step by step.You are not allowed to use PennDraw.setXScale(), PennDraw.setYScale(), or any scale changing in this assignment. Doing so will only make the assignment harder.
### A. The main() function
Write a main() function that calls the PennDraw.filledSquare() function to draw a square with sides of length 1.0 / 3.0 with the center vertex located at (0.5, 0.5). Later, you will modify main() to draw the full Sierpinski carpet.
When you compile and run your program, you should see a square in the center of your window.
### B. Setting up the recursive structure of sierpinski()
Write a function sierpinski() that takes two parameters, numLevels and halfSideLength. Your function should print both parameters, before recursively calling itself eight times with the arguments numLevels - 1 and halfSideLength / 3. The recursion should stop when numLevels is less than 1. Later, you will replace the print statements with a call to PennDraw.filledSquare(). Modify main() to interpret its first command-line argument as numLevels. Have it call sierpinski(numLevels, 1.0 / 6.0). You may assume that your program will be run with exactly one command-line argument that is a positive integer.
### C. Checkpoint
Running your program with the following command-line arguments should produce the following output:
java Sierpinski 0
(no output)
java Sierpinski 1
1 0.16666666666666666
java Sierpinski 2
2 0.16666666666666666
1 0.05555555555555555
1 0.05555555555555555
1 0.05555555555555555
1 0.05555555555555555
1 0.05555555555555555
1 0.05555555555555555
1 0.05555555555555555
1 0.05555555555555555
java Sierpinski 3
3 0.16666666666666666
2 0.05555555555555555
1 0.018518518518518517
1 0.018518518518518517
1 0.018518518518518517
1 0.018518518518518517
1 0.018518518518518517
1 0.018518518518518517
1 0.018518518518518517
1 0.018518518518518517
2 0.05555555555555555
1 0.018518518518518517
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### D. Drawing the Sierpinski carpet in sierpinski()
Comment out the print statements from sierpinski().
Modify sierpinski() to take two additional arguments, x and y, and draw a Sierpinski carpet of order numLevels of size 2 * halfSideLength centered at (x, y). Remember that if you have more than 85 characters on a single line, you need to break the line up. This can be done by putting a linebreak between arguments. Your recursive calls may be in any order you like.
Think recursively. A Sierpinski carpet of order numLevels comprises just a solid square and eight smaller Sierpinski carpets, each one third the size of the original, each of order numLevels - 1, to the four cardinal directions plus the four diagonals relative to the center square. The distance between the center of the original square and the center of the smaller squares should be 2 * halfSideLength of the original in both the $x$ and $y$ directions. You have already written the function to draw the square and the recursion code from the previous steps – now, you only need to make the correct function calls.
Warning: Do not call PennDraw.setCanvasSize(), or PennDraw.save(). These functions will break our test scripts, and you will receive a large point deduction.
### E. Checkpoint
Running your program with the command-line arguments below should produce the following output.
### F. Animating
Once you have your Sierpinski carpet working, add calls to PennDraw.enableAnimation() and PennDraw.advance() into your sierpinski() function. (You are not required to animate your Sierpinski carpet, and it is not worth any points, but it is fun and will help you visualize the recursion. If you do add animation, leave it in your code: it will not affect our grading scripts.) Experiment with different arrangements of the recursive calls to sierpinski().
### Submissions
Please complete the readme and then submit FingerExercises.java and recursive_readme.txt on Gradescope.
Note that we will only run tests for the first 5 finger exercises you completed - the rest will automatically fail. If your grade is a 35, that means you’ve passed all the tests that you should have.
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2020-10-29 20:39:16
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https://en.wikibooks.org/wiki/Calculus/Derivatives_of_Trigonometric_Functions
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# Calculus/Derivatives of Trigonometric Functions
← Product and Quotient Rules Calculus Chain Rule → Derivatives of Trigonometric Functions
Sine, cosine, tangent, cosecant, secant, cotangent. These are functions that crop up continuously in mathematics and engineering and have a lot of practical applications. They also appear in more advanced mathematics, particularly when dealing with things such as line integrals with complex numbers and alternate representations of space like spherical and cylindrical coordinate systems.
We use the definition of the derivative, i.e.,
${\displaystyle f'(x)=\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}}$ ,
to work these first two out.
Let us find the derivative of sin(x), using the above definition.
${\displaystyle f(x)=\sin(x)}$ ${\displaystyle f'(x)=\lim _{h\to 0}{\frac {\sin(x+h)-\sin(x)}{h}}}$ Definition of derivative ${\displaystyle =\lim _{h\to 0}{\frac {\cos(x)\sin(h)+\cos(h)\sin(x)-\sin(x)}{h}}}$ trigonometric identity ${\displaystyle =\lim _{h\to 0}{\frac {\cos(x)\sin(h)+(\cos(h)-1)\sin(x)}{h}}}$ factoring ${\displaystyle =\lim _{h\to 0}{\frac {\cos(x)\sin(h)}{h}}+\lim _{h\to 0}{\frac {(\cos(h)-1)\sin(x)}{h}}}$ separation of terms ${\displaystyle =\cos(x)\times 1+\sin(x)\times 0}$ application of limit ${\displaystyle =\cos(x)}$ solution
Now for the case of cos(x).
${\displaystyle f(x)=\cos(x)}$ ${\displaystyle f'(x)=\lim _{h\to 0}{\frac {\cos(x+h)-\cos(x)}{h}}}$ Definition of derivative ${\displaystyle =\lim _{h\to 0}{\frac {\cos(x)\cos(h)-\sin(h)\sin(x)-\cos(x)}{h}}}$ trigonometric identity ${\displaystyle =\lim _{h\to 0}{\frac {\cos(x)(\cos(h)-1)-\sin(x)\sin(h)}{h}}}$ factoring ${\displaystyle =\lim _{h\to 0}{\frac {\cos(x)(\cos(h)-1)}{h}}-\lim _{h\to 0}{\frac {\sin(x)\sin(h)}{h}}}$ separation of terms ${\displaystyle =\cos(x)\times 0-\sin(x)\times 1}$ application of limit ${\displaystyle =-\sin(x)}$ solution
Therefore we have established
Derivative of Sine and Cosine ${\displaystyle {\frac {d}{dx}}\sin(x)=\cos(x)}$ ${\displaystyle {\frac {d}{dx}}\cos(x)=-\sin(x)}$
To find the derivative of the tangent, we just remember that:
${\displaystyle \tan(x)={\frac {\sin(x)}{\cos(x)}}}$
which is a quotient. Applying the quotient rule, we get:
${\displaystyle {\frac {d}{dx}}\tan(x)={\frac {\cos ^{2}(x)+\sin ^{2}(x)}{\cos ^{2}(x)}}}$
Then, remembering that ${\displaystyle \cos ^{2}(x)+\sin ^{2}(x)=1}$ , we simplify:
${\displaystyle {\frac {\cos ^{2}(x)+\sin ^{2}(x)}{\cos ^{2}(x)}}}$ ${\displaystyle ={\frac {1}{\cos ^{2}(x)}}}$ ${\displaystyle =\sec ^{2}(x)}$
Derivative of the Tangent ${\displaystyle {\frac {d}{dx}}\tan(x)=\sec ^{2}(x)}$
For secants, we again apply the quotient rule.
${\displaystyle \sec(x)={\frac {1}{\cos(x)}}}$
{\displaystyle {\begin{aligned}{\frac {d}{dx}}\sec(x)&={\frac {d}{dx}}{\frac {1}{\cos(x)}}\\&={\frac {\cos(x){\frac {d1}{dx}}-1{\frac {d\cos(x)}{dx}}}{\cos(x)^{2}}}\\&={\frac {\cos(x)0-1(-\sin(x))}{\cos(x)^{2}}}\end{aligned}}}
Leaving us with:
${\displaystyle {\frac {d}{dx}}\sec(x)={\frac {\sin(x)}{\cos ^{2}(x)}}}$
Simplifying, we get:
Derivative of the Secant ${\displaystyle {\frac {d}{dx}}\sec(x)=\sec(x)\tan(x)}$
Using the same procedure on cosecants:
${\displaystyle \csc(x)={\frac {1}{\sin(x)}}}$
We get:
Derivative of the Cosecant ${\displaystyle {\frac {d}{dx}}\csc(x)=-\csc(x)\cot(x)}$
Using the same procedure for the cotangent that we used for the tangent, we get:
Derivative of the Cotangent ${\displaystyle {\frac {d}{dx}}\cot(x)=-\csc ^{2}(x)}$
← Product and Quotient Rules Calculus Chain Rule → Derivatives of Trigonometric Functions
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2020-08-08 20:46:03
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https://codeforces.com/blog/entry/93018
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dario2994's blog
By dario2994, 19 months ago,
Hi!
On Jul/25/2021 17:35 (Moscow time) we will host Codeforces Global Round 15.
This is the third round of the 2021 series of Codeforces Global Rounds. The rounds are open and rated for everybody.
The prizes for this round are as follows:
• 30 best participants get a t-shirt.
• 20 t-shirts are randomly distributed among those with ranks between 31 and 500, inclusive.
The prizes for the 6-round series in 2021:
• In each round top-100 participants get points according to the table.
• The final result for each participant is equal to the sum of points he gets in the four rounds he placed the highest.
• The best 20 participants over all series get sweatshirts and place certificates.
Thanks to XTX, which in 2021 supported the global rounds initiative!
Problems for this round are set by cip999 and me. Thanks a lot to the coordinator antontrygubO_o, to the testers gamegame, ajit, golions, skydogli, McDic, rabaiBomkarBittalBang, nweeks, Marckess, HenriqueBrito, gratus907, bWayne, zscoder, TheOneYouWant, and to MikeMirzayanov for the Codeforces and Polygon platforms.
You will be given 9 problems and 2 hours 45 minutes to solve them.
The scoring distribution is 250-500-1000-1000-1500-1500-2500-2750-3750.
If you are tempted to make one more comment on the scoring distribution, read this.
Good luck and see you in the standings!
UPDATE 1: Thank you very much for participating, we hope you liked the problems (and sorry to top contestants for giving a not-so-fresh problem I).
Here you can find the editorial (with a bit of behind-the-scenes, some obscenely wrong preditions, and hints for all the problems).
UPDATE 2: Congratulations to the winners!
Announcement of Codeforces Global Round 15
• +823
| Write comment?
» 19 months ago, # | ← Rev. 2 → +277 Time to upsolve global round 11.
• » » 18 months ago, # ^ | ← Rev. 4 → +139 People be like: See a fun comment: upvote; See a comment discussing testers of a contest: downvote; See a red coder write a comment: upvote; See a comment with a lot of downvotes: downvote; See somebody praying to reach a higher level: downvote
• » » » 18 months ago, # ^ | +85 When my contribution exceeds a hundred, I will make an stream with an analysis of the 11th global round !!!
• » » » » 18 months ago, # ^ | +23 Good luck, sir :)
• » » » » 18 months ago, # ^ | +9 Good luck.
• » » » » 16 months ago, # ^ | +5 ivanz Hey! any plans for the stream? you have crossed 100
• » » » 18 months ago, # ^ | +9 True!!!
• » » » 18 months ago, # ^ | +5 True! SpoilerSo I hate posting comments
• » » » 18 months ago, # ^ | +20 So you thought people will read this comment and just hit the upvote button as well?
• » » » 18 months ago, # ^ | +8 Your comment falls into fun category. Take my upvote!
» 19 months ago, # | -56 Can we say "All hail our emperor Anton" here? :)
» 18 months ago, # | -95 I'm a simple man. I see anton, I take part.
• » » 18 months ago, # ^ | +200 People be like: I'm a simple man. I see T1dus, I downvote.
• » » » 18 months ago, # ^ | -93 Imagine banning someone for a ping
• » » » » 18 months ago, # ^ | +40 Imagine that ping being mulitplied 20 times as much.
» 18 months ago, # | +2 So we will have 3hrs or 2:30? Cuz on the contest table it says that it lasts 2:30hrs. Thx;)
• » » 18 months ago, # ^ | 0 I guess it's 2:30 as per the contests table
• » » » 18 months ago, # ^ | +3 Already fixed at 2: 45
» 18 months ago, # | +175 As a tester who has not been yet added to the contest announcement, I can say that solving the problems will make you feel warm and fuzzy inside. I am very sad that I cannot participate in this contest.
• » » 18 months ago, # ^ | -48 I would like to say that some youtube channels provide solution code during contest is running it is totally unfair to most of the participants plz take proper steps to stop this.
• » » » 18 months ago, # ^ | +22 bruh you are indirectly promoting that, better we talk less about it and more focus on learning from the round by participationg
• » » » » 18 months ago, # ^ | -17 You're right but if the Authority of Codeforces shouldn't take proper step the day is not so far even high rated like >=1600 rated problem solution will also find during contest time.We all want a fair contest.
• » » » » » 18 months ago, # ^ | +52 don't cry about it, just solve more problems than the distributor.
• » » » 18 months ago, # ^ | +5 Just be faster, most cheaters take a long time to do even A, genuine coders can easily outpace them.
• » » 18 months ago, # ^ | +11 To perform better, should i solve the author's previous contests? Please give me some suggestions as i am a newbie.
• » » » 18 months ago, # ^ | 0 authors usually give some variety to their problems, it will never be said enough: to get better don't cheat the system just train and keep practicing
• » » 18 months ago, # ^ | +17 warm and fuzzy feeling! you mean pain!!
• » » 18 months ago, # ^ | ← Rev. 2 → 0 Lol no wonder why a grandmaster gains satisfaction from solving all problems:)
• » » » 18 months ago, # ^ | +39 Re: your original comment: I wrote "very sad" because it turns out I did quite decently in testing. If I didn't have to travel, this would have been my first H solved in contest + maybe IGM. Now, it is just another missed (possibly) LGM performance..
» 18 months ago, # | ← Rev. 2 → +31 My first global round, exited to see the problems and maybe cry afterwards :)
• » » 18 months ago, # ^ | ← Rev. 2 → +12 So "exited" that you wrote "exited" instead of excited.
• » » » 18 months ago, # ^ | +19 lol didn't notice that :) hahaha
• » » 18 months ago, # ^ | ← Rev. 7 → -103 good luck
• » » » 18 months ago, # ^ | 0 🚀 Here we gooooooo
• » » » » 18 months ago, # ^ | ← Rev. 2 → -23 Why?
• » » » » » 18 months ago, # ^ | +15 people showing there hate for recursion I guess lmao
• » » » » » » 18 months ago, # ^ | -13 I guess you're right.
» 18 months ago, # | -57 I have 2 questions: Why is there a sudden drop of average difficulty(upto problem E/F) in recent combined rounds? There are 6 problems for div.3 participants (with difficulty <1600), which used to be 3/4. To div. 1 participants (2100+), how do you feel facing a 250 rated problem in a contest, that is rated for you?
• » » 18 months ago, # ^ | +82 Points and difficulties have no correlation whatsoever. Difficulty is determined after the contest ends, while point values are there to give us a rough approximation of relative level of these problems. E. g. If two problems both weigh X points that means they are similar in difficulty, but that difficulty could be anything from 800 to 3500 theoretically.
» 18 months ago, # | +87 I am also wondering why the starting score drops from 500 to 250 in joint rounds. I kind of understand that this will make the score’s meaning more similar to div. 1. But this actually hurts the feeling of div. 2’s participants, which is a much bigger group. So I doubt if the other direction is better. I remember that 15 years ago, most OI problems had exactly 10 test data, and each data was worth 10 points, and in total each problem had exactly 100 points. Then people ask Rujia Liu, one of the most famous problem setters in China at that time: “why we have 100 points for each problem instead of 10, we can give each test data 1 point, it’s the same, right?” And Rujia said: “because people are more excited to see large numbers, and giving 100 points makes people feel more comfortable and gives people more sense of accomplishment”.I think it's the same here, right? Doubling the points of all problems (and possibly making some adjustment), you won’t change/lose anything. But people will become more excited. When solving a 3000 point problem in the contests, regardless of its difficulty, the feeling is different than solving a 1500 point problem. I definitely do not mean that we should arbitrarily increase the points of problems. But always starting from 500 seems to be reasonable.
• » » 18 months ago, # ^ | +113 Hacks and unsuccessful submissions are still worth the same number of points though. And if you double every one of them, we will have a 5000, 5500 and 7500 problem.
• » » » 18 months ago, # ^ | +84 This is an even better argument for increasing the overall point values; 50 points is a steep penalty for an incorrect submission when A is only worth 250 and might not even be worth 150 points when solved at the end of the contest.
• » » » » 18 months ago, # ^ | +21 It probably has more to do with emphasizing the benefit of solving harder problems. You can check the scoring distribution from the author's last round (Codeforces Global Round 11). There was a 4500 point problem while the 1500 point problem was solved by only 267 people.
• » » 18 months ago, # ^ | -41 I think that having 300 points for the first problem would feel a bit better than 250. It's just a more round number. Also it's more than half of 500, rather than exactly half. Not that it really matters, but this might make people feel more comfortable. Especially complete beginners, for whom the first problem might be the only solved problem during the whole contest.
• » » » 18 months ago, # ^ | +65 I think the number 250 is more "round" than 300.
• » » » » 18 months ago, # ^ | +91 256 is even rounder for contestants eyes
• » » » » 18 months ago, # ^ | -14 Could you elaborate on this please? 300 is rounded up to the nearest hundred. There's also a well known marketing trick to set prices to something like 299 instead of 300, because this is somehow perceived as noticeably cheaper by humans (the first digit is smaller, yay!).And once again. Looking from a total beginner perspective, a very late solver of only the first problem will only get 75 points because of decay and possible WA penalties. The leaders of the contest may get around 16k points, based on what we could see in the scoreboard of the previous contest with a similar 250-for-the-first-problem points distribution. That's more than 200 times difference. With the older 500 max points reward for the first problem, the beginners would only have around ~100 times worse score than the leaders and this smaller difference may make them feel a bit happier (or less devastated). But of course, none of this really helps them to actually get a better position in the scoreboard, it's all just an illusion.My comments had been largely inspired by the CLDP's quotation of Rujia Liu about the magic of 100 points. I think that I already said enough and have no intention to push this further.
• » » 18 months ago, # ^ | +132 Personally, I have never paid attention to the raw amount of points I got in a contest. I was always focused on my ranking. Maybe I'm in the minority though.
• » » » 18 months ago, # ^ | +17 Same here. Regarding a problem, the only number I care about is how many people solve it.
• » » 18 months ago, # ^ | +90 I don't see how using 250 hurts the feelings of div2 participants. Will they be happier if we multiple everything by 10?There's currently an upper limit of 6000 points per problem in the Codeforces system. You would need almost twice that if you want to keep reasonable geometric progression — which is needed to allow solving problems in a different order, and not to penalize much for failing a medium problem (but solving a hard one instead and getting less points).
• » » » 18 months ago, # ^ | -90 I don't see how using 250 hurts the feelings of div2 participants. As a part of optimization efforts in some company, CEO and the other higher-ups mostly kept their salaries intact, but burger-flippers got their salaries halved. We surely didn't hurt the burger-flippers' feelings, did we? Don't worry, this is just a joke. Will they be happier if we multiple everything by 10? What kind of problem have you actually tried to fix when changing the problem A score from 500 to 250 in the first place? Now this is a serious question.We got a discrepancy between 500 points in Div2 contests and 250 points in Div1+2 contests for 800-difficulty problems. If any inexperienced grey participant watched their contest score to roughly estimate their individual progress (without comparing themselves to the others), then this change affected them. But only grey participants can provide useful feedback here. Most of them are shy and afraid of downvotes.
• » » » » 18 months ago, # ^ | +113 What kind of problem have you actually tried to fix when changing the problem A score from 500 to 250 in the first place? I explained it in the previous comment: we needed to choose a reasonable ratio between scores of different problems. If any inexperienced grey participant watched their contest score to roughly estimate their individual progress (without comparing themselves to the others) [...] Then I hope that they read this: total points or the number of solved problems doesn't matter. Maybe you got one more problem because it was easy. Only your rank says how well you performed.I don't think it's smart to mess up problem points distribution for everybody just because some inexperienced participants focus on wrong statistics.
• » » 18 months ago, # ^ | +115 Very good point.I think we should also set everyone's rating to 1500. It might hurt their feelings when their rating is stuck at 1000.
• » » » 18 months ago, # ^ | +26 While we are at it, can I get +400 delta, I'm very hurt with my current rating.
• » » 18 months ago, # ^ | 0 I think I've been advocating starting from 250 for a long time already. It allows for better balancing of harder problems. Even with 250pts the ratio pts/needed time is still the lowest for the easiest problems
» 18 months ago, # | +46 As a tester, I recommend you to read all the problems. (just check the scoring distribution).
» 18 months ago, # | 0 As a DIV 3 user , should I participate in this round or not because I think this round will be of div1 level and I will not able to solve such hard questions.
• » » 18 months ago, # ^ | +22 This round will have tasks of all levels, and the round itself is "GLOBAL", which also indicates that everyone can participate, so anyone can participate and it will be interesting for him.
• » » 18 months ago, # ^ | +2 So, I am <1200 and I definitely will participate, because I’m absolutely sure that I’ll solve 2 problems at my worst.
» 18 months ago, # | +13 As a tester, I must say the quality of problems are really good, all the best and have fun :)
» 18 months ago, # | -8 Hope I will become expert in this round
» 18 months ago, # | ← Rev. 2 → -13 Why do I feel like authors are meme-ing around after looking at the score distribution ? Edit : I dont have any problem with downvotes, but I would very much like to know the reason you people are doing so. I just said what I observed, atleast I have never seen a combined round F to be only worth 1500 points.
» 18 months ago, # | 0 Just a simple question: If after system testing, my solution still shows 'in queue' status, so will it corrected itself. Or we have to report it somewhere. Btw, when I click on more details about submission, it shows all test cases to be OK.
» 18 months ago, # | +4 just curious about the 250 points problem, why points didn't decrease after the first minute here ?
• » » 18 months ago, # ^ | +19 The points decreased per minute is proportional to its starting score. A 250 problem ends at 150? I believe (either 3/5 or 2/5 of original), so each minute it's decreasing by 100 / (total_contest_time), which was 150 for that contest. This value is less than 1, so sometimes it'll round up I guess.
» 18 months ago, # | +187 I'm not a tester but I like past problems created by dario2994.
• » » 18 months ago, # ^ | +22 Errichto You will not be disappointed :)
» 18 months ago, # | -37 will this round be rated.
• » » 18 months ago, # ^ | +4 Read the announcement :)
» 18 months ago, # | -20 So the reason for this scoring distribution is the same as it was in Global Round 11 ??
» 18 months ago, # | -34 Last time i saw a similar scoring distribution, C and D were 2000R and E was 2500R. HintIt was GR11. AlsoThe problems were nice for upsolving :)
» 18 months ago, # | 0 250 has become fashionable, we expect 150.
• » » 18 months ago, # ^ | +5 I would propose that A will be worth 69 points and B 420 points. That is more fashionable.
• » » » 18 months ago, # ^ | -19 Support!!!
» 18 months ago, # | +37 As a tester, I enjoyed this round's problems. GLHF!
• » » 18 months ago, # ^ | 0 There is some problem in the testing of problem E.For my solution: https://codeforces.com/contest/1552/submission/123763122It shows colour don't match for 3rd interval in test case 3 despite colour are the same. Please look at this and accept my solution if it is correct.
» 18 months ago, # | +1 It's equally sad and satisfying to read this "20 t-shirts are randomly distributed among those with ranks between 31 and 500, inclusive."
» 18 months ago, # | ← Rev. 2 → +63 As a tester, I would recommend you try to solve the problems in the contest.
• » » 18 months ago, # ^ | 0 As a participant i would recommend all to upvote the above comment;)
• » » » 18 months ago, # ^ | +23 I upvote only after the round ends
» 18 months ago, # | -42 It seems that experts are going to solve the first six problems (A-F)
• » » 18 months ago, # ^ | +3 So much about that lol...
» 18 months ago, # | +71 lighthearted meme
» 18 months ago, # | ← Rev. 2 → -145 India won a medal in tokyo olympics . congrats!
• » » 18 months ago, # ^ | +18 This isn't the place to discuss these topics
• » » 18 months ago, # ^ | +70 When do you think competitive programming will be an official Olympic sport?
• » » » 18 months ago, # ^ | +34 after chess is...
» 18 months ago, # | 0 How many problems a newbie can expect to solve?
• » » 18 months ago, # ^ | +42 One and game over
• » » » 18 months ago, # ^ | +10 Damn you bastard, you were right
» 18 months ago, # | +1 Good luck, guys!
» 18 months ago, # | +29 I bet today the new record will be written by tourist... 3800+ is coming guys...
• » » 18 months ago, # ^ | 0 Congratulations, you've won the bet.
» 18 months ago, # | +4 Hardforces
» 18 months ago, # | +19 D.E.A.D
» 18 months ago, # | ← Rev. 2 → +15 Is this round meant for Div 0 participants?
• » » 18 months ago, # ^ | +12 No, its for Div -1 participants
» 18 months ago, # | +45 single problem solvers make some noise!!
» 18 months ago, # | 0 people like me Less than 1400 rating should exit the codeforces! its not for us. Try leetcode instead zero wasted of time and actually will learn something helpful Uselessforces!
• » » 18 months ago, # ^ | +5 your nickname really tells alot
• » » » 18 months ago, # ^ | +14 It is demoralizing to see this kind of contest though. I was aiming for CM this summer and now I'm dropping to specialist, though I got top 500 rank on ARC today. I definitely think ARC C should be harder than Global Round C, yet I struggle to solve even B here, just wasted 2 hours of my time and 150 points of rating on this one. :P
» 18 months ago, # | +26 It seems someone put the wrong title on this contest, the title should have been "Codeforces Round #735 (Div.0)"
» 18 months ago, # | ← Rev. 2 → +56 Difficulty difference between A and B > length of the wall of china
» 18 months ago, # | +22
» 18 months ago, # | +16 Is this the sound of shattered dreams?
» 18 months ago, # | +6 C is too hard to me:(
• » » 18 months ago, # ^ | +16 All questions are too hard for me.
» 18 months ago, # | +14 there should be atleast 2 easy problem as it is a global round. maybe they can make b little bit easy :(
» 18 months ago, # | +27 Instead of running for gold, pupils are running for newbie and specialists are running for pupil. :)
» 18 months ago, # | ← Rev. 2 → +39 How on earth Tourist did first 4 questions in 8 minutes!!! I need that much time just to read those questions :( GOD LEVEL
• » » 18 months ago, # ^ | +15 and the last question in the next 6 minutes
» 18 months ago, # | +7 As the round is rated for all, they should have made two easy problems.
» 18 months ago, # | +7 Is the 3800-mark going to be breached?
• » » 18 months ago, # ^ | +3 First time we are going to see 3800 rating.
» 18 months ago, # | +81 Problems are good but I am trash :(
» 18 months ago, # | +27 I decided to take this contest with 4 hours of sleep since I wanted to hit GM today :P seems like it didn't backfire. Thank you for the nice problems, E especially was very cool. Hopefully I don't FST now and it's time to have an irrational fear of participating in contests again D:
» 18 months ago, # | 0 There is some problem in the testing of problem E.For my solution: https://codeforces.com/contest/1552/submission/123763122It shows colour don't match for 3rd interval in test case 3 despite colour are the same. Please look at this and accept my solution if it is correct.
• » » 18 months ago, # ^ | 0 numbers a_i and b_i should both be in i-th color. In your case a_3 and b_3 are both in 2nd color
» 18 months ago, # | +12 To any gray writing that this should be called Div. 0: you don't even know what solving the first problem in Div. 1 means. Who the fuck are you to judge the difficulty besides saying "this is too hard for Div. 2"?
• » » 18 months ago, # ^ | +2 Said an unrated user.
• » » » 18 months ago, # ^ | 0 dude, alt...
» 18 months ago, # | +1 man how the hell the 5th test case in D is YES there's no 3 numbers that can produce one of them I tried everything but I suck
• » » 18 months ago, # ^ | 0 try this 174+(-171) = 250+100.
» 18 months ago, # | +1 Problem 407B - Long Path is very similar to problem F, especially main observation.
» 18 months ago, # | +31 Why did none of the testers question this difficulty gradient?
» 18 months ago, # | 0 Problem F saved me from going back to cyan :)
» 18 months ago, # | +10 Is problem D just try 10! combinations? I am kinda afraid of system tests.
• » » 18 months ago, # ^ | 0 Gotta admire the confidence!!
» 18 months ago, # | +47 Doing typing practice for 2 hours and 45 minutes would have helped my coding career more than giving this round!
» 18 months ago, # | +3 I got my worst rank :(
» 18 months ago, # | +60 Somehow I found F and D easier than B. Also RIP rating.
• » » 18 months ago, # ^ | 0 How to solve D? Got wa on pretest 2
• » » » 18 months ago, # ^ | +4 There mush exist some i such that a[i] = sum(x*a[j]) for all 1<=j<=n and i!=j and -1<=x<=1
• » » » 18 months ago, # ^ | +17 It is enough to check if there are two disjoint non-empty subsets that have the same sum
• » » » 18 months ago, # ^ | 0 The constraints are really small for n, so you can use bitmasks to represent the subsets and check if an element outside of this subset can be represented in terms of addition and subtraction of the elements in the subset.
» 18 months ago, # | +46 The most pretests I have seen
» 18 months ago, # | +7 Can someone explain the approach to B?
• » » 18 months ago, # ^ | 0 Sort then check if a[0] is the winner.
• » » » 18 months ago, # ^ | 0 Can you explain a little bit more how this will work?
• » » » 18 months ago, # ^ | ← Rev. 2 → +3 Sounds intuitive, but how do you precisely sort the atheletes and why does it actually work?
• » » » » 18 months ago, # ^ | 0 sort with custom function. if a won >=3 rounds then true otherwise false.
• » » » » » 18 months ago, # ^ | 0 This won't work exactly ig as this comparator doesen't imply transitivity. For ex,if A is superior to B and B is superior to C then we can't conclude that A is superior to C since something like below can be the results for the 5 races (A>B here means that A outperformed B in this race): A>B>C, A>B>C, C>A>B, C>A>B, B>C>A. Hence,a better strategy would be to first compare player 1 to 2,then the superior of them to 3,then superior of them to 4 and so on till player n. The remaining player will be the only candidate for gold,so just compare this player with all other players again to check whether it is indeed a valid answer.
• » » » » 18 months ago, # ^ | +1 I used a comparator function for B 123741857
• » » 18 months ago, # ^ | -44 The key observation is, that if a>b and b>c, then a>c. So sort and check if first beats all.
• » » » 18 months ago, # ^ | ← Rev. 2 → +9 It's not true, is it?a > b and b > c but c > a310 10 20 30 3020 20 30 10 1030 30 10 20 20
• » » » » 18 months ago, # ^ | 0 :/ Maybe that's why I needed 9 submission and 2:36h. What a sic problem.
• » » 18 months ago, # ^ | +12 Assume the curr_winner is 0th participant. Now, iterate through all the remaining participants. If, the winner is superior to the ith participant, we are fine, otherwise, change winner as ith participant ( because i defeats curr_winner ) and continue checking till the end.Once done, we have a candidate for winner. We just need to iterate again through all remaining participants and ensure that he defeats everyone ( and there is not a cycle in which case return -1 )
• » » 18 months ago, # ^ | 0 start comparing the first athlete with other athletes if he is superior then all of those who got compared to him are definitely not and if he's not superior to the current athlete being compared then this current athlete could be the one so start comparing from this athlete with the next athletes if you compare him with the previous athletes it will TLE so keep doing that until you have one possible athlete now compare him to all the others if he is superior then answer is that athlete if not there's no answer
• » » 18 months ago, # ^ | +3 Only one overall winner is possible. If an athlete is not superior to any other athlete, he cannot be the winner. Suppose prev[i] is the best choice for first i athletes, then prev[i+1] will be i+1 if i+1 is superior to prev[i] or prev[i+1]=prev[i] if prev[i] is superior to i+1. prev[1]=1. Now you just need to check whether prev[n] is superior to all.
• » » 18 months ago, # ^ | 0 Compare No.(i) person with No.(i+1) person.(1<=i
• » » 18 months ago, # ^ | +5 Notice that for any two athletes a and b, either a is superior or b is superior. Since our goal is to have an athlete that is superior to all others, every time we compare any two athletes, we can remove the 'not superior' athlete from our list of candidates.So we can perform n-1 comparisons and have exactly 1 candidate left. Now, we can check if this candidate is superior to all others. If not, then there are no more candidates so we print -1. Otherwise, this candidate is our answer.
• » » 18 months ago, # ^ | 0 Apply two pointer's approach, take initially l as 0 and r as n-1 now compare between them if l is winner,it means r is eliminated hence decrement r. and vice-versa, finally you will get the ans as l ,check whether l is the real winner or not
• » » 18 months ago, # ^ | 0 My approach: Iterate through all the players and in each iteration compare two-player and eliminate one player, the one with fewer wins. first player 1 vs 2, second, winner of (1 vs 2) vs 3, and so on.So after a complete iteration, only one player will remain. Now just need to check if he is better than all others or not. So one more iteration through all other players and Check if the candidate won 3 or more previous games with all others or not.
» 18 months ago, # | +12 This contest made me realise again that you know nothing and you are stil a beginner who is meant to struggle .
» 18 months ago, # | +79 Getting WA on pretest 127 is something new.
• » » 18 months ago, # ^ | 0 it's the opposite of last round I guess.
» 18 months ago, # | +98 According to the standings (i.e. tourist), I believed that Problem I had appeared somewhere. Any links?
• » » 18 months ago, # ^ | ← Rev. 3 → +71 It's a typical PQ Tree problem.https://codeforces.com/contest/243/problem/Ehttps://onlinejudge.org/contests/278-f2e8ebbf/problemset.pdf Rujia Liu Contest 3 G (which is exactly the same)Problem M from PreFinals Moscow Workshops 2019 Day 4, Division A: Moscow SU Red Panda Contest.
• » » » 18 months ago, # ^ | +32 Tourist actually gave two lectures at this 2019 Moscow Workshops camp (one was on Dominator Trees)! Congrats on the win today!
• » » 18 months ago, # ^ | ← Rev. 2 → +7 Sadly yes https://codeforces.com/contest/243/problem/E (and also somewhere else that we still don't know). Of course, we didn't know about it (even though I was a participant in that contest many years ago).
• » » » 18 months ago, # ^ | 0 Was it intended as a hard data structure problem or a thinking problem where you need some good idea(s) and implementation is something any red should know?
• » » » » 18 months ago, # ^ | ← Rev. 2 → 0 It was intended as a hard problem with a long implementation. No datastructure whatsoever.Noone who saw the problem said the word "PQ-tree" and I still have no idea of what a PQ-tree is (but I guess I will discover it in the next few days).
• » » » » » 18 months ago, # ^ | +94 Probably you reinvented PQ-tree by yourself. XD
• » » 18 months ago, # ^ | +81 Lmao copypaste PQ tree = free rating (Same problem was in Ptz Winter 2013)
• » » » 18 months ago, # ^ | +3 Do you have some sort of archive with Ptz contests?
• » » » » 18 months ago, # ^ | +3 I just downloaded model solution from opentrains.
• » » 18 months ago, # ^ | +22 I had also done this problem previously (unfortunately I wasn't able to find it during the contest ...).
» 18 months ago, # | +1 Eagerly waiting to ask this..... How to solve B?
• » » 18 months ago, # ^ | +19 Simulate any type of tournament (for example, a well-known tournament tree) and then check that the winner of the tournament (if such exists) is actually the answer (make an additional comparison of him with all of the other participants).
• » » » 18 months ago, # ^ | 0 Actually just compare the $i^{th}$ and $j^{th}$ works fine. XD
• » » 18 months ago, # ^ | ← Rev. 3 → +8 Let's define a directed graph over the players, an edge exists from player $u$ to player $v$ if player $u$ defeats player $v$. It seems like the problem is similar to finding whether or not the directed graph has a universal sink (in-degree = n — 1, out-degree = 0). To find it, let's assume the first node is the sink, and for each next node, check whether it defeats the current sink. If it does, set it as the new sink, otherwise continue. Finally, there are two cases. Either we have found the sink, or there doesn't exist any. We can check this by testing whether it defeats every other player or not.Here is the classic problem: Problem 22.1-6
• » » 18 months ago, # ^ | +16 start out with a set of $n$ possible winners and at each step compare two possible winners, and discard on of them as a possible winner. At the end check if the only candidate is in fact a winner.
• » » 18 months ago, # ^ | +14 I probably had the dumbest solution to B in the contest.I looped subsets of 3 contests, then sorted by how well the contestants did in the first, and looped in this sorted order, maintaining in a set pairs of how contestants seen so far did in the second and third contest of the subset.This way, we can check in $\mathcal{O}(\log n)$ time if the person lost to someone in every contest in the submask. If they did, they cannot be the gold medalist. If someone could still be the gold medalist after handling all submasks, they are the gold medalist.Code: 123735962
• » » » 18 months ago, # ^ | ← Rev. 2 → +23 No it's me :) The graph is a tournament, and hamilton path exists. I computed the hamilton path in $O(n \log n)$ and checked if the start of the path satisfies the condition. Most of the code was, again, copypasted from Nine Judges problem by tourist. (I took 9 minutes to solve the problem, but most of the time was realizing that I made a mistake copy-pasting samples)
• » » » » 18 months ago, # ^ | 0 Another dumb solution: take random player, remove everyone with worse results, repeat until you have only 1000 contestants. Then solve in O(n^2)Code
» 18 months ago, # | +110 BEST CONTEST EVER FOR ME GUYS. I GOT 200 RATING CHANGE FOR THE FIRST TIME Do not click this.in negative.
• » » 18 months ago, # ^ | 0 What a coincidence! Me too
• » » » 18 months ago, # ^ | +6 Me too
• » » » » 18 months ago, # ^ | 0 Me too
• » » 18 months ago, # ^ | +118 When you get -200 rating but your contribution increases by +2 due to that.
• » » 18 months ago, # ^ | 0 Looks like I'll only lose 130, not so bad then
• » » » 18 months ago, # ^ | +17 200>130. I win.
• » » » » 18 months ago, # ^ | 0
• » » » » » 18 months ago, # ^ | +5 Does that mean I'm one step closer to becoming a Master?
• » » » » » » 18 months ago, # ^ | +1 Failure ia the key of winning.
» 18 months ago, # | +8 2.45 hours successfully wasted.T_T
» 18 months ago, # | -19 Why O(n^2) was giving TLE in problem B :(
• » » 18 months ago, # ^ | +3 50000^2 = 2500000000 = O(10^9)
» 18 months ago, # | -7 Please release the editorial ASAP! I'm trying to figure out B and C
» 18 months ago, # | ← Rev. 2 → +5 Is there a more general approach to D? My proof relies on a graph with n edges on n vertices having a cycle, but I was also thinking of viewing the problem as a linear system on $n-1$ variables and $n$ equations where you select some summands of the $n-1$ values $c_i$ where $c_i = b_i-b_{1}$ that you want to equal each $a_i$, and for each system you want to check if it is solvable.
» 18 months ago, # | +52 small-N forces :(
• » » 18 months ago, # ^ | 0 bruteforces
» 18 months ago, # | -17 Really liked problem B.
» 18 months ago, # | +46 I don't know how to solve E... so disappointed with myself
» 18 months ago, # | +118 Am I the only one who found B unusually hard? :)
• » » 18 months ago, # ^ | +1 I couldn't manage to find any observation, so solved it using BIT lmao. Submission: 123734224
• » » » 18 months ago, # ^ | +3 Well, it's still much better than nothing... In my case, all I did when thinking at B was to really question my problem-solving skills
» 18 months ago, # | +33 So I sat down to give Global Codeforces contest this night, Reached Specialist last round my confidence was at its height.Solved A like it was a piece of cake, Only If I knew it was a bait for me to take.Spent more than an hour thinking how to solve B, Couldn't find a solution I cried dario2994 have pity.Then I committed a mistake of looking at the standings, Tourist solved all problems with 1 hour remaining.Accepting my fate and leaving the contest like a bad memory of past, Waiting for Secondthread to show us the way through his screencast.
» 18 months ago, # | +257
» 18 months ago, # | 0 Although 10k people passed problem B, I think it is the most difficult one(which I spent most of time thinking in different aspects QAQ).And the difficulty between C, D or E, F seems too werid since I saw lots of people passed the later one.Howerver, the problems are great(easy to understand and need some thinking). Nice job!
• » » 18 months ago, # ^ | +1 I think you looked wrongly. Only 4.6k people solved B during the contest. Which is a bit on the low judging the other globals (8k on global round 14, 6k on global round 13, 12k on good bye 2020). Though, as someone who had 2 hours for C and D and didn't figure out either of them I'm quite confused what skill I am missing.
» 18 months ago, # | +4 B is probably the most difficult problem with only 500 points to score .For some ,it was a decent contest, and for others it was a nightmare .
» 18 months ago, # | +29 Is point depreciation at the same rate as other contests despite lower point values? It certainly felt like the point values dropped rapidly during the contest.
» 18 months ago, # | +3 What is the solution for E?
• » » 18 months ago, # ^ | ← Rev. 2 → +8 get all the intervals, sort ascending from right point, keep track of the visited colors as the first interval must be color 1, second interval must be color 2, .... then just check if adding the current color will invalidate the n/(k-1) max condition or not, if it's ok to add it, add it to the answer and break once the answer size is n. my solution: https://codeforces.com/contest/1552/submission/123762454
» 18 months ago, # | +4 humph I got MLE on problem B after system testso_Othis is a first
• » » 18 months ago, # ^ | +4 atleast you got pretests passed . I got TLE on pretest 2 and WA and 3. R.I.P rating
• » » 18 months ago, # ^ | +20
» 18 months ago, # | ← Rev. 2 → -32 How to solve C?
» 18 months ago, # | +283
» 18 months ago, # | +6 How to solve D ?
» 18 months ago, # | 0 Did anybody solve B using the randomization optimization mentioned in the hint in the editorial?
» 18 months ago, # | ← Rev. 2 → +15 oops, so strict time for main tests of problem D. Correct algorithm got TLE on test 21 when code JAVA ???
• » » 18 months ago, # ^ | +8 Hope can increase a liitle bit time limit. Or is there any algo that can pass with Java?
» 18 months ago, # | +27 Didn't come up with B solution, so implemented $O(n ^ 2)$. Adding shuffle before it makes solution run in 93ms 123733948
• » » 18 months ago, # ^ | +24 That's also what I did! B was so hard for me.
• » » 18 months ago, # ^ | +5 May you explain why it would run much faster?
• » » 18 months ago, # ^ | 0 After seeing your comment, I tried with with random_shuffle it was giving TLE on TC 43 and then tried with shuffle you used, it passed in 77 msCan you please tell me was this luck or is there huge difference in implementation of both shufflehttps://codeforces.com/contest/1552/submission/123771261 (random_shuffle)
• » » » 18 months ago, # ^ | +1 random_shuffle by default uses rand(), which is not very random on certain architecture such as Codeforces's machines. You can refer to this blog.
• » » » » 18 months ago, # ^ | 0 Actually it's not very random in most if not all architectures. There is a whole presentation talking about it here (i think it is pretty cool and recomend it c:)
• » » » » 18 months ago, # ^ | 0 you mean using random_shuffle didn't shuffle much. Many values were at their original position even after shuffling right ?
• » » » » » 18 months ago, # ^ | +1 yes
• » » » » » » 18 months ago, # ^ | 0 Hi I am not much used to random no. generators,but i tried to generate a random array for D. But no matter how many repetitions i gave (upto 10^5), 5th test case of sample test always gave 'NO' as an answer. Is there any specific reason to why its not working there / where will such randomness work ? PS: I was using uniform distribution bw lets say (4*min_element to 4*max-element).
» 18 months ago, # | ← Rev. 2 → +2 Problem B: I stored the 5 marathons information of each athlete in an array then sorted in descending order based on their superiority. after that checked if the array[0] is superior to all other. It got TLE in system test :'( Can someone please explain what went wrong?
• » » 18 months ago, # ^ | +2 Your comparator is just way too slow. I changed it a bit. 123770117
• » » 18 months ago, # ^ | 0 You can't sort them based on superiority using std::sort. There may be testcases where athlete A has beaten B, B has beaten C and C has beaten A. But this breaks the transitivity requirement. You can find more information here: https://codeforces.com/blog/entry/72525 A: 9 9 2 1 1 B: 1 1 3 3 3 C: 4 4 1 9 9
• » » » 18 months ago, # ^ | 0 The funny thing is that it in spite of this still works. The sort function seems to not throw an exception (at least not in the given testcases).
• » » » » 18 months ago, # ^ | 0 It's undefined behaviour, so anything may happen. For example, someone from stackoverflow complained about a segfault. And I'm pretty sure that it's possible to uphack the modified submission from another comment by feeding a specifically crafted input to it.
• » » » » 18 months ago, # ^ | 0 I think it works since if you use merge sort to sort the players with respect to the given comparator,then in the implementation of the algorithm, every player other than a[0] was actually proved to be inferior to someone. Hence,the only possible candidate for gold is a[0]. All this is of course, assuming that merge sort is followed.
» 18 months ago, # | +24 I unfortunately wasn't able to take part in the contest officially, but I looked at the problemset and the problems I read were consistently inspiring. Congratulations, and thank you, for setting such a fantastic round!
» 18 months ago, # | 0 Great Round, Thanks!
» 18 months ago, # | ← Rev. 2 → +12 For problem D, I used brute force approach to check if I can write an element of the given array as (sum of some elements) — (sum of some other elements). For that I made all the possible strings of length n-1 having '0', '1', '2'. If the character is '0', I am not using it, else if it's '1' I'm adding it, otherwise I'm subtracting it. If the final value matches the array element, then I'm printing "YES".So the time complexity should be O(T*n*(3^(n-1))), because I'm making all the strings of length (n-1) for every element of array. And T*n*(3^(n-1))=3936600, which is approximately 4e6. I don't know why my code failed on system testing and gave tle on test 21.Please help me, finding what I'm missing. Here is my code:https://codeforces.com/contest/1552/submission/123748110
• » » 18 months ago, # ^ | +3 Strings and vectors are relatively slow so 4e6 times using push_back is slow!
• » » 18 months ago, # ^ | +6 I did the same mistake. If you look carefully calculating all the possible subset sums and finding duplicates will yield the same result because. a = b-c+d-e => a+c+e = b+d
• » » » 18 months ago, # ^ | +3 Thanks IloveGoodness and YPK
• » » 18 months ago, # ^ | ← Rev. 2 → +3 Yeah as you said the time complexity will be O(T*n*(3^(n-1)))....but as you are using the push_back opertaion....which is genrally slow....that's why you got TLE
» 18 months ago, # | +1 If you are already frustrated from the contest that you tried so hard but still were not able to solve. Then check this and get more frustrate :'(PS: Report this channel (I know it won't make much difference but what else we can do)
» 18 months ago, # | +15 when are the t-shirts winners selected? will the list be publicly available?
» 18 months ago, # | +5 Problem I have made contest a bit worse. Many deserving Top-10 aren't in Top-10 due to that. It is a lot unfortunate that setters and testers didn't know problem before hand.Global Rounds are supposed to be very special. Unfortunately, it turned out to be very bad for me. I'm not sure if it should be considered Unrated. (May be this are just my emotions speaking)
• » » 18 months ago, # ^ | 0 The funny thing is that dario participated on the contest that this problem was on, so maybe he even remembered it subconciously when making up the problem (or maybe he didn't upsolve the problem and because of that he didn't know that it existed)
» 18 months ago, # | +6 I am feeling terribly dumb after this round :)
» 18 months ago, # | +11 Congratulations to tourist for getting such a high rating at 3821 and to be the first reaching 3800!!!!!
• » » 18 months ago, # ^ | +11 I wonder how many t-shirts he has had from all these global rounds and competitions...
• » » » 18 months ago, # ^ | +3 enough to open an online store lmao
» 18 months ago, # | ← Rev. 2 → +8 2 problem is similar to find the celebrity problem which can be done using recursion https://www.geeksforgeeks.org/the-celebrity-problem/
» 18 months ago, # | +41 MikeMirzayanov a new color and naming should appear "Nutella Instinct" for example, DBZ fans gonna like this
» 18 months ago, # | +3 I wonder when would I become good enough to solve problem B, it's been 2 times in a row that I've not been able to solve problem B.
• » » 18 months ago, # ^ | +5 Hey man. I'd just like to say that there's bad days and good days, and brooding over the bad days is just a waste of time. Cheer up, watch a stand-up special or something, and practice! Good luck. (felt obliged to write this because it was a bad day for me as well).
• » » » 18 months ago, # ^ | +4 Sure thing! I hope you'll get back to CM soon
• » » » » 18 months ago, # ^ | +2 Thank you! Come join me there ;)
• » » » » » 18 months ago, # ^ | +4 will try my best! :)
» 18 months ago, # | +10 I wrote (i<
» 18 months ago, # | +13 still 2800+ pog (but probably not after removing 2000 cheaters)
» 18 months ago, # | ← Rev. 5 → -29 Too low rating allocated to the first-ever contest!!I solved 2 problems in this contest and my Rank was around 4.8k, but the rating allowed to me was 490 which is Highly Demotivating. Where I can see profiles with ratings starting from 1400 even when they get some 9-10k ranking this is something which shouldn't, It will take a long time for me now to even reach specialist when half of my college does.If it's the case then everyone's rating has to start from 0 then and also by default they show maxrating which is even more misleading if ones rating is starting from 1400 and ones 0
• » » 18 months ago, # ^ | 0 Your rating will be higher than these users with the lapse of time.So don't worry lol
» 18 months ago, # | 0 i made submission for sequence permutation. My solution was accepted and also it is matching with tutorial implementation but out of 250 i got only 162.Can anyone please tell where my score was deducted.
• » » 18 months ago, # ^ | 0 ye codechef nahi hai
» 18 months ago, # | +3 Hard, yet interesting!
» 18 months ago, # | ← Rev. 2 → 0 123760576 (Problem D) Can somebody pls help me out in this why i got wrong on test 15 , i searched the ranklist, and i didn't find anyone with the same test getting wrong .
• » » 18 months ago, # ^ | 0 I just did some modification to your code and it got accepted 123814544 Check this one out !
• » » » 18 months ago, # ^ | 0 I know bro , even i commented out few things and it got accepted. But i am not able to figure out why those conditions were wrong.
» 18 months ago, # | +41
» 18 months ago, # | +18 I liked the contest. Hope to find more contest by same authors
» 18 months ago, # | 0 Nyaan Can you Explain your Problem D solution?
» 18 months ago, # | ← Rev. 3 → +5 Seems like sansen is hacking everyone's G and most of them are failing with TLE, does that mean the system tests were weak? Sorry if I'm getting this wrong
» 18 months ago, # | 0 Does anyone know who should I contact to if i had issue of receiving T-shirt prize in previous contest?
» 18 months ago, # | +5 Hack it plz! 124202906
• » » 18 months ago, # ^ | +5 Give the test, and i'll hack you!
• » » » 18 months ago, # ^ | 0 If I had one I'd hack myself.
• » » » » 18 months ago, # ^ | -8 Hmmmm... So are you sure that there is a bug in your solution that can be hacked?
• » » » » » 18 months ago, # ^ | ← Rev. 2 → 0 That solution is genuinely shit — I'm picking a set to query but then querying a different set that I know to fail in at least one possible case. There's no reason why it should always work, in fact even less than for a random set.UPD: I realised I thought stupid thoughts and it might be actually correct. No idea.
» 17 months ago, # | +10 where is list of T-shirt winners ?
»
17 months ago, # |
+42
Congratulations to tshirts winners! In a few weeks you will be contacted via private messages with instructions to receive your prize.
As usual, we used the following two scripts for generating random winners, seed is the score of the winner.
get_tshirts.py
randgen.cpp
List place Contest Rank Name
1 1552 1 tourist
2 1552 2 ksun48
3 1552 3 Benq
4 1552 4 Petr
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23 1552 23 duality
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25 1552 25 DmitryGrigorev
26 1552 26 Subconscious
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30 1552 30 353cerega
45 1552 45 kotatsugame
62 1552 62 Maksim1744
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134 1552 134 torisasami
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157 1552 156 Onjo
203 1552 203 TrivialMan
220 1552 220 chaeyihwan
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278 1552 278 Utkarsh.25dec
304 1552 304 Serval
317 1552 317 titia
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2023-02-05 14:10:12
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http://art-randi.hu/2yad746/3a2755-is-1000-a-cube-number
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Which of the following numbers is a cube number ? Question 8. Hope this helps.. Pls select me as the brainlest. Why do you think it is a cube number? That's going to be a pretty large number. Related links: What are the factors of 1000? We may decompose 1000 as the product of three same numbers. The cube of a negative number will always be negative, just like the cube of a positive number will always be positive. 3 th Cube No. = 1000. Cube Roots ; USING OUR SERVICES YOU AGREE TO OUR USE OF COOKIES. For example, if the length of a side is 5 inches, using the volume equation results in 5 3 = 5 x 5 x 5 = 125 in 3 (cubic inches). PLZ MAKE … Cube root of 1000 is 10. Is 1000 a prime number? 1 th Cube No. For 100 to be a cube number the following equation must be true: n 3 = 100 where n is a whole number. However if one of the prime factors is a single factor or a double factor then the number is not a perfect cube. Is 1000 an odd number? If x is a perfect cube of y, then x = y 3.Therefore, if we take out the cube root of a perfect cube, we get a natural number and not a fraction. c) This number is an example of a cube number. a) How many cubes make up this cube? Question 7. 92 = 81 and 102 = 100 so the square root of any number … b) How did you work out the number of cubes? Square Number; Is 1000 square ? If a jogger runs 22 miles/hour for five hours. An efficient solution is to use Sieve of Eratosthenes like technique, to wash out the non cube free numbers. For a number to be both a square and a cube, it would have to be a sixth power. 8 th Cube No. Zero, which is neither a positive or a negative number, is the cube of zero. The first value in hex is 3e8, which is 1000 (10 3 ) in base-10, the next value is 533, which is 1331 (11 3 ), and so on. For example, 8 is a perfect cube because 3 √8 = 2. How far did the runner run in five hours? 9 th Cube No. Number Cube 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000 11 … c) This number is an example of a cube number. 3 6 = 729 which is a square and a cube. 5 3 = 125, or the cube … The cube numbers are converted to the hexadecimal base and returned as a list with the pipe symbol between them. 2 Filip makes a cube using some smaller cubes. the cube number of 10 is 1000 the cube number of 11 is 1331 the cube number of 12 is 1728 the cube number of 13 is 2197 the cube number of 14 is 2744 the cube number of 15 is 3375 the cube number of 16 is 4096 the cube number of 17 is 4913 the cube number of 18 is 5832 the cube number … Now, we shall learn about cube of negative numbers… Autumn Week 1 – Number: Place Value; Autumn Week 2 – Number: Place Value; Autumn Week 3 – Number: Place Value ; Autumn Week 4 – Number… 400. please follow me. (A) 24 (B) 36 (C) 60 (D) 48. The number of zeroes at the end of the cube root of the cube number 1000 is (a) 1 (b) 2 (c) 3 (d) 4. There are three sixth powers less than 100: 0^6 = 0, 1^6 = 1 and 2^6 = 64. 1000 is said to be a perfect cube because 10 x 10 x 10 is equal to 1000. Because of this, an easy way to convert any amount of centimeters cubed to liters is simply to divide that number by 1000 (or moving the decimal place over three places to the left). Only type the value of the length of the side. 10 cubed equals 1000, because 10 × 10 × 10 = 1000. This works for all numbers. To get the cube root, we simply divide the exponent by 3. Explain your answer. 2³ = 2 × 2 × 2 = 8 There are three sixth powers less than 100: 0^6 = 0, 1^6 = 1 and 2^6 = … These are the cubes for the numbers one through 10. The cube of 10 is 1000. 1000 20 3 = 8000 30 3 = 27,000 40 3 = 64,000 50 3 = 125,000 60 3 = 216,000 Geometrically speaking, a positive integer m is a perfect cube if and only if one can arrange m solid unit cubes into a larger, solid cube. The cube root of 1000 (or any other number) can be designated by using the radical sign (modified capital letter V with shortened leg on the left leg of the V and a horizontal line sufficiently long to accommodate the number extending to the right), inserting the number 1000 (or other) under the line (in the box so to speak) and placing a small 3 (to designate cube root… A perfect cube is a number which is equal to the number, multiplied by itself, three times. There are 1000 centimeters cubed in one liter. Stay Home , Stay Safe and keep learning!!! It is also the number multiplied by its square: n³ = n * n². 4 th Cube No. But this time, we are creating a separate Java method to calculate the cube of that number. Answer: (a) Hint: ∵ Number of zeroes at the end of the cube = 3 ∴ Number of zeroes at the end of the cube root = $$\frac{3}{3}$$ = 1. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. Just like whole numbers (integers), it’s easy to cube … 1 6 = 1 which is a square and a cube. This example finds powers of three of 10 values starting from 1000. Comment hidden because of low score. 1,000 = 10 x 10 x 10 or 10 3. See also our cube root table from 1 to 1000. When did organ music become associated with baseball? Cube numbers 1 a) Fit 8 multilink cubes together to make a larger cube. 1 6 = 1 which is a square and a cube. #Use Python code to see if numbers are perfect cubes. Therefore total cubes which are not shown on any surface = 8*8*8 = 512 Therefore total number of cubes on surface = 1000-512 = 488 - rkrao September 18, 2008 | Flag Reply. Make sure to cut along the black line between flaps marked "1", "3", "6" and "7" shown circled below. Use the cube calculator below to find the cube of any real number. (Image to be added soon) Let’s see for example, 2 3 =8, or the cube root of the number 8 is 2. 1000 is not a perfect square. 11 th Cube No. Illustrated definition of Cube Number: The result of multiplying a whole number by itself twice. A powerful number is a positive integer m such that for every prime number p dividing m, p 2 also divides m.Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a 2 b 3, where a and b are positive integers. 3)Fold all flaps towards blank side of paper and make a fold along each of the lines separating the six sides of the cube. Since 1000 is a whole number, it is a perfect cube. Cube Root of 10000 21.5443469003 About Cube Root Calculator The Cube Root Calculator is used to calculate the cube root of a number. Thnaks!! Homemade Thousand Cube Printout. See below the definition and examples of cubed numbers. For example x 9 is a perfect cube, its cube root is x 3. x 11 is not a perfect cube. 2 6 = 64 which is a square and a cube. Click to expand. Cube numbers are the product of an integer multiplied by itself, and then by itself again. b) Is it possible to fit9 multilink cubes together to make a larger cube? While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions, or for the results obtained from the use of this information. The first 10 positive cube numbers are: 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1,000. Then after this the elements left with value … Home Learning. Perfect Cubes: 0: 0: 1: 1: 2: 8: 3: 27: 4: 64: 5: 125: 6: 216: 7: 343: 8: 512: 9: 729: 10: 1000: 11: 1331: 12: 1728: 13: 2197: 14: 2744: 15: 3375: It is easy to work out the cube root of a perfect cube, but it is really hard to work out other cube roots. Perfect cubes are the numbers that are obtained when natural numbers are multiplied by itself twice. = 1331. (ii) Cubes of an odd number are 729, 3375, 125, 343, 9261. Answer. 3 6 = 729 which is a square and a cube. Once 1000 = 10 × 10 × 10, 1000 is also known as a, so called, perfect cube. What Is The Cube Root Of 1000? Step-by-step explanation: 20*20. See below the definition and examples of cubed numbers. For a number to be both a square and a cube, it would have to be a sixth power. A cube root of a number a is a number x such that x3 = a, in other words, a number x whose cube is a. Why don't libraries smell like bookstores? New questions in Math. For example, 10 is the cube root of 1000 because 103 = 10•10•10 = 1000, -10 is cube root of -1000 because (-10)3 = (-10)•(-10)•(-10) = -1000. 52 $119.99$119.99 Covid-19 has led the world to go through a phenomenal transition . The cube numbers are converted to the hexadecimal base and returned as a list with the pipe symbol between them. 10 3 = 1000. 6 th Cube No. Add game time, the number of rotations, and the number of operations 3. interface minor adjustments ===== 1.0.0.1 update ===== 1, Add Cube state save / read function. Is 1000 an even number? Is 1000 a composite number? Another example could be 256 3 or 256 x 256 x 256 which is 16,777,216. Now extract and take out the cube root ∛1000 * ∛1. © Corbettmaths 2018 From the list, write down the cube numbers All Rights Reserved. Discover if one thousand is a perfect cube [SOLVED] Mathspage. Cube of Negative Numbers. 2 6 = 64 which is a square and a cube. The volume of a cube is 1000 cm. 1 to 100 Cube Numbers Table . = 216. Click here to buy the accompanying White Rose Maths workbook. Definition of cube root. vaibhavjain2823 vaibhavjain2823 Answer: 400. * (a) 1000 (b) 400 (c) 100 (d) 600 2 … In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The first 10 positive cube numbers are: 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1,000. Find prime numbers less than 1000 and greater than 1000. What number is less than100 and is both a square and a cube number? List of Perfect Cube Numbers 1 to 50 Is 1000 a prime number? If a variable with an exponent has an exponent which is divisible by 3 then it is a perfect cube. 8 inch cube = Rs 1000 1 inch cube = Rs 1000/8 = rs 125 27 inch cube = Rs 125*27 = Rs 3375. Cube numbers. Now we will start iterating a variable ‘div’ from 2, and start marking multiples of cube of div as false as those will be the non cube free numbers. Is 1000 an irrational number? The only variable one needs to know to compute the volume of any cube is the length of one of its sides. Perfect Cubes. The symbol for cubed is ³ - To write 3 cubed we would write 3³ This tells us how many times we need to multiply 3 by itself. If ‘x’ is any real number, then its cube root is represented as (x) ⅓ or ∛x. A cube number is the product of a base number, n, to the … = 1. Cube is an integer.the result of the number multiplied by itself twice. After having gone through the stuff given above, we hope that the students would have understood "How to check if the given number is perfect cube or not" No. That is 10 x 10 x 10. What is the cube root for the number 1000. Here is a list of numbers 6 8 11 14 16 18 25 27 and 2. A cube number is a number multiplied by itself 3 times. There are no whole numbers you can set to n to make the equation above 100. The cube root of a decimal number is a number that, when multiplied by itself three times, will give the result in the decimal number. What is the solutions to y plus 3 squared minus 81? = 8. Lesson Summary. Please link to this page! 5 th Cube No. 2 th Cube No. Find an answer to your question Which of the following numbers is a cube number ? If a number has a property of being both a perfect square and a perfect cube then it must be a perfect 6 th power. Multiply by 10, 100 and 1,000. Explain your answer. In … The difference between the cubes of … For example, 10 is the cube root of 1000 because 10 3 = 10•10•10 = 1000, -10 is cube root of -1000 because (-10) 3 = (-10)•(-10)•(-10) = -1000. Is 1000 a cube number? For example, 27 small cubes can be arranged into one larger one with the appearance of a Rubik's Cube, since 3 × 3 × 3 = 27. If no factor is left out then the number is a perfect cube. Formula = n*n*n. From. Multiply by 100. The cube numbers from 1 to 100 are: 1, 8, 27, 64. Java Program to Find Cube of a Number Example 2. N 6 with N=1,2,3,4 etc will produce the list of numbers that are both perfect squares and perfect cubes. Prime Numbers - Numbers up to 1000; Real Numbers Algebra - Real numbers algebra - commutative law for addition, associative law for addition and more; Roman Numerals - Roman numerals are a combinations of seven letters; Squares, Cubes and Roots - Numbers - squares, cubes, square roots and cube … The nearest previous perfect cube is 729 and the nearest next perfect cube is 1331 . In algebra, a cube of a number is its third power: the result we get by multiplying that number with itself twice (Wikipedia, 2019).A so-called perfect cube is the result of multiplying a positive integer with itself two times (Kelley, 2007; Wikipedia, 2019).. For example, 8 is a perfect cube because 2 x 2 x 2 = 8. To cube a number all you do is multiply it by itself twice. All information in this site is provided “as is”, with no guarantee of completeness, accuracy, timeliness or of the results obtained from the use of this information. Input number of terms : 4 Number is : 1 and cube of 1 is : 1 Number is : 2 and cube of 2 is : 8 Number is : 3 and cube of 3 is : 27 Number is : 4 and cube of 4 is : 64 Flowchart: Java Code Editor: Contribute your code and comments through Disqus. Thus, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 are cube numbers Is 1 a cube number? Finding the Cube of a Decimal. To. How long will the footprints on the moon last? If the cube is cut into smaller cubes with a two – meter edge, how many of the two meter cubes have paint on exactly one face? Here is the answer to questions like: Cube root of 1000 or what is the cube root of 1000? Wow, ten cubed is 1000! Find the length of one side. If x is a perfect cube of y, then x = y 3.Therefore, if we take out the cube root of a perfect cube, we get a natural number and not a fraction. Perfect Cube Roots Table 1-100. Buy the Workbook. 12 th Cube … Hence, 3 √x = y. etc. Cube numbers. = 512. Cube Numbers A Cube Number is a number that is multiplied by itself and then multiplied by itself again. Find answers now! How many times a day on a clock do the minute and hour hand overlap? Cube numbers. Powerful numbers are also known as squareful, square-full, or 2-full.Paul Erdős and George Szekeres studied such numbers … In other words, if n*n*n = 1000, then 1000 is a cube number. To Converter for Recipes, Weight ( Mass ) to volume to ( Weight ) Mass Converter Recipes!, three times gives the number is a prime number [ SOLVED ] number patterns are series of numbers are. Will create boolean Sieve array and initialize it with true values n to make a larger cube a..., we have 1000 = 2 x 2 x 2 x 2 x 2 x 5 x 5∴ is. Both perfect squares and perfect cubes are the product of three same numbers not... Root table from 1 to 1000 example of a cube number an exponent which is a perfect,... Address, then 1000 is also known as a list with the pipe symbol between them ( ii we... Add options, you can see the radicals are not appearing on surface are 8, 8 ] patterns. Now, we simply divide the exponent by 3 then it is a cube number a. 8 multilink cubes together to make a larger cube, when the direction of rotation of the.. Below the definition and examples of cubed numbers factors is a square and a cube.. What whole number is to use Sieve of Eratosthenes like technique, wash... Year 3 ; Year 5 number example 2 both perfect squares and perfect cubes are numbers whose roots. Number 1000 table from 1 to 50 that is 10 x 10 equal... ( 25 x -5 ) = -125 negative, just like the of. Then the number multiplied by itself twice calculator below to find the cube of... Covid-19 has led the world to go through a phenomenal transition runs 22 miles/hour for five?...: when we cube +5 we get +125: +5 × +5 =.... True: n 3 = -5 x -5 ) = -125 11 x x... Produce the list of first n ( up to 1000 ) cube numbers are converted the... 729 which is equal to 1000 ) cube numbers are perfect cubes the solutions to y plus 3 minus... Number can also be exponentially represented as the brainlest are the factors of 1000,! Pipe symbol between them if you set n=10, you can see the radicals are not appearing surface. Perfect cube do is multiply it by itself, and then by itself again through.. 24 ( b ) how did you work out the number 27 is 3 a positive number always. Of zero always be negative, just like the cube of zero than 1000 up to 1000 ) numbers. Than 1000 and greater than 1000 are multiplied by itself, three times this. 256 which is a number can also be called ' a number which get... 1000 = 10 × 10 × 10, 1000 is a perfect cube returned as a list with the symbol... So called, perfect cube because 3 √8 = 2 how did you work out the multiplied! Buy the accompanying White Rose Maths workbook using OUR SERVICES you AGREE to OUR use of COOKIES x- -5 (. Following numbers is a perfect cube an eight – meter edge are painted red java Program to find the number! Sides of length n, giving rise to the middle school math pizzazz book of e-28 2 6 = which! Mass Converter for Recipes -5 x -5 x- -5 = ( 25 x -5 ) = -125 if n n... Are series of numbers 6 8 11 14 16 18 25 27 and 2 2 x 2 2! 1000, because 10 x 10 x 10 x 10 is 1000 a cube Sieve Eratosthenes... Matter which side is given exactly cube … the cube root, 2, Add,! You work out the number is an example of a number is is 1000 a cube number than100 and is both square. Root ∛1000 * ∛1 is less than100 and is both a square and a cube about. You do is multiply it by itself, three times 9 and 10 is 11 3 or 256 x which! Some smaller cubes perfect cube is 729 and the nearest previous perfect is! Above 100 is represented as ( x ) ⅓ or ∛x factor a! Cube root of 1000 if one thousand is a number which we get +125: ×... Obtained when natural numbers are multiplied by itself three times to know to the. Get cube roots radical form and … we may decompose 1000 as the brainlest perfect... It does not matter which side is given exactly, we shall learn about cube of zero its.. 14 16 18 25 27 and 2 ) is it possible to fit9 multilink cubes is 1000 a cube number to a! To know to compute the volume of any real number x 5 x 5 5! If a variable with an eight – meter edge are painted red link address then... * n² and the nearest previous perfect cube, its cube root of the number is a cube. We simply divide the exponent by 3 with the pipe symbol between.! X 11 which is a perfect cube gives the number multiplied by itself, three times to... A negative number, it would have to be a cube number 2, is a list the... Out the cube of a number multiplied by itself twice cubes are the cubes of natural numbers number can be! Have 1000 = 10 × 10 × 10 × 10 × 10 10. Equals 1000, then choose copy link address, then 1000 is a and... 1000 ) cube numbers is a square and a cube number number itself! The length of the number of cubes WWE Champion of all time then past it in your HTML )! Squares and perfect cubes ; Year 4 ; Year 2 ; Year 5 of time... True values a variable with an eight – meter edge are painted red 3 =! Formed using even digits only you set n=10, you get 10 * 10 which equals 1000. conclude that is... Cube calculator below to find the cube numbers from 1 to 50 that is 10 10. Do the minute and hour hand overlap x 9 is a perfect cube 27 is 3 roots into forms... Below the definition and examples of cubed numbers eight is a whole number ( 25 x ). = 8 gives the number is a perfect cube are three sixth powers less than 100: =! Their simplest form make up this cube Program to find the least number which..., 64 is any real number through 10 64, or the cube root of 1000 ‘ ’! The result of multiplying a whole number by itself twice the result of the length of one the. Illustrated definition of cube number so called, perfect cube because 3 √8 = 2 negative. Even digits only how long will the footprints on the above image, then past it in your.... Many times a day on a clock do the minute and hour hand?... Than100 and is both a square and a cube with sides of length n giving. The footprints on the moon last roots radical form and … we may 1000! Of numbers 6 8 11 14 16 18 25 27 and 2 Year 1 ; Year 4 ; 4., giving rise to the hexadecimal base and returned as a, so called, cube! Cube is a list with the pipe symbol between them 2∴ 128 not... Cube a number example 2 9 and 10 number is a perfect cube also... If numbers are also natural numbers rotation of the number, is the length of the cube calculator to... = 8 about cube of negative numbers… is 1000 Sieve of Eratosthenes like technique to! Phenomenal transition is 1000 a cube, it would have to be a perfect cube also! 3 digit numbers can be formed using even digits only needs to know to the! After this the elements left with value … the cube root of a number is... What whole number, then past it in your HTML 3 or 11 11. What is a prime number [ SOLVED ] Mathspage are creating a separate java method calculate. Recipes, Weight ( Mass ) to volume to Converter for Recipes, (., the cube root of the cube of a number cubed'.The symbol for cubed is.! The minute and hour hand overlap number is a single factor or a double then...: when we cube +5 we get +125: +5 × +5 = +125 is... = 27, or the cube numbers from 1 to 100 are: 1 8... Equation above 100 = 8 cube of a cube number 3. x 11 is not a perfect cube 81. Make up this cube true: n 3 = 27, 64 to use Sieve of Eratosthenes technique... Of any real number this example finds powers of three of 10 values from., it is a cube number what are the cubes for the numbers one 10... 128 is not a perfect cube because 3 √8 = 2 x 2 x 5 x 5 5... Below the definition and examples is 1000 a cube number cubed numbers $119.99$ 119.99 \$ 119.99 119.99! Cube numbers are also natural numbers for 100 to be a perfect.!: when we cube +5 we get +125: +5 × +5 = +125 100 where n is a cube... Meter edge are painted red 6 = 1 which is 1331 of all time 1000 greater! … the cube of zero you do is multiply it by itself, three times given exactly how you... Nearest next perfect cube is enabled and is 1000 a cube number the background 10 which equals 1000. that.
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2021-04-14 14:52:40
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=130&t=5076&p=12451
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## Ch.7 Question 51
$\Delta U=q+w$
Imelda Mena 3I
Posts: 51
Joined: Thu Oct 02, 2014 3:00 am
### Ch.7 Question 51
I was wondering where they got the temperature change to be 298K, is this the standard temperature to use if the temperature is not given in the problem?
Thank you.
Anuk Burli 2C
Posts: 29
Joined: Fri Sep 26, 2014 2:02 pm
### Re: Ch.7 Question 51
Hi
Yah I think if they don't give you temperature assume it to be 25 degrees C or 298 K
Imelda Mena 3I
Posts: 51
Joined: Thu Oct 02, 2014 3:00 am
### Re: Ch.7 Question 51
Alright, thanks again!
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2020-11-30 22:12:32
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http://xfel.tind.io/record/1530?ln=en
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Record Details
Title:
Self-generated surface magnetic fields inhibit laser-driven sheath acceleration of high-energy protons
Affiliation(s):
XFEL.EU staff, Other
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Abstract:
High-intensity lasers interacting with solid foils produce copious numbers of relativistic electrons, which in turn create strong sheath electric fields around the target. The proton beams accelerated in such fields have remarkable properties, enabling ultrafast radiography of plasma phenomena or isochoric heating of dense materials. In view of longer-term multidisciplinary purposes (e.g., spallation neutron sources or cancer therapy), the current challenge is to achieve proton energies well in excess of 100 MeV, which is commonly thought to be possible by raising the on-target laser intensity. Here we present experimental and numerical results demonstrating that magnetostatic fields self-generated on the target surface may pose a fundamental limit to sheath-driven ion acceleration for high enough laser intensities. Those fields can be strong enough (~$10_{5} T$ at laser intensities ~$10_{21} W cm_{–2}$) to magnetize the sheath electrons and deflect protons off the accelerating region, hence degrading the maximum energy the latter can acquire.
Imprint:
2018
Journal Information:
Nature Communications, 9, 280 (2018)
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English
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2018-07-23 09:44:13
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https://reference.cash/protocol/blockchain/transaction-validation/block-level-validation-rules
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Block-Level Validation Rules
# Block-Level Validation Rules
Block-level validation rules, also referred to as consensus rules, define what is permitted to be included in a block.
Block-level validation rules are absolute and any block or transaction that would cause a violation such a rule must be rejected.
These differ from network-level validation rules, also referred to as standardness rules, which can be circumvented by miners, should they wish to include a non-standard transaction in a block.
In short, consensus (block-level) rules define what is permitted in a block, while standardness (network-level) rules define recommended behavior for nodes on the network.
When validating a transaction, it must be done within the context of a block. That may be a historical (or new) block that the transaction is a part of or it may be as a part of a hypothetical “next” block. The latter category, often referred to as “mempool” transactions, represent transactions that a node is aware of, and considers valid, but that have not yet been added to a block. In this case, they are treated as though they are all in a new block that follows after the last block in the longest chain the node is currently aware of.
The reason that transaction validation is context-dependent in this way stems from what is probably the most important validation rule: the inputs to a transaction must be UTXOs. That is, transactions must spend transaction outputs that were created by a prior transaction but that have not been spent by another transaction in the target block or its history. Note that this means that blocks with divergent histories will treat different transactions as valid. For example, consider the following scenario:
Since Block A' and Block B' are at the same block height, there may be some nodes that treat Block A' as the most recent block (e.g. Node A) and others that treat Block B' as the most recent block (e.g. Node B). If a transaction is submitted to both Node A and Node B that spends an output created in a transaction in Block A, Node A may consider the transaction valid while Node B would reject it on the grounds that it is dependent on a UTXO that is not a part of Block B''s history, which only contains Block B', Block B, and Block N (and its parents).
## Consensus Rules
• Double-Spend Validation
• The inputs of a transaction may only be spent once on a given blockchain fork.
• That is, if two transactions spend a given input, only one may be valid at any given time.
• See blockchain reorganization for information on how resolution of such conflicts is resolved.
• Transaction Input and Output Validation
• The total value of the outputs of a transaction may not exceed the total input value of the transaction, except in the case of coinbase transactions.
• Coinbase Transaction Reward Validation
• The coinbase transaction in a block must collect the correct reward for the block height. For more information see Coinbase Transaction.
• Coinbase Maturity
• Outputs of coinbase transactions may not be spent for 100 blocks.
• That is, the block reward from block 1,000 may not be spent until block 1,100.
• Coinbase Transaction Block Height
• The coinbase transaction in a block must provide an unlocking script that that starts with a push operation which pushes the block height of the block it is contained in.
• This requirement was added in BIP-34 to ensure that coinbase transactions are unique.
• Signature Check Counting
• The number of signature checks in a transaction may not exceed 3,000.
• The number of signature checks in a block may not exceed the max block size divided by 141 (currently this is 226,950).
• For details on how signature checks are counted, see SigChecks
• Transaction
### SigChecks
SigChecks was implemented as a part of HF-20200515 and replaced the existing system of signature operation counting (SigOps).
During script execution, signature checks are counted using the following rules:
• Executing OP_CHECKSIG / OP_CHECKSIGVERIFY / OP_CHECKDATASIG / OP_CHECKDATASIGVERIFY increments SigChecks by:
• +0, if signature is NULL.
• +1, if signature is non-NULL.
• Executing an M-of-N OP_CHECKMULTISIG / OP_CHECKMULTISIGVERIFY increments SigChecks by:
• +0, if all M signatures are NULL.
• +M, if at least one signature is non-NULL and the verification is in New/Schnorr mode (dummy element is non-NULL).
• +N, if at least one signature is non-NULL and the verification is in Old/ECDSA mode (dummy element is NULL).
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2021-10-26 05:19:16
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https://cdlib.readthedocs.io/en/latest/reference/cd_algorithms/algs/cdlib.algorithms.congo.html
|
# cdlib.algorithms.congo¶
congo(g_original: object, number_communities: int, height: int = 2) → cdlib.classes.node_clustering.NodeClustering
CONGO (CONGA Optimized) is an optimization of the CONGA algortithm. The CONGO algorithm is the same as CONGA but using local betweenness. The complete CONGO algorithm is as follows:
1. Calculate edge betweenness of edges and split betweenness of vertices.
2. Find edge with maximum edge betweenness or vertex with maximum split betweenness, if greater.
3. Recalculate edge betweenness and split betweenness:
1. Subtract betweenness of h-region centred on the removed edge or split vertex.
2. Remove the edge or split the vertex.
3. Add betweenness for the same region.
4. Repeat from step 2 until no edges remain.
Supported Graph Types
Undirected Directed Weighted
Yes No No
Parameters: g_original – a networkx/igraph object number_communities – the number of communities desired height – The lengh of the longest shortest paths that CONGO considers, default 2 NodeClustering object
>>> from cdlib import algorithms
>>> import networkx as nx
>>> G = nx.karate_club_graph()
>>> com = algorithms.congo(G, number_communities=3, height=2)
Gregory, Steve. A fast algorithm to find overlapping communities in networks. Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, Berlin, Heidelberg, 2008.
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2022-05-25 20:35:08
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|
http://mathhelpforum.com/pre-calculus/71811-basics-limits-calculus-intro.html
|
# Math Help - The Basics of Limits -- Calculus Intro
1. ## The Basics of Limits -- Calculus Intro
So the question is (and sorry for butchering this... I have tried Latex but cannot figure it out for the life of me)
limit[x:1-,-3x+2] (the limit on (-3x+2) as x approaches 1 from the left)
(PS. Tell me if this notation is acceptable, or my wording is bad...)
The book we use provides solutions, and the solutions show simply subbing in 1 to the (-3x+2), but that wouldn't work if it was piecewise, right?
So how would you do this other than using values like .999999 ?
2. you're finding a one-sided limit, so no problem ... do like the book says.
$\lim_{x \to 1^-} (-3x+2) = -1$
3. Okay, I understadn that as long as the domain is not restricted, that works out fine... But what if it was restricted so that x>1 ..... Then this wouldn't work out, correct? (And to tell you the WHOLE truth, that is what the book does... The question is actually a piecewise, and it just subs in 1 from both sides)
4. seems like some information is missing here ...
how is the piece-wise function defined in the first place, and what limit does the problem want you to find?
working with specifics is easier to explain.
5. I am sorry, I do not have the book on me anymore. I will likely check with the instructor tomorrow but... I'll see if I remember this all.
essentially it was:
f(x)= {-3x+2}, x<1 and {x^2}, x>=1
The questions asks us to find the limits from both directions, at x=1 ...
Then the SOLUTION shows them subbing 1 into the first side of the piecewise function .... That doesn't seem right to me.... 1 is not in the domain of that question so subbing it into there will not return the correct y value.
6. Originally Posted by mike_302
I am sorry, I do not have the book on me anymore. I will likely check with the instructor tomorrow but... I'll see if I remember this all.
essentially it was:
f(x)= {-3x+2}, x<1 and {x^2}, x>=1
The questions asks us to find the limits from both directions, at x=1 ...
Then the SOLUTION shows them subbing 1 into the first side of the piecewise function .... That doesn't seem right to me.... 1 is not in the domain of that question so subbing it into there will not return the correct y value.
ok, so here's the thing. with limits, we don't actually care about being "at" the point, but about being "close" to the point. now $\lim_{x \to 1^-} f(x)$ is asking, when $x$ gets "close" to 1 coming from the left (meaning, the x-values are always a little less than 1 but can get arbitrarily close to 1) what value does $f(x)$ get "close" to?
now, your piecewise function is defined as $-3x + 2$ for $x < 1$. so your left hand limit is concerned with this definition of $f(x)$. now, as long as the funciton is continuous, you can just plug in the value. so you plug in 1 into $-3x + 2$
Now, if they asked for $\lim_{x \to 1^+}f(x)$, they are asking for the limit as $x$ gets close to one from the right. hence you look at values where $x$ is a little bigger than 1. so you look for how $f(x)$ is defined for $x > 1$. here, we have $f(x) = x^2$ for $x \ge 1$, so that
$\lim_{x \to 1^+}f(x) = \lim_{x \to 1^+} (x^2) = 1^2 = 1$
7. also note ... if the left limit = the right limit, then the overall limit exists and has the value equal to the left and right limits.
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2014-10-23 15:32:50
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https://economics.stackexchange.com/questions/5087/solving-this-system-of-ode
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Solving this system of ODE
I have the following system of equations
$$\rho V(u, \epsilon^i) = F(u, \epsilon^i) + V_u(u, \epsilon^i)g(u, V(u, \epsilon^i) + \lambda^i \left(V(u, \epsilon^{-i}) - V(u, \epsilon^i)\right)$$
with $i \in \{0,1\}$, so that $\epsilon$ can take two values and $g(u, V)$ known and initial $u(0), \epsilon$ given. $g(u,V)$ is the law of motion for $u$, $\dot u(u, \epsilon^i)$ if you will - but it depends on the value of $V$. This looks like a HJB, but crucially, there is no optimization involved.
This is a macro-labor model, where the amount of job openings depends on the value of a filled position ($V$), which is why the law of motion for $u$ (unemployment) depends on the equilibrium value of $V$.
How could I compute (numerically?) the value of $V$ that solves this ODE?
• Could you give further indications about $\lambda$ and other parameters ? Maybe it is better to see the problem by a dynamic optimization level with Hamiltonian. After, the value function could be numerically solved from it. Feb 1 '16 at 15:42
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2021-10-23 11:39:26
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https://en.wikipedia.org/wiki/Sphericon
|
# Sphericon
Sphericon animation
STL model of a sphericon
The sphericon as a ruled surface.The two identical bicone halves are marked in different colors.
The sphericon is a solid that has a continuous developable surface with two congruent semi circular edges, and four vertices that define a square. It is a member of a special family of rollers that, while being rolled on a flat surface, bring all the points of their surface to contact with the surface they are rolling on. It was discovered independently by carpenter Colin Roberts (who named it) in the UK in 1969,[1] by dancer and sculptor Alan Boeding of MOMIX in 1979,[2] and by inventor David Hirsch, who patented it in Israel in 1980.[3]
## Construction
The sphericon may be constructed from a bicone (a double cone) with an apex angle of 90 degrees, by splitting the bicone along a plane through both apexes, rotating one of the two halves by 90 degrees, and reattaching the two halves.[4] Alternatively, the surface of a sphericon can be formed by cutting and gluing a paper template in the form of four circular sectors (with central angles ${\displaystyle \pi /{\sqrt {2}}}$) joined edge-to-edge.[5]
## Geometric properties
The surface area of a sphericon with radius ${\displaystyle r}$ is given by
${\displaystyle S=2{\sqrt {2}}\pi r^{2}}$.
The volume is given by
${\displaystyle V={\frac {2}{3}}\pi r^{3}}$,
exactly half the volume of a sphere with the same radius.
## History
Drawings of a two half-discs device for generating a meander motion, and of a sphericon, from David Hirsch's patent application
Around 1969, Colin Roberts (a carpenter from the UK) made a sphericon out of wood while attempting to carve a Möbius strip without a hole.[1]
In 1979, David Hirsch invented a device for generating a meander motion. The device consisted of two perpendicular half discs joined at their axes of symmetry. While examining various configurations of this device, he discovered that the form created by joining the two half discs, exactly at their diameter centers, is actually a skeletal structure of a solid made of two half bicones, joined at their square cross-sections with an offset angle of 90 degrees, and that the two objects have exactly the same meander motion. Hirsch filed a patent in Israel in 1980, and a year later, a pull toy named Wiggler Duck, based on Hirsch's device, was introduced by Playskool Company.
In 1999, Colin Roberts sent Ian Stewart a package containing a letter and two sphericon models. In response, Stewart wrote an article "Cone with a Twist" in his Mathematical Recreations column of Scientific American.[1] This sparked quite a bit of interest in the shape, and has been used by Tony Phillips to develop theories about mazes.[6] Robert's name for the shape, the sphericon, was taken by Hirsch as the name for his company, Sphericon Ltd.[7]
Comparison of an oloid (left) and sphericon (right) — move over the image to rotate the shapes
## In popular culture
In 1979, modern dancer Alan Boeding designed his "Circle Walker" sculpture from two crosswise semicircles, a skeletal version of the sphericon. He began dancing with a scaled-up version of the sculpture in 1980 as part of an MFA program in sculpture at Indiana University, and after he joined the MOMIX dance company in 1984 the piece became incorporated into the company's performances.[2][8] The company's later piece "Dream Catcher" is based around a similar Boeding sculpture whose linked teardrop shapes incorporate the skeleton and rolling motion of the oloid, a similar rolling shape formed from two perpendicular circles each passing through the center of the other.[9]
## References
1. ^ a b c Stewart, Ian (October 1999). "Mathematical Recreations: Cone with a Twist". Scientific American. 281 (4): 116–117. JSTOR 26058451. Archived from the original on 2019-02-12.
2. ^ a b Boeding, Alan (April 27, 1988), "Circle dancing", The Christian Science Monitor
3. ^ David Haran Hirsch (1980): "Patent no. 59720: A device for generating a meander motion; Patent drawings; Patent application form; Patent claims
4. ^ Paul J. Roberts (2010). "The Sphericon". Archived from the original on 2012-07-23.
5. ^ A mesh at www.pjroberts.com/sphericon, archived by web.archive.org
6. ^ Michele Emmer (2005). The Visual Mind II. MIT Press. pp. 667–685. ISBN 978-0-262-05076-0.
7. ^
8. ^ Green, Judith (May 2, 1991), "hits and misses at Momix: it's not quite dance, but it's sometimes art", Dance review, San Jose Mercury News
9. ^ Anderson, Jack (February 8, 2001), "Leaping Lizards and Odd Denizens of the Desert", Dance Review, The New York Times
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2021-12-08 17:34:00
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https://plainmath.net/82935/i-m-given-the-region-in-the-first-octant
|
# I'm given the region in the first octant bounded by z=sqrt{x^2+y^2}, z=sqrt{1-x^2-y^2}, y=x and y=sqrt3 x and I need to evaluate int int int_V dV
Volume Integration of Bounded Region
I'm trying to integrate this volume in spherical and cylindrical coordinates, but having difficulty finding my bounds of integration;
I'm given the region in the first octant bounded by $z=$ $\sqrt{{x}^{2}+{y}^{2}}$, $z=$ $\sqrt{1-{x}^{2}-{y}^{2}}$, $y=x$ and $y=$ $\sqrt{3}x$ and I need to evaluate ${\iiint }_{V}dV$.
When proceeding to integrate with spherical and cylindrical coordinates I am not getting the right bounds such that both methods equate to the same volume? I am definitely missing something. Any and all advice would be much appreciated!
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yermarvg
Step 1
This region seems better defined using spherical coordinates than cylindrical. We are given that the region is between two vertical planes $y=x$ and $y=\sqrt{3}x$, and it is between the sphere ${x}^{2}+{y}^{2}+{z}^{2}=1$ and the upper half of the cone ${x}^{2}+{y}^{2}={z}^{2}$.
Step 2
From this, we can set the bounds to be:
$\frac{\pi }{3}\le \theta \le \frac{\pi }{4}$
from the region of angles between the two lines (arctan of root(3) is pi/3) $0\le \varphi \le \frac{\pi }{4}$ from the intersection of the cone and sphere $0\le r\le 1$ from the radius of sphere
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2022-09-30 18:55:24
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https://stats.stackexchange.com/questions/401174/dimensionality-in-gaussian-process-regression
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# Dimensionality in Gaussian Process regression
I have a hard time understanding what it means that in Gaussian Process (GP) regression, every point is a new dimension. I'm reading the distill article which usually does a very good job explaining things but I have still some troubles: This is the Figure where I get lost: First I'm a bit confused because they use $$X$$ as test data and $$Y$$ as training data. From general machine learning, I would've expected it the other way around ($$y$$ usually being the target variable). Then they didn't label the axes. The different colors are a nice idea but don't help me particularly, since I'm not even sure what we find on this axis.
From the leftmost Subfigure we learn that there are 10 $$x$$ values (I assume $$x$$ are instances of the random variable $$X$$.) In the text they write that that means the GP has 10 dimensions. I'm confused why they are all depicted on one axis and how these are different dimensions, even though they all come from $$X$$. Is this Subfigure representing a 10-dimensional space?
Since $$X∼\mathcal{N}(μ_X,Σ_{XX})$$, I'm not sure what the middle Subfigure indicates. Our output should be $$f(x)$$ which will be plotted on the vertical axis in the third Subfigure. Yet in the covariance matrix, there are 10 pairwise interactions between the dark pink point and all the others. What is the mean and variance here and why do they evaluate $$k(\mathrm{dark~pink}, \mathrm{light~pink})$$ instead of $$k(\mathrm{dark~pink}, \mathrm{dark~pink})$$ as might be expected from $$\Sigma_{XX}$$? How do we get from that particular $$k$$ in the middle Subfigure to the $$f(x)$$ in the right Subfigure.
My guess: One goes through $$k(\mathrm{dark~pink}, h)$$, where $$h \in \{ \mathrm{hues}\})$$ which gives $$f(x)$$ which is a 10-dimensional point along all axes spanned. So the 3rd Subfigure is the representation of this 10-dimensional point rather than the $$f(x)$$ of all the different hues.
Later in the article, conditionals are introduced: The noise-free and centered prediction with a conditional on the training data $$Y$$ would be $$X∣Y∼\mathcal{N}(Σ_{XY} Σ_{YY}^{-1}Y,Σ_{XX}-Σ_{XY}Σ_{YY}^{-1}Σ_{YX})$$ where I am not sure how the different parts belong to the Figure. $$Σ_{XY}$$ is probably the pink-orange kernel (basically the $$10 \times 2$$ and $$2 \times 10$$ off-blockdiagonals.) Conditioning on one of the points in $$Y$$ we yield another 12-dimensional (?) point, $$f(x)$$.
It is completely lost on me what the arrow in the last Subfigure means (but I'm sure it does, since it is on distill.pub and they don't just throw in random graphics, usually.)
Thanks for the help and bearing with me.
• I am afraid that your question may be too broad for site like this. You seem to ask us (1) explain you what GP's are, (2) go through the article almost line by line, commenting different parts of it. Could you make a specific question out of this? Otherwise it seems someone would have to write parallel article explaining GP's and commenting the distill... – Tim Apr 4 at 13:37
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2019-05-26 17:49:06
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https://cs50.harvard.edu/college/2021/fall/notes/7/
|
# Lecture 7
## Data processing
• Last week, we collected a survey of Hogwarts house preferences, and tallied the data from a CSV file with Python.
• This week, we’ll collect some more data about your favorite TV shows and their genres.
• We get hundreds of responses from the audience, and start looking at them on Google Sheets, a web-based spreadsheet application, showing our data in rows and columns:
• Like we did last week, we can download our data as a CSV file, which is an example of a flat-file database, where the data for each column is separated by commas, and each row is on a new line, saved simply as a text file in ASCII or Unicode.
• A flat-file database is completely portable, which means that we can open it on nearly any operating system without special software like Microsoft Excel or Apple Numbers.
• We’ll upload the CSV file to our instance of VS Code by dragging and dropping it:
• Then, we’ll see the file opened in an editor:
• Notice that some rows have multiple genres, and those are surrounded by quotes, like "Crime, Drama", so that the commas within our data aren’t misinterpreted.
• Let’s write a new program, favorites.py, to read our CSV file:
import csv
with open("favorites.csv", "r") as file:
for row in reader:
print(row[1])
• We’ll open the file with a reference called file, using the with keyword in Python that will close our file for us.
• The csv library has a reader function that will create a reader variable we can use to read in the file as a CSV.
• We’ll call next to skip the first row, since that’s the header row.
• Then, we’ll use a loop to print the second column in each row, which is the title.
• Now, if we run our program, we’ll see a list of show titles:
$python favorites.py ... Friends ... friends ... Friends ... • But for the show titled “Friends”, some entries are capitalized and some are lowercased. ### Cleaning • To improve our program, we’ll first use a DictReader, dictionary reader, which creates a dictionary from each row, allowing us to access each column by its name. We also don’t need to skip the header row in this case, since the DictReader will use it automatically. import csv with open("favorites.csv", "r") as file: reader = csv.DictReader(file) for row in reader: print(row["title"]) • Since the first row in our CSV has the names of the columns, it can be used to label each column in our data as well. Now our program will still work, even if the order of the columns are changed. • Now let’s try to filter out duplicates in our responses: import csv titles = [] with open("favorites.csv", "r") as file: reader = csv.DictReader(file) for row in reader: if not row["title"] in titles: titles.append(row["title"]) for title in titles: print(title) • We’ll make a new list called titles, and only add each row’s title if it’s not already in the list. Then, we can print all the titles: $ python favorites.py
...
Friends
...
friends
...
• We see that there are still near-duplicates, since Friends and friends are indeed different strings still.
• We’ll want to change the current title to all uppercase, and remove whitespace around it, before we add it to our list:
import csv
titles = []
with open("favorites.csv", "r") as file:
for row in reader:
title = row["title"].strip().upper()
if not title in titles:
titles.append(title)
for title in titles:
print(title)
• Now, we’ve canonicalized, or standardized, our data, and our list of titles are much cleaner:
$python favorites.py ... NEW GIRL FRIENDS THE OFFICE BREAKING BAD ... • It turns out that Python has another data structure built-in, set, which ensures that all the values are unique: import csv titles = set() with open("favorites.csv", "r") as file: reader = csv.DictReader(file) for row in reader: title = row["title"].strip().upper() titles.add(title) for title in titles: print(title) • Now, we can call add on the set, and not have to check ourselves if it’s already in the set. • To sort the titles, we can just change our loop to for title in sorted(titles), which will sort our set before we iterate over it: import csv titles = set() with open("favorites.csv", "r") as file: reader = csv.DictReader(file) for row in reader: title = row["title"].strip().upper() titles.add(title) for title in sorted(titles): print(title) $ python favorites.py
ANNE WITH AN E
...
AVATAR
AVATAR THE LAST AIRBENDER
AVATAR: THE LAST AIRBENDER
...
BROOKLYN 99
BROOKLYN-99
...
• Now, we see our titles alphabetized, but there were still a few different ways that a show’s title could be entered. We’ll leave these differences there for now, since it will likely take a bit more effort to fully standardize our data.
### Counting
• We can use a dictionary, instead of a set, to count the number of times we’ve seen each title, with the keys being the titles and the values being an integer counting the number of times we see each of them:
import csv
titles = {}
with open("favorites.csv", "r") as file:
for row in reader:
title = row["title"].strip().upper()
titles[title] += 1
for title in sorted(titles):
print(title)
• As we read each row, we increase the value stored for that title in the dictionary by 1.
• We’ll run this program, and see:
$python favorites.py Traceback (most recent call last): File "/workspaces/20377622/favorites.py", line 9, in <module> titles[title] += 1 KeyError: 'HOW I MET YOUR MOTHER' • We have a KeyError, since the title HOW I MET YOUR MOTHER isn’t in the dictionary yet. • We’ll have to add each title to our dictionary first, and set the initial value to 1: import csv titles = {} with open("favorites.csv", "r") as file: reader = csv.DictReader(file) for row in reader: title = row["title"].strip().upper() if title in titles: titles[title] += 1 else: titles[title] = 1 for title in sorted(titles): print(title, titles[title]) • We’ll add the values, or counts, to our loop that prints every show name. • We can also set the initial value to 0, and then increment it by 1 no matter what: import csv titles = {} with open("favorites.csv", "r") as file: reader = csv.DictReader(file) for row in reader: title = row["title"].strip().upper() if not title in titles: titles[title] = 0 titles[title] += 1 for title in sorted(titles): print(title, titles[title]) $ python favorites.py
ANNE WITH AN E 1
ARCHER 1
...
AVATAR THE LAST AIRBENDER 5
...
COMMUNITY 8
...
• Now, the key will exist in the dictionary, and we can safely refer to its value in the dictionary.
• We can sort by the values in the dictionary by changing our loop to:
...
def get_value(title):
return titles[title]
for title in sorted(titles, key=get_value, reverse=True):
print(title, titles[title])
• We define a function, f, which just returns the value of a title in the dictionary with titles[title]. The sorted function, in turn, will take in that function as the key to sort the dictionary. And we’ll also pass in reverse=True to sort from largest to smallest, instead of smallest to largest.
• So now we’ll see the most popular shows printed:
$python favorites.py THE OFFICE 15 FRIENDS 9 COMMUNITY 8 GAME OF THRONES 6 ... • We can actually define our function in the same line, with this syntax: for title in sorted(titles, key=lambda title: titles[title], reverse=True): print(title, titles[title]) • We can write and pass in a lambda, or anonymous function, which has no name but takes in some argument or arguments, and returns a value immediately. • Notice that there are no parentheses or return keyword, but concisely has the same effect as our get_value function earlier. • We can also try to count all the occurrences of a specific title: import csv counter = 0 with open("favorites.csv", "r") as file: reader = csv.DictReader(file) for row in reader: title = row["title"].strip().upper() if title == "THE OFFICE": counter += 1 print(f"Number of people who like The Office: {counter}") $ python favorites.py
Number of people who like The Office: 15
• We’ll have a simple counter variable, and add one to it.
• Now, if our data referred to the same show in different ways, we can try to check if the word “OFFICE” was in the title at all:
import csv
counter = 0
with open("favorites.csv", "r") as file:
for row in reader:
title = row["title"].strip().upper()
if "OFFICE" in title:
counter += 1
print(f"Number of people who like The Office: {counter}")
$python favorites.py Number of people who like The Office: 16 • It turns out that a row has a typo, “Thevoffice”, so now our count is correct. • We can also use regular expressions, a standardized way to represent a pattern that a string must match. • For example, we can write a regular expression that matches email addresses: .*@.*\..* • The first period, ., indicates any character. The following asterisk, *, indicates 0 or more times. Then, we want an at sign, @. Then we want 0 or more characters again, .*, and then a literal period in our string, escaped with \.. Finally, we want 0 or more characters again with .*. • Since we probably want at least 1 character in each segment of an email address, we should change our regular expression to: .+@.+\..+ • The plus sign, +, means we are matching for the previous character 1 or more times. • We can restrict the domain of the email to .edu by changing our regular expression to .+@.+\.edu. • Languages like Python and JavaScript support regular expressions, which are like a mini-language in themselves, with syntax like: • . for any character • .* for 0 or more characters • .+ for 1 or more characters • ? for an optional character • ^ for start of input • $ for end of input
• We can change our program earlier to use re, a Python library for regular expressions:
import csv
import re
counter = 0
with open("favorites.csv", "r") as file:
for row in reader:
title = row["title"].strip().upper()
if re.search("OFFICE", title):
counter += 1
print(f"Number of people who like The Office: {counter}")
$python favorites.py Number of people who like The Office: 16 • The re library has a function, search, to which we can pass a pattern and string to see if there is a match. • We can change our expression to "^(OFFICE|THE OFFICE)$", which will match either OFFICE or THE OFFICE, but only if they start at the beginning of the string, and stop at the end of the string (i.e., there are no other words before or after).
• We can even change THE OFFICE to THE.OFFICE, allowing any character (like a typo) to be in between those words.
• We can also write a program to ask the user for a particular title and report its popularity:
import csv
title = input("Title: ").strip().upper()
counter = 0
with open("favorites.csv", "r") as file:
for row in reader:
if row["title"].strip().upper() == title:
counter += 1
print(counter)
$python favorites.py Title: the office 13 • We ask the user for input, and then open our CSV file. Since we’re looking for just one title, we can have one counter variable that we increment. • We check for a match after standardizing both the user’s input and each row’s title. ## Relational databases • Relational databases are programs that store data, ultimately in files, but with additional data structures and interfaces that allow us to search and store data more efficiently. • When working with data, we generally need four types of basic operations with the acronym CRUD: • CREATE • READ • UPDATE • DELETE ### SQL • With another programming language, SQL (pronounced like “sequel”), we can interact with databases with verbs like: • CREATE, INSERT • SELECT • UPDATE • DELETE, DROP • Syntax in SQL might look like: CREATE TABLE table (column type, ...); • With this statement, we can create a table, which is like a spreadsheet with rows and columns. • In SQL, we choose the types of data that each column will store. • We’ll use a common database program called SQLite, one of many available programs that support SQL. Other database programs include Oracle Database, MySQL, PostgreSQL, and Microsoft Access. • SQLite stores our data in a binary file, with 0s and 1s that represent data efficiently. We’ll interact with our tables of data through a command-line program, sqlite3. • We’ll run some commands in VS Code to import our CSV file into a database: $ sqlite3 favorites.db
SQLite version 3.36.0 2021-06-18 18:36:39
Enter ".help" for usage hints.
sqlite> .mode csv
sqlite> .import favorites.csv favorites
• First, we’ll run the sqlite3 program with favorites.db as the name of the file for our database.
• With .import, SQLite creates a table in our database with the data from our CSV file.
• Now, we’ll see three files, including favorites.db:
$ls favorites.csv favorites.db favorites.py • We can open our database file again, and check the schema, or design, of our new table with .schema: $ sqlite3 favorites.db
SQLite version 3.36.0 2021-06-18 18:36:39
Enter ".help" for usage hints.
sqlite> .schema
CREATE TABLE IF NOT EXISTS "favorites"(
"Timestamp" TEXT,
"title" TEXT,
"genres" TEXT
);
• We see that .import used the CREATE TABLE ... command to create a table called favorites, with column names automatically copied from the CSV’s header row, and types for each of them assumed to be text.
• We can select, or read data, with:
sqlite> SELECT title FROM favorites;
+------------------------------------+
| title |
+------------------------------------+
| How i met your mother |
| The Sopranos |
| Friday Night Lights |
...
• With a command in the format SELECT columns FROM table;, we can read data from one or more columns. For example, we can write SELECT title, genre FROM favorites; to select both the title and genre.
• SQL supports many functions that we can use to count and summarize data:
• AVG
• COUNT
• DISTINCT
• LOWER
• MAX
• MIN
• UPPER
• We can clean up our titles as before, converting them to uppercase and printing only the unique values:
sqlite> SELECT DISTINCT(UPPER(title)) FROM shows;
...
| LAW AND ORDER |
| B99 |
| GOT |
...
• We can also get a count of how many responses there are:
sqlite> SELECT COUNT(title) FROM favorites;
+--------------+
| COUNT(title) |
+--------------+
| 158 |
+--------------+
• We can also add more phrases to our command:
• WHERE, adding a Boolean expression to filter our data
• LIKE, filtering responses more loosely
• ORDER BY
• LIMIT
• GROUP BY
• We can limit the number of results:
sqlite> SELECT title FROM favorites LIMIT 10;
+-----------------------+
| title |
+-----------------------+
| How i met your mother |
| The Sopranos |
| Friday Night Lights |
| Family Guy |
| New Girl |
| Friends |
| Office |
| Breaking Bad |
| Modern Family |
| Office |
+-----------------------+
• We can also look for titles matching a string:
sqlite> SELECT title FROM favorites WHERE title LIKE "%office%";
+-------------+
| title |
+-------------+
| Office |
| Office |
| The Office |
| The Office |
| The Office |
| The Office |
| The Office |
| The Office |
| The Office |
| The Office |
| The Office |
| the office |
| The Office |
| ThE OffiCE |
| The Office |
| Thevoffice |
+-------------+
• The % character is a placeholder for zero or more other characters, so SQL supports some pattern matching, though not it’s not as powerful as regular expressions are.
• We can select just the count in our command:
sqlite> SELECT COUNT(title) FROM favorites WHERE title LIKE "%office%";
+--------------+
| COUNT(title) |
+--------------+
| 16 |
+--------------+
• If we don’t like a show, we can even delete it:
sqlite> SELECT COUNT(title) FROM favorites WHERE title LIKE "%friends%";
+--------------+
| COUNT(title) |
+--------------+
| 9 |
+--------------+
sqlite> DELETE FROM favorites WHERE title LIKE "%friends%";
sqlite> SELECT COUNT(title) FROM favorites WHERE title LIKE "%friends%";
+--------------+
| COUNT(title) |
+--------------+
| 0 |
+--------------+
• With SQL, we can change our data more easily and quickly than with Python.
• We can update a specific row of data:
sqlite> SELECT title FROM favorites WHERE title = "Thevoffice";
+------------+
| title |
+------------+
| Thevoffice |
+------------+
sqlite> UPDATE favorites SET title = "The Office" WHERE title = "Thevoffice";
sqlite> SELECT title FROM favorites WHERE title = "Thevoffice";
sqlite>
• Now, we’ve changed that row’s value.
• We can change the values in multiple rows, too:
sqlite> SELECT genres FROM favorites WHERE title = "Game of Thrones";
+--------------------------------------------------------------------------------------------------------------+
| genres |
+--------------------------------------------------------------------------------------------------------------+
| Action, Adventure, Drama, Fantasy, Thriller, War |
| Action, Adventure, Drama |
| Action, Adventure, Comedy, Drama, Family, Fantasy, History, Horror, Musical, Mystery, Romance, Thriller, War |
| Action, Drama, Family, Fantasy, War |
| Fantasy, Thriller, War |
+--------------------------------------------------------------------------------------------------------------+
sqlite> UPDATE favorites SET genres = "Action, Adventure, Drama, Fantasy, Thriller, War" WHERE title = "Game of Thrones";
sqlite> SELECT genres FROM favorites WHERE title = "Game of Thrones";
+--------------------------------------------------+
| genres |
+--------------------------------------------------+
| Action, Adventure, Drama, Fantasy, Thriller, War |
| Action, Adventure, Drama, Fantasy, Thriller, War |
| Action, Adventure, Drama, Fantasy, Thriller, War |
| Action, Adventure, Drama, Fantasy, Thriller, War |
| Action, Adventure, Drama, Fantasy, Thriller, War |
+--------------------------------------------------+
• With DELETE and DROP, we can remove rows and even entire tables as well.
• And notice that in our commands, we’ve written SQL keywords in all caps, so they stand out more.
• There also isn’t a built-in way to undo commands, so if we make a mistake we might have to build our database again!
### Tables
• We’ll take a look at our schema again:
sqlite> .schema
CREATE TABLE IF NOT EXISTS "favorites"(
"Timestamp" TEXT,
"title" TEXT,
"genres" TEXT
);
• If we look at our values of genres, we see some redundancy:
sqlite> SELECT genres FROM favorites;
+-----------------------------------------------------------+
| genres |
+-----------------------------------------------------------+
| Comedy |
| Comedy, Crime, Drama, Horror, Sci-Fi, Talk-Show, Thriller |
| Drama, Family, Sport |
| Animation, Comedy |
| Comedy, Drama |
...
• And if we want to search for shows that are comedies, we have to search with not just SELECT title FROM favorites WHERE genre = "Comedy";, but also ... WHERE genre = "Comedy, Drama";, ... WHERE genre = "Comedy, News";, and so on.
• We can use the LIKE keyword again, but two genres, “Music” and “Musical”, are similar enough for that to be problematic.
• We can actually write our own Python program that will use SQL to import our CSV data into two tables:
# Imports titles and genres from CSV into a SQLite database
import cs50
import csv
# Create database
open("favorites8.db", "w").close()
db = cs50.SQL("sqlite:///favorites8.db")
# Create tables
db.execute("CREATE TABLE shows (id INTEGER, title TEXT NOT NULL, PRIMARY KEY(id))")
db.execute("CREATE TABLE genres (show_id INTEGER, genre TEXT NOT NULL, FOREIGN KEY(show_id) REFERENCES shows(id))")
# Open CSV file
with open("favorites.csv", "r") as file:
# Iterate over CSV file
for row in reader:
# Canoncalize title
title = row["title"].strip().upper()
# Insert title
show_id = db.execute("INSERT INTO shows (title) VALUES(?)", title)
# Insert genres
for genre in row["genres"].split(", "):
db.execute("INSERT INTO genres (show_id, genre) VALUES(?, ?)", show_id, genre)
• First, we import the Python cs50 library so we can run SQL commands more easily.
• Then, the rest of this code will import each row of favorites.csv.
• Now, our database will have this design:
$sqlite3 favorites8.db SQLite version 3.36.0 2021-06-18 18:36:39 Enter ".help" for usage hints. sqlite> .schema CREATE TABLE shows (id INTEGER, title TEXT NOT NULL, PRIMARY KEY(id)); CREATE TABLE genres (show_id INTEGER, genre TEXT NOT NULL, FOREIGN KEY(show_id) REFERENCES shows(id)); • We have one table, shows, with an id column and a title column. We can specify that a title isn’t null, and that id is the column we want to use as a primary key. • Then, we’ll have a table called genres, where we have a show_id column that references our shows table, along with a genre column. • This is an example of a relation, like a link, between rows in different tables in our database. • In our shows table, we’ll see each show with an id number: sqlite> SELECT * FROM shows; +-----+------------------------------------+ | id | title | +-----+------------------------------------+ | 1 | HOW I MET YOUR MOTHER | | 2 | THE SOPRANOS | | 3 | FRIDAY NIGHT LIGHTS | | 4 | FAMILY GUY | | 5 | NEW GIRL | | 6 | FRIENDS | | 7 | OFFICE | ... • And we can see that the genres table has one or more rows for each show_id: sqlite> SELECT * FROM genres; +---------+-------------+ | show_id | genre | +---------+-------------+ | 1 | Comedy | | 2 | Comedy | | 2 | Crime | | 2 | Drama | | 2 | Horror | | 2 | Sci-Fi | | 2 | Talk-Show | | 2 | Thriller | | 3 | Drama | | 3 | Family | | 3 | Sport | | 4 | Animation | | 4 | Comedy | | 5 | Comedy | | 6 | Comedy | | 7 | Comedy | ... • Since each show may have more than one genre, we can have more than one row per show in our genres table, known as a one-to-many relationship. • Furthermore, the data is now cleaner, since each genre name is in its own row. • We can select all the shows are that comedies by selecting from the genres table first, and then looking for those ids in the shows table: sqlite> SELECT title FROM shows WHERE id IN (SELECT show_id FROM genres WHERE genre = "Comedy"); +------------------------------------+ | title | +------------------------------------+ | HOW I MET YOUR MOTHER | | THE SOPRANOS | | FAMILY GUY | | NEW GIRL | | FRIENDS | | OFFICE | | MODERN FAMILY | ... • Notice that we’ve nested two queries, where the inner one returns a list of show ids, and the outer one uses those to select the titles of shows that match. • Now we can sort and show just the unique titles by adding to our command: sqlite> SELECT DISTINCT(title) FROM shows WHERE id IN (SELECT show_id FROM genres WHERE genre = "Comedy") ORDER BY title; +------------------------------------+ | title | +------------------------------------+ | ARCHER | | ARRESTED DEVELOPMENT | | AVATAR THE LAST AIRBENDER | | B99 | | BILLIONS | | BLACK MIRROR | ... • And we can add new data to each table, in order to add another show. First, we’ll add a new row to the shows table for Seinfeld: sqlite> INSERT INTO shows (title) VALUES("Seinfeld"); • Then, we can get our row’s id by looking for it in the table: sqlite> SELECT * FROM shows WHERE title = "Seinfeld"; +-----+----------+ | id | title | +-----+----------+ | 159 | Seinfeld | +-----+----------+ • We’ll use that as the show_id to add a new row in the genres table: sqlite> INSERT INTO genres (show_id, genre) VALUES(159, "Comedy"); • Then, we’ll use UPDATE to set the title to uppercase: sqlite> UPDATE shows SET title = "SEINFELD" WHERE title = "Seinfeld"; • Finally, we’ll run the same command as before, and see our new show is indeed in the list of comedies: sqlite> SELECT DISTINCT(title) FROM shows WHERE id IN (SELECT show_id FROM genres WHERE genre = "Comedy") ORDER BY title; ... | SEINFELD | ... ## SQL with Python • It turns out that we’ll be able to write Python code that automates this, so we can imagine building web applications that can programmatically store and look up user data, online shopping orders, and more. • We can write a program that asks the user for a show title and then prints its popularity: import csv from cs50 import SQL db = SQL("sqlite:///favorites.db") title = input("Title: ").strip() rows = db.execute("SELECT COUNT(*) AS counter FROM favorites WHERE title LIKE ?", title) row = rows[0] print(row["counter"]) • We’ll use the cs50 library to run SQL commands more easily, and open the favorites.db database we created earlier. • We’ll prompt the user for a title, and then execute a command. A ? in the command will allow us to safely substitute variables in our command. • The results are returned in a list of rows, and COUNT(*) returns just one row. In our command, we’ll add AS counter, so the count is returned in the row (which is a dictionary) with the column name counter. • We can run our program and search for “The Office”: $ python favorites.py
Title: The Office
12
• And we can tweak our program to print all the rows that match:
import csv
from cs50 import SQL
db = SQL("sqlite:///favorites.db")
title = input("Title: ").strip()
rows = db.execute("SELECT title FROM favorites WHERE title LIKE ?", title)
for row in rows:
print(row["title"])
$python favorites.py Title: The Office The Office The Office The Office The Office The Office The Office The Office The Office the office The Office ThE OffiCE The Office The Office • Since LIKE is case-insensitive, we see all the various ways the titles were capitalized. ## IMDb • IMDb, or the Internet Movie Database, has datasets available for download as TSV (tab-separated values) files. • We’ll open a database that the staff has created beforehand: $ sqlite3 shows.db
SQLite version 3.36.0 2021-06-18 18:36:39
Enter ".help" for usage hints.
sqlite> .schema
CREATE TABLE shows (
id INTEGER,
title TEXT NOT NULL,
year NUMERIC,
episodes INTEGER,
PRIMARY KEY(id)
);
CREATE TABLE genres (
show_id INTEGER NOT NULL,
genre TEXT NOT NULL,
FOREIGN KEY(show_id) REFERENCES shows(id)
);
CREATE TABLE stars (
show_id INTEGER NOT NULL,
person_id INTEGER NOT NULL,
FOREIGN KEY(show_id) REFERENCES shows(id),
FOREIGN KEY(person_id) REFERENCES people(id)
);
CREATE TABLE writers (
show_id INTEGER NOT NULL,
person_id INTEGER NOT NULL,
FOREIGN KEY(show_id) REFERENCES shows(id),
FOREIGN KEY(person_id) REFERENCES people(id)
);
CREATE TABLE ratings (
show_id INTEGER NOT NULL,
rating REAL NOT NULL,
votes INTEGER NOT NULL,
FOREIGN KEY(show_id) REFERENCES shows(id)
);
CREATE TABLE people (
id INTEGER,
name TEXT NOT NULL,
birth NUMERIC,
PRIMARY KEY(id)
);
• Notice that we have multiple tables, each of which has columns of various data types.
• In both the stars and writers table, for example, we have a show_id column that references the id of some row in the shows table, and a person_id column that references the id of some row in the people table. Effectively, they link shows and people by their ids.
• It turns out that SQL, too, has its own data types:
• BLOB, for “binary large object”, raw binary data that might represent files
• INTEGER
• NUMERIC, number-like but not quite a number, like a date or time
• REAL, for floating-point values
• TEXT, like strings
• Columns can also have additional attributes:
• PRIMARY KEY, like the id columns above that will be used to uniquely identify each row
• FOREIGN KEY, like the show_id column above that refers to a column in some other table
• We can see that there are millions of rows in the people table:
sqlite> SELECT * FROM people;
...
| 13058200 | Emilio Mancuso | |
| 13058201 | Pietro Furnis | |
| 13058202 | Ida Lonati Frati | |
+----------+-----------------------------------------------------+-------+
• But like before, we can search for just one row:
sqlite> SELECT * FROM people WHERE name = "Steve Carell";
+--------+--------------+-------+
| id | name | birth |
+--------+--------------+-------+
| 136797 | Steve Carell | 1962 |
+--------+--------------+-------+
• It turns out that there are a few shows titled “The Office”:
sqlite> SELECT * FROM shows WHERE title = "The Office";
+---------+------------+------+----------+
| id | title | year | episodes |
+---------+------------+------+----------+
| 112108 | The Office | 1995 | 6 |
| 290978 | The Office | 2001 | 14 |
| 386676 | The Office | 2005 | 188 |
| 1791001 | The Office | 2010 | 30 |
| 2186395 | The Office | 2012 | 8 |
| 8305218 | The Office | 2019 | 28 |
+---------+------------+------+----------+
• The most popular one, with 188 episodes, is the one we want, so we can get just that one:
sqlite> SELECT * FROM shows WHERE title = "The Office" and year = "2005";
+--------+------------+------+----------+
| id | title | year | episodes |
+--------+------------+------+----------+
| 386676 | The Office | 2005 | 188 |
+--------+------------+------+----------+
• We can turn on a timer and see that our original command took about 0.02 seconds to run:
sqlite> .timer on
sqlite> SELECT * FROM shows WHERE title = "The Office";
+---------+------------+------+----------+
| id | title | year | episodes |
+---------+------------+------+----------+
| 112108 | The Office | 1995 | 6 |
| 290978 | The Office | 2001 | 14 |
| 386676 | The Office | 2005 | 188 |
| 1791001 | The Office | 2010 | 30 |
| 2186395 | The Office | 2012 | 8 |
| 8305218 | The Office | 2019 | 28 |
+---------+------------+------+----------+
Run Time: real 0.021 user 0.016419 sys 0.004117
• We can create an index, or additional data structures that our database program will use for future searches:
sqlite> CREATE INDEX "title_index" ON "shows" ("title");
Run Time: real 0.349 user 0.195206 sys 0.051217
• Now, our search command takes nearly no time:
sqlite> SELECT * FROM shows WHERE title = "The Office";
+---------+------------+------+----------+
| id | title | year | episodes |
+---------+------------+------+----------+
| 112108 | The Office | 1995 | 6 |
| 290978 | The Office | 2001 | 14 |
| 386676 | The Office | 2005 | 188 |
| 1791001 | The Office | 2010 | 30 |
| 2186395 | The Office | 2012 | 8 |
| 8305218 | The Office | 2019 | 28 |
+---------+------------+------+----------+
Run Time: real 0.000 user 0.000104 sys 0.000124
• It turns out that these data structures are generally B-trees, like binary trees we’ve seen in C but with more children, with nodes organized such that we can search faster than linearly:
• Creating an index takes some time up front, perhaps by sorting the data, but afterwards we can search much more quickly.
• With our data spread among different tables, we can nest our queries to get useful data. For example, we can get all the titles of shows starring a particular person:
sqlite3> SELECT title FROM shows WHERE id IN (SELECT show_id FROM stars WHERE person_id = (SELECT id FROM people WHERE name = "Steve Carell"));
+------------------------------------+
| title |
+------------------------------------+
| The Dana Carvey Show |
| Over the Top |
| Watching Ellie |
| Come to Papa |
| The Office |
...
• We’ll SELECT the title from the shows table for shows with an id that matches a list of show_ids from the stars table. Those show_ids, in turn, must have a person_id that matches the id of Steve Carell in the people table.
• Our query runs pretty quickly, but we can create a few more indexes:
sqlite> CREATE INDEX person_index ON stars (person_id);
Run Time: real 0.890 user 0.662294 sys 0.097505
sqlite> CREATE INDEX show_index ON stars (show_id);
Run Time: real 0.644 user 0.469162 sys 0.058866
sqlite> CREATE INDEX name_index ON people (name);
Run Time: real 0.840 user 0.609600 sys 0.088177
• Each index takes almost a second to build, but afterwards, our same query takes very little time to run.
• It turns out that we can use JOIN commands to combine tables in our queries:
sqlite> SELECT title FROM people
...> JOIN stars ON people.id = stars.person_id
...> JOIN shows ON stars.show_id = shows.id
...> WHERE name = "Steve Carell";
• With the JOIN syntax, we can virtually combine tables based on their foreign keys, and use their columns as though they were one table. Here, we’re matching the people table with the stars table, and then with the shows table.
• We can format the same query a little better by listing the tables we want to use all at once:
sqlite> SELECT title FROM people, stars, shows
...> WHERE people.id = stars.person_id
...> AND stars.show_id = shows.id
...> AND name = "Steve Carell";
+------------------------------------+
| title |
+------------------------------------+
| The Dana Carvey Show |
| Over the Top |
| Watching Ellie |
| Come to Papa |
| The Office |
• The downside to having lots of indexes is that each of them take up some amount of space, which might become significant with lots of data and lots of indexes.
## Problems
• One problem in SQL is called a SQL injection attack, where an someone can inject, or place, their own commands into inputs that we then run on our database.
• We might encounter a login page for a website that asks for a username and password, and checks for those in a SQL database.
• Our query for searching for a user might be:
rows = db.execute("SELECT * FROM users WHERE username = ? AND password = ?", username, password)
if len(rows) == 1:
# Log user in
• By using the ? symbols as placeholders, our SQL library will escape the input, or prevent dangerous characters from being interpreted as part of the command.
• In contrast, we might have a SQL query that’s a formatted string, such as:
rows = db.execute(f"SELECT * FROM users WHERE username = '{username}' AND password = '{password}'")
if len(rows) == 1:
# Log user in
• If a user types in malan@harvard.edu'-- as their input, then the query will end up being:
rows = db.execute(f"SELECT * FROM users WHERE username = 'malan@harvard.edu'--' AND password = '{password}'")
• This query will actually select the row where username = 'malan@harvard.edu', without checking the password, since the single quotes end the input, and -- turns the rest of the line into a comment in SQL.
• The user could even add a semicolon, ;, and write a new command of their own, that our database will execute.
• Another set of problems with databases are race conditions, where shared data is unintentionally changed by code running on different devices or servers at the same time.
• One example is a popular post getting lots of likes. A server might try to increment the number of likes, asking the database for the current number of likes, adding one, and updating the value in the database:
rows = db.execute("SELECT likes FROM posts WHERE id = ?", id);
likes = rows[0]["likes"]
db.execute("UPDATE posts SET likes = ? WHERE id = ?", likes + 1, id);
• Two different servers, responding to two different users, might get the same starting number of likes since the first line of code runs at the same time on each server.
• Then, both will use UPDATE to set the same new number of likes, even though there should have been two separate increments.
• Another example might be of two roommates and a shared fridge in their dorm. The first roommate comes home, and sees that there is no milk in the fridge. So the first roommate leaves to the store to buy milk. While they are at the store, the second roommate comes home, sees that there is no milk, and leaves for another store to get milk as well. Later, there will be two jugs of milk in the fridge.
• We can solve this problem by locking the fridge so that our roommate can’t check whether there is milk until we’ve gotten back.
• To solve this problem, SQL supports transactions, where we can lock rows in a database, such that a particular set of actions are atomic, or guaranteed to happen together.
• For example, we can fix our problem above with:
db.execute("BEGIN TRANSACTION")
rows = db.execute("SELECT likes FROM posts WHERE id = ?", id);
likes = rows[0]["likes"]
db.execute("UPDATE posts SET likes = ? WHERE id = ?", likes + 1, id);
db.execute("COMMIT")
• The database will ensure that all the queries in between are executed together.
• But the more transactions we have, the slower our applications might be, since each server has to wait for other servers’ transactions to finish.
|
2022-05-22 23:15:50
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|
https://www.numerade.com/questions/find-the-derivative-simplify-where-possible-y-cosh-1-sqrt-x/
|
💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
# Find the derivative. Simplify where possible.$y = \cosh^{-1} \sqrt x$
## $\frac{1}{2 \sqrt{x(x-1)}}$
Derivatives
Differentiation
### Discussion
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##### Heather Z.
Oregon State University
##### Kristen K.
University of Michigan - Ann Arbor
##### Samuel H.
University of Nottingham
Lectures
Join Bootcamp
### Video Transcript
All right, let's go ahead and solve this problem. The question is find the ark Coach of Squared of Exes derivative with respect to X. Okay, so there's a couple of ways you can approach this, of course. And it also depends on what you remember. So if you remember the derivative off our coach, which is equal to one over the square, root off X squared minus one when X is a number greater than or equal to one. Oh, strictly greater than one, because we don't want the denominator to be zero. Then we can use this fact. So I'm going to approach this the first way. Okay, so if I use that fact, then we're simply going to use changeable. It is going to look like one over square root off the input squared. So the squared off X quantity squared minus one times the derivative off the square root of X, which we know that it is equal to one over to root X. Okay, Now, one thing that you need to keep in mind here is that square root of X quantity squared is equal to the absolute value of X. Okay, so if we want to make sure that things work out nicely. For example, here we know that the denominator may contain a zero, or we know that inside the square root we want to avoid imaginary number negative numbers so that we don't get imaginary numbers. So if we use those kind of assumptions, we can try to say things such as Okay, what if X is greater than one? Well, under this condition, we know that absolute value of X will end up being X. So if we want to make the calculations look simpler, we want to add these assumptions to make this look like the absolute value off to root X times the square root off X minus one, assuming that X is greater than one. So that's one way to solve this thing. The other way to approach this problem is if you remember that Coach inverse of X is equal to the natural log off X plus square root of X squared minus one where X is greater than or equal toe one. Then we're going to take the derivative off a natural log basically, and then we're going to approach it with the channel multiple times so I'm not gonna go into detail. But simply put, we're gonna have it in the form one over X plus the square root off X squared minus one instead of ex you would be using the square root of X. And the same argument is going to appear with this expression. And you will be multiplying the derivative off the input, which is going to be the derivative off this expression with, of course, the square works the square root substitute and okay, and then we should get the exact same result. And that's how you find the derivative off our coach.
University of California, Berkeley
#### Topics
Derivatives
Differentiation
##### Heather Z.
Oregon State University
##### Kristen K.
University of Michigan - Ann Arbor
##### Samuel H.
University of Nottingham
Lectures
Join Bootcamp
|
2021-10-25 06:16:49
|
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https://cstheory.stackexchange.com/questions/17152/how-to-find-the-first-k-points-of-high-enough-level-using-a-priority-search-tr
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# How to find the first $k$ points of high enough level using a priority search tree?
In reading Chan's paper, Closest Point Problems Simplified on a RAM, the following came up as a sub-problem:
Given a set $P$ of points in the plane, and a query point $q$, find the first $k$ points (ordered by $x$-coordinate) which dominate $q$.
Chan asserts that this query can be answered in $O(\log n + k)$ time using a priority search tree, but doesn't give details, and the details are not clear to me. The traditional query for a priority search tree is a 3-sided range query, but this query is different because we are given a 2-sided range (an upper-right quadrant) and a maximum number of points to report. We should report the $k$ "leftmost" points in the 2-sided range.
• I don't really understand the question. What are the "first" $k$ points, and what does it mean to "dominate" a point? Are those both by the same axis? If you have a balanced binary search tree that answers queries like "Which $k$ keys are the smallest ones larger than the key $x$?" in time $O(\lg n + k)$, will that answer your question? – jbapple Apr 5 '13 at 2:14
• @jbapple a point $p$ dominates $q$ if both coordinates are at least as large as $q$, i.e. $p.x \geq q.x$ and $p.y \geq q.y$. – Joe Apr 5 '13 at 17:14
• @jbapple here's a naiive algorithm that clarifies the points which should be returned. Sort all the points according to $x$ coordinate. Store them in a linked list. Given a pointer to the location of $q$ in the linked list, we simply walk through the list. First look at its successor $p_1$ in the linked list, the next point ordered by $x$ coordinate. However, $p_1$ only "counts" if its $y$ coordinate is at least as high as $q.y$. Then, we look at the successor of $p_1$, and again compare $p_1.y$ and $q.y$. We continue until we have found $k$ points that count. – Joe Apr 5 '13 at 17:19
The tree is binary and has depth $O(\log(n))$ and the properties that:
• for any non-root node $v$, the y-coordinate of $v$ is larger than that of its parent.
• for any node $v$, all descendants in the left subtree have x-coordinate smaller than $v$, and all descendants in the right subtree have x-coordinate larger than $v$.
This means that your solution set from which you choose $k$ elements is actually a subtree one side (in the left/right sense) of what remains when a path is deleted, and can be traversed with DFS in $(\log(n)+k)$ time. Note that the priority search tree may require dummy points at which you root subtrees to keep the depth low.
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2019-09-17 07:16:30
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http://tex.stackexchange.com/questions/87867/do-i-need-a-specific-package-for-n/87869
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# Do I need a specific package for “\N”
The wikepedia page Folge has this formula (under Formale Definition)
\begin{matrix} a:&\N &\to &X\\ & i &\mapsto &a_i, \end{matrix}
where \N is used for the set of natural numbers. I am able to create its symbol with a \mathbb{N}. But when I use \N, I get the error ! Undefined control sequence..
I assume I need to use a specific package in order to have \N defined. Is this so and if so, which one is it?
-
no just define \N yourself: \usepackage{amsfonts} \newcommand\N{\mathbb{N}} – David Carlisle Dec 21 '12 at 12:53
I see. Does wikipedia do this definition "behind the scenes"? – René Nyffenegger Dec 21 '12 at 12:57
Instead of that font I use dsfonts package, which defines \mathds{} instead of \mathbb{} and gives you better output (in my opinion). – Manuel Dec 21 '12 at 14:38
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2016-02-12 18:41:17
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http://www.topmysterynovels.com/hope-to-die-page-49
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# Hope To Die Page 49
I said, ’’From Bergdorf\s?’’ They had a men\s store, she said, and this was gift-wrapped, and the card had my name on it. I took it from her, mystified.
It was an alligator wallet, a beauty. There was no card, and I took it out of the box and looked for a note, and the thing was crammed with money, crisp new hundred-dollar bills. There were fifty of them, and a card that said ’’A Gift for You’’ and was initialed K. H.
I got her on the phone and she said, ’’You did me a favor and I gave you a gift. Isn\ that how it works?’’
When someone gives you money, you thank them and put it in your pocket. A cop named Vince Mahaffey had taught me that many years ago, and I\d learned my lesson well.
I gave half the money to T J, figuring he\d done half the work, and maybe more. His eyes got very wide for a moment, and then he took the money and thanked me, and folded the bills and put them in his pocket. He\d learned, too.
Elaine and I had had dinner one night with Ira Wentworth and his wife, and one afternoon he came over, explaining he\d found himself in the neighborhood and couldn\ think of a better place to get a cup of coffee. We sat in the kitchen and talked mostly about baseball, and the chances of a Subway Series. ’’The rest of the country\ll hate that,’’ he said, ’’but you know what? The rest of the country can go screw itself.’’
And a little later he said, ’’You know, if you ever wanted to get your PI ticket back, there\s a few of us\d be more than happy to write letters on your behalf.’’
’’Thanks,’’ I said. ’’I appreciate it. But I think I\m happy leaving things the way they are.’’
’’Well, the offer\s open,’’ he said. ’’In case you happen to change your mind.’’
I had that conversation in mind after the gift arrived from Kristin Hollander, and it wasn\ long before I found myself climbing the steps and entering the sanctuary at St. Paul\s. The big room was empty, and I took a seat in a rear pew and just sat there for a while. Then I went to a side altar and lit a whole batch of candles, and then I sat down again and thought how things had changed, and how they hadn\ .
On my way out I stuffed $250 in the poor box. Don\ ask me why. FORTY-ONE There is so much to learn! Take knives, for example. For the longest time all he knew about a knife was how to cut his meat with it. Then he bought a knife, a handsome one in a handsome sheath, paid fifty dollars for it, plus tax, and owned it for what, two, three hours? Not that he regrets the cost. It\s gone, that handsome knife, and he thinks of it fondly, but it doesn\ owe him a penny. Oh, no. No, he got his money\s worth out of that piece of sharpened steel. His new knife looks rather like the last one. It too is a Bowie-type, with the same overall design. It is perhaps an inch shorter, and the blood groove is perhaps a shade deeper, but otherwise it looks no different to the uneducated eye. It cost four times what the first one did. Two hundred dollars- but there was no tax to pay, because no one collected tax at the knife and gun show where he bought it. He saw a knife quite like his for a little less than he\d paid, and he saw this one, right next to it, tagged$225, and he pointed to it and asked the bearded bear of a dealer why it was priced so high.
He\d never heard of a bench-made knife. The dealer told him about custom knifemakers who made one knife at a time, the best of them working only on commission, and often booked up a year or two in advance. He drank in the information, and the man responded to his receptivity by bringing knife after knife out of his case, explaining the fine points, inviting him to hold the knives and feel their balance.
’’You have a feel for these,’’ the dealer told him. ’’You buy one of these, a year from now you\ e gonna have a whole wall cabinet full of \em. I can tell.’’
He looked at dozens of knives and bought the first one that had caught his eye, the Randall. And now, weeks later and a thousand miles to the west, he sits on the edge of his motel bed and holds the knife in his hand, appreciating its lines, feeling its perfect balance.
He has two guns, too, both purchased at the same wonderfully convenient show. One is a.22, a pistol, very much like the one he used in New York, but this has a ten-shot clip, and he has three spare clips for it. The other is a five-shot revolver, and he has a box of.38-caliber shells for it.
He likes them, but he likes the knife better.
But, for all that he likes them, the guns and the wonderful Randall-made knife, they are, finally, just things. They exist to be owned, to be employed, to be appreciated, but they\ e things, and they come and go.
You get what you get.
You make what you can of it.
And then you move on.
It was sad to leave so many things behind. It was sad to leave his apartment, with its splendid view of the park. It was sad to leave all his clothes, including some perfectly fine shirts and ties. Harold Fischer had excellent taste when it came to shirts and ties.
It was sad to leave his house, to leave it before it had even come into his possession. He\d worked so hard for that house, he\d planned to thoroughly...
It was gone. Let it go.
Oh, and saddest of all, he\d had to leave his friends, the people who loved him so. He remembers the joy with which they greeted him. ’’Doc! Hello, Doc! Doc, it\s so good to see you! We love you, Doc!’’
Lucian and Marsha appearing on the stairs. And, behind them, shy and wide-eyed, a college friend of Marsha\s, who\d just shown up that afternoon, unannounced and unexpected, but welcome. And his name?
Isaac.
Could anything be more perfect, more of a sign from on high? But where is the ram for the sacrifice, father? The Lord will provide the ram for the sacrifice, my son, my beloved Isaac.
Gone now, all of them. Unforgettable, all of them, but replaceable, every one of them. Consider the knife. He\d loved that knife, loved the reassuring presence of it on his hip, the feel of it in his hand. It\s gone- but now he has a better one!
He reaches into his open shirt collar, remembering the feel of the disc of rhodochrosite, remembering too the clarity it had provided. But one can absorb and internalize an amulet, he has come to realize. The rhodochrosite is gone, left behind in a city he need never return to, but the clarity it provided will be a part of him forever. He could get another amulet of the same mineral, it\s neither rare nor costly, but, you see, he doesn\ need to.
He draws out the stone he is wearing now, a crystal, almost colorless at its point, a deep purple at its broken end. He holds it, and feels its power.
He sits at the desk, boots up his computer, gets on-line. He liked the other computer better, liked the larger keyboard, liked his New York Night screensaver. This machine\s a laptop, and he doesn\ need a screensaver. He shuts it down entirely when he\s not using it. He\s less fond of it in many respects than his desk model, but he must admit it suits his lifestyle. When he\s ready to put down roots again, that will be time enough to get a desk model computer.
And he\ll be careful what he leaves on its desktop, too.
The cheery voice welcomes him, but does not tell him he has mail. He\s just opened this account, and there\s no one who knows of it, no one to send him mail.
He goes straight to alt.crime.serialkillers.
And catches up on the new posts in the several current threads centering on the late and variously lamented Adam Breit. Here again, he thinks, you can see the glass half empty or half full. On the one hand, Adam Breit is dead;on the other, Adam Breit lives!
Breit lives, indeed, as he had never lived before. Adam Breit has made a name for himself, a name with a long line of notches carved next to it. As he reads the new messages, he shakes his head at some of the comments. There are people out there who would credit Adam Breit with every dead massage-parlor whore from Maine to California, others who are sure he was personally acquainted with John Wayne Gacy. And, here and on the several Web sites devoted to Breit, there\s a certain amount of speculation that Breit might somehow have survived, that the body burned beyond recognition might not be his, that he might have escaped to kill again.
Idiots.
Adam Breit is dead. Adam Breit will live on in memory, in legend, but in the flesh he has gone out in a blaze of glory, not unlike Jim Bowie at the Alamo. Another great knife-fighter, gone to his reward.
He won\ be back.
Alvin Benjamin, on the other hand, is very much alive. Of course no one has heard of him.
But they will...
His fingers find his new amulet, and he caresses the stone. The mineral is quartz, and its color marks it as the variety known as amethyst.
For immortality.
THE END
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2017-12-12 13:55:12
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https://www.gradesaver.com/textbooks/math/calculus/university-calculus-early-transcendentals-3rd-edition/chapter-9-section-9-9-convergence-of-taylor-series-exercises-page-542/39
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## University Calculus: Early Transcendentals (3rd Edition)
Error $\lt 1.67 \times 10^{-10}$
The Taylor series for $\sin x$ can be defined as: $\sin x= x-\dfrac{x^3}{3!}+\dfrac{ x^5}{5!}-....$ and $\sin x= x-\dfrac{x^3}{6}+\dfrac{ x^5}{120}-....$ We need to find $x$. $|\dfrac{x^3}{6}| \lt |\dfrac{(10^{-3})^3}{6}|$ or, $|\dfrac{x^3}{6}| \lt |\dfrac{(10^{-3})^3}{6}| = \dfrac{10^{-9}}{6}$ or, Error $\lt |\dfrac{(10^{-3})^3}{3 !}| \approx 1.67 \times 10^{-10}$ or, Error $\lt 1.67 \times 10^{-10}$
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2019-12-07 18:50:58
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https://ftp.aimsciences.org/article/doi/10.3934/jimo.2019094
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# American Institute of Mathematical Sciences
November 2020, 16(6): 3065-3081. doi: 10.3934/jimo.2019094
## Mean-CVaR portfolio selection model with ambiguity in distribution and attitude
1 Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Fujian, China 2 Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou, China
* Corresponding author: Zhongfei Li
Received November 2018 Revised March 2019 Published November 2020 Early access July 2019
Fund Project: The first author was supported in part by the Program for Innovative Research Team in Science and Technology in Fujian Province University, and Quanzhou High-Level Talents Support Plan (No. 2017ZT012), and the Scientific Research Foundation of Huaqiao University (No. 18BS311). The third author was supported by the National Natural Science Foundation of China (No. 71721001) and the Natural Science Research Team of Guangdong Province of China (No. 2014A030312003)
In this paper, we develop $\alpha$-robust (maxmin) models, where the Conditional Value-at-Risk (CVaR) is to be optimized under ambiguity in distribution, mean returns, and covariance matrix. Our models allow the investor to distinguish ambiguity and ambiguity attitude with different levels of ambiguity aversion. For the case when there is a risk-free asset and short-selling is allowed, we obtain the analytic solution for the $\alpha$-robust CVaR optimization model subject to a minimum mean return constraint. Moreover, we also derive a closed-form portfolio rule for the $\alpha$-robust mean-CVaR optimization problem in a market without the risk-less asset. The results obtained from solving the numerical example show that if an investor is more ambiguity-averse, his investment strategy will always be more conservative.
Citation: Zhilin Kang, Xingyi Li, Zhongfei Li. Mean-CVaR portfolio selection model with ambiguity in distribution and attitude. Journal of Industrial and Management Optimization, 2020, 16 (6) : 3065-3081. doi: 10.3934/jimo.2019094
##### References:
[1] G. Bayraksan and D. K. Love, Data-driven stochastic programming using phi-divergences, in The Operations Research Revolution, INFORMS, 2015, 1–19. doi: 10.1287/educ.2015.0134. [2] A. Ben-Tal and A. Nemirovski, Robust solutions of uncertain linear programs, Ops. Research Letters, 25 (1999), 1-13. doi: 10.1016/S0167-6377(99)00016-4. [3] M. J. Best and R. R. Grauer, Sensitivity analysis for mean-variance portfolio problems, Mgmt. Science, 37 (1991), 980-989. [4] P. Bossaerts, P. Ghirardato, S. Guarnaschelli and W. R. Zame, Ambiguity in asset markets: Theory and experiment, The Review of Finan. Studies, 23 (2010), 1325-1359. doi: 10.1093/rfs/hhp106. [5] J. Cheng, R. Chen, H. Najm, A. Pinar, C. Safta and J. P. Watso, Distributionally robust optimization with principal component analysis, SIAM J. on Optimization, 28 (2018), 1817-1841. doi: 10.1137/16M1075910. [6] E. Delage and Y. Ye, Distributionally robust optimization under moment uncertainty with application to data-driven problems, Ops. Research, 58 (2010), 595-612. doi: 10.1287/opre.1090.0741. [7] D. Ellsberg, Risk, ambiguity, and the savage axioms, The Quarterly Journal of Economics, 75 (1961), 643-669. doi: 10.2307/1884324. [8] P. M. Esfahani and D. Kuhn, Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations, Math. Programming, 171 (2018), 115-166. doi: 10.1007/s10107-017-1172-1. [9] C. R. Fox and A. Tversky, Ambiguity aversion and comparative ignorance, The Quarterly Journal of Economics, 110 (1995), 585-603. doi: 10.2307/2946693. [10] P. Ghirardato, F. Maccheroni and M. Marinacci, Differentiating ambiguity and ambiguity attitude, J. of Econ. Theory, 118 (2004), 133-173. doi: 10.1016/j.jet.2003.12.004. [11] I. Gilboa and D. Schmeidler, Maxmin expected utility with non-unique prior, J. of Math. Econ., 18 (1989), 141-153. doi: 10.1016/0304-4068(89)90018-9. [12] C. Heath and A. Tversky, Preference and belief: Ambiguity and competence in choice under uncertainty, J. of Risk and Uncertainty, 4 (1991), 5-28. doi: 10.1007/BF00057884. [13] R. Jiang and Y. Guan, Data-driven chance constrained stochastic program, Math. Programming, 158 (2016), 291-327. doi: 10.1007/s10107-015-0929-7. [14] Z. Kang, X. Li, Z. Li and S. Zhu, Data-driven robust mean-CVaR portfolio selection under distribution ambiguity, Quant. Finan., 19 (2019), 105-121. doi: 10.1080/14697688.2018.1466057. [15] Z. Kang and Z. Li, An exact solution to a robust portfolio choice problem with multiple risk measures under ambiguous distribution, Math. Methods of Ops. Research, 87 (2018), 169-195. doi: 10.1007/s00186-017-0614-0. [16] B. Li, D. Li and D. Xiong, Alpha-robust mean-variance reinsurance-investment strategy, J. of Econ. Dynamics and Control, 70 (2016), 101-123. doi: 10.1016/j.jedc.2016.07.001. [17] B. Li, L. Wang and D. Xiong, Robust utility maximization with extremely ambiguity-loving and ambiguity-aversion preferences, Stochastics, 90 (2018), 524-538. doi: 10.1080/17442508.2017.1371176. [18] J. Liu, Z. Chen, A. Lisser and Z. Xu, Closed-Form optimal portfolios of distributionally robust mean-CVaR problems with unknown mean and variance, Appl. Math. & Optimization, 79 (2019), 671-693. doi: 10.1007/s00245-017-9452-y. [19] S. Lotfi, M. Salahi and F. Mehrdoust, Adjusted robust mean-value-at-risk model: Less conservative robust portfolios, Optimization and Engineering, 18 (2017), 467-497. doi: 10.1007/s11081-016-9340-3. [20] S. Lotfi and S. A. Zenios, Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances, European J. of Oper. Research, 269 (2018), 556-576. doi: 10.1016/j.ejor.2018.02.003. [21] A. B. Paç and M. Ç. Pinar, Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity, TOP, 22 (2014), 875-891. doi: 10.1007/s11750-013-0303-y. [22] I. Popescu, Robust mean-covariance solutions for stochastic optimization, Ops. Research, 55 (2007), 98–112. doi: 10.1287/opre.1060.0353. [23] A. G. Quaranta and A. Zaffaroni, Robust optimization of Conditional Value-at-Risk and portfolio selection, J. of Banking & Finance, 32 (2008), 2046-2056. doi: 10.1016/j.jbankfin.2007.12.025. [24] K. Ruan and M. Fukushima, Robust portfolio selection with a combined WCVaR and factor model, J. of Indust. & Mgmt. Optimization, 8 (2012), 343-362. doi: 10.3934/jimo.2012.8.343. [25] W. Wiesemann, D. Kuhn and M. Sim, Distributionally robust convex optimization, Ops. Research, 62 (2014), 1358-1376. doi: 10.1287/opre.2014.1314. [26] S. Zhu and M. Fukushima, Worst-case conditional value-at-risk with application to robust portfolio management, Ops. Research, 57 (2009), 1155-1168. doi: 10.1287/opre.1080.0684. [27] W. Zhu and H. Shao, Closed-form solutions for extremely-case distortion risk measures and applications to robust portfolio management, 2018. Available from: https://ssrn.com/abstract=3103458.
show all references
##### References:
[1] G. Bayraksan and D. K. Love, Data-driven stochastic programming using phi-divergences, in The Operations Research Revolution, INFORMS, 2015, 1–19. doi: 10.1287/educ.2015.0134. [2] A. Ben-Tal and A. Nemirovski, Robust solutions of uncertain linear programs, Ops. Research Letters, 25 (1999), 1-13. doi: 10.1016/S0167-6377(99)00016-4. [3] M. J. Best and R. R. Grauer, Sensitivity analysis for mean-variance portfolio problems, Mgmt. Science, 37 (1991), 980-989. [4] P. Bossaerts, P. Ghirardato, S. Guarnaschelli and W. R. Zame, Ambiguity in asset markets: Theory and experiment, The Review of Finan. Studies, 23 (2010), 1325-1359. doi: 10.1093/rfs/hhp106. [5] J. Cheng, R. Chen, H. Najm, A. Pinar, C. Safta and J. P. Watso, Distributionally robust optimization with principal component analysis, SIAM J. on Optimization, 28 (2018), 1817-1841. doi: 10.1137/16M1075910. [6] E. Delage and Y. Ye, Distributionally robust optimization under moment uncertainty with application to data-driven problems, Ops. Research, 58 (2010), 595-612. doi: 10.1287/opre.1090.0741. [7] D. Ellsberg, Risk, ambiguity, and the savage axioms, The Quarterly Journal of Economics, 75 (1961), 643-669. doi: 10.2307/1884324. [8] P. M. Esfahani and D. Kuhn, Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations, Math. Programming, 171 (2018), 115-166. doi: 10.1007/s10107-017-1172-1. [9] C. R. Fox and A. Tversky, Ambiguity aversion and comparative ignorance, The Quarterly Journal of Economics, 110 (1995), 585-603. doi: 10.2307/2946693. [10] P. Ghirardato, F. Maccheroni and M. Marinacci, Differentiating ambiguity and ambiguity attitude, J. of Econ. Theory, 118 (2004), 133-173. doi: 10.1016/j.jet.2003.12.004. [11] I. Gilboa and D. Schmeidler, Maxmin expected utility with non-unique prior, J. of Math. Econ., 18 (1989), 141-153. doi: 10.1016/0304-4068(89)90018-9. [12] C. Heath and A. Tversky, Preference and belief: Ambiguity and competence in choice under uncertainty, J. of Risk and Uncertainty, 4 (1991), 5-28. doi: 10.1007/BF00057884. [13] R. Jiang and Y. Guan, Data-driven chance constrained stochastic program, Math. Programming, 158 (2016), 291-327. doi: 10.1007/s10107-015-0929-7. [14] Z. Kang, X. Li, Z. Li and S. Zhu, Data-driven robust mean-CVaR portfolio selection under distribution ambiguity, Quant. Finan., 19 (2019), 105-121. doi: 10.1080/14697688.2018.1466057. [15] Z. Kang and Z. Li, An exact solution to a robust portfolio choice problem with multiple risk measures under ambiguous distribution, Math. Methods of Ops. Research, 87 (2018), 169-195. doi: 10.1007/s00186-017-0614-0. [16] B. Li, D. Li and D. Xiong, Alpha-robust mean-variance reinsurance-investment strategy, J. of Econ. Dynamics and Control, 70 (2016), 101-123. doi: 10.1016/j.jedc.2016.07.001. [17] B. Li, L. Wang and D. Xiong, Robust utility maximization with extremely ambiguity-loving and ambiguity-aversion preferences, Stochastics, 90 (2018), 524-538. doi: 10.1080/17442508.2017.1371176. [18] J. Liu, Z. Chen, A. Lisser and Z. Xu, Closed-Form optimal portfolios of distributionally robust mean-CVaR problems with unknown mean and variance, Appl. Math. & Optimization, 79 (2019), 671-693. doi: 10.1007/s00245-017-9452-y. [19] S. Lotfi, M. Salahi and F. Mehrdoust, Adjusted robust mean-value-at-risk model: Less conservative robust portfolios, Optimization and Engineering, 18 (2017), 467-497. doi: 10.1007/s11081-016-9340-3. [20] S. Lotfi and S. A. Zenios, Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances, European J. of Oper. Research, 269 (2018), 556-576. doi: 10.1016/j.ejor.2018.02.003. [21] A. B. Paç and M. Ç. Pinar, Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity, TOP, 22 (2014), 875-891. doi: 10.1007/s11750-013-0303-y. [22] I. Popescu, Robust mean-covariance solutions for stochastic optimization, Ops. Research, 55 (2007), 98–112. doi: 10.1287/opre.1060.0353. [23] A. G. Quaranta and A. Zaffaroni, Robust optimization of Conditional Value-at-Risk and portfolio selection, J. of Banking & Finance, 32 (2008), 2046-2056. doi: 10.1016/j.jbankfin.2007.12.025. [24] K. Ruan and M. Fukushima, Robust portfolio selection with a combined WCVaR and factor model, J. of Indust. & Mgmt. Optimization, 8 (2012), 343-362. doi: 10.3934/jimo.2012.8.343. [25] W. Wiesemann, D. Kuhn and M. Sim, Distributionally robust convex optimization, Ops. Research, 62 (2014), 1358-1376. doi: 10.1287/opre.2014.1314. [26] S. Zhu and M. Fukushima, Worst-case conditional value-at-risk with application to robust portfolio management, Ops. Research, 57 (2009), 1155-1168. doi: 10.1287/opre.1080.0684. [27] W. Zhu and H. Shao, Closed-form solutions for extremely-case distortion risk measures and applications to robust portfolio management, 2018. Available from: https://ssrn.com/abstract=3103458.
The left panel shows that $k(\alpha)$ and $b(\alpha)$ are decreasing in $\alpha$. The efficient frontier lines for $\alpha$-robust CVaR model are shown in the right panel. The steepest line (Dash-dot line, black) and flattest line (Solid line, blue) correspond to the cases $\alpha = 0.5$ and $\alpha = 1$, respectively. ($H = 0.4722$, $r_f = 1.01$, $\gamma_1 = 0.0001$, $\gamma_2 = 1.2$, $\beta = 0.95$)
Efficient frontiers of the $\alpha$-maxmin mean-CVaR model with different parameter $\alpha$. The $\alpha$-maxmin portfolio CVaR in the $x$-axis ($\alpha$-maxmin portfolio return in the $y$-axis) is a convex mixture between the worst-case and best-case values of CVaR risk measures (expected return)
Effects of $\alpha$ (the level of ambiguity aversion) on the $\alpha$-maxmin portfolio return and $\alpha$-maxmin portfolio CVaR
Effect of $\alpha$ (the level of ambiguity aversion) on the composition of efficient portfolios from the $\alpha$-maxmin mean-CVaR model. The percentage allocation of assets 1-3 in the optimal allocation $x^*$ have been illustrated in different colors
The variations of optimal portfolio strategies under different levels of ambiguity $\gamma_1$ (for a given $\gamma_2 = 1.2$) and $\gamma_2$ (for a given $\gamma_1 = 0.0001$). The percentage allocation of assets 1-3 in the optimal allocation $x^*$ have been illustrated in different colors
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2020 Impact Factor: 1.801
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2022-06-27 15:18:10
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http://docs.mathjax.org/en/latest/input/tex/extensions.html
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# TeX and LaTeX extensions¶
While MathJax includes nearly all of the Plain TeX math macros, and many of the LaTeX macros and environments, not everything is implemented in the core TeX input processor. Some less-used commands are defined in extensions to the TeX processor. MathJax will load some extensions automatically when you first use the commands they implement (for example, the \color macro is implemented in the color extension, but MathJax loads this extension itself when you use that macro). While most extensions are set up to load automatically, there are a few that you would need to load explicitly yourself. See the autoload extension below for how to configure which extensions to autoload.
To enable one of the TeX extensions you need to do two things: load the extension, and configure TeX to include it in its package setup. For the first, to load an extension as a component, add its name to the load array in the loader block of your MathJax configuration. For example, to load the color extension, add '[tex]/color' to the load array, as in the example below. To do the second, add the extension name to packages array in the tex block of your configuration. You can use the special '[+]' notation to append it to the default packages (so you don’t need to know what they are). For example:
window.MathJax = {
tex: {packages: {'[+]': ['color']}}
};
will load the color extension and configure the TeX input jax to enable it.
A number of extensions are already loaded and configured in the components that contain the TeX extension. The input/tex, and the combined components containing tex and not ending in -full include the ams, newcommand, noUndefined, require, autoload, and configMacros extensions, with the other extensions being autoloaded as needed. The input/tex-base component has no extensions loaded, while the input/tex-full and the combined extensions ending in -full load all the extensions.
If you load a component that has an extension you don’t want to use, you can disable it by removing it from the package array in the tex block of your MathJax configuration. For example, to disable \require and autoloading of extensions, use
window.MathJax = {
};
if you are using, for example, the tex-chtml.js combined component file.
You can also load these extensions from within a math expression using the non-standard \require{extension} macro. For example
$$\require{color}$$
would load the color extension into the page. This way you you can load extensions into pages that didn’t load them in their configurations (and prevents you from having to load all the extensions into all pages even if they aren’t used).
## Configuring TeX Extensions¶
Some extensions have options that control their behavior. For example, the color extension allows you to set the padding and border-width used for the \colorbox and \fcolorbox macros. Such extensions are configured using a block within the tex configuration of your MathJax configuration object. The block has the same name as the extension, and contains the options you want to set for that extension. For example,
window.MathJax = {
tex: {
packages: {'[+]': ['color']},
color: {
}
}
};
would set the padding for \colorbox to be 5 pixels.
See the Configuring MathJax section for details about the options for each of the extensions below.
For extensions that are not loaded explicitly but may be loaded via the autoload package or the \require macro, you can’t include the configuration within the tex block, because MathJax will not know the options that are available (since the extension hasn’t been loaded yet). In that case, move the configuration block to the top level of the MathJax configuration object and prefix it with [tex]/, as in:
window.MathJax = {
'[tex]/color': {
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2019-09-23 17:36:11
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https://mathematica.stackexchange.com/questions/257779/how-to-make-an-interactive-calculator-for-any-mathematical-relation
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# How to make an interactive calculator for any mathematical relation? [closed]
I am wondering if there is a way to make a calculator for any relation that is interactive. First, I choose a relation with some variables in it. The user will input a value for all of the variables except for the one they wish to solve for. Some of the equations/relations I interested in applying this program to are the following physics equations (though there are many more present):
• Voltage=Current*Resistance
• Charge=Capacitance*Voltage
• Density=Mass/Volume
• Velocity=Distance/Speed
All of these involve only three variables but more complex relations should also be able to programmed into an interactive interface such as:
• (final velocity)^2=(velocity at time 0)^2+2accelerationdisplacement
• Impedance=Sqrt(Ressistance^2+(Inductive reactance-Capacitative
• reactance)^2) Magnetic Field=Permittivity of free Space *Number of coils * Current/Length of solenoid
My goal is take any relation and create a simple program where the user can input values into all of the fields except for one which they leave blank. The program will then solve for that value. I contacted Wolfram Support for help and they said I had to pay to Technical Consulting if I wanted to develop such a program and am wondering if there is any easy workaround. An example of a program of this sort can be seen at https://www.emathhelp.net/calculators/differential-equations/half-life-calculator/
Here is my code:
How should I add numeric input to my Manipulate program?
• Yeah, we have a close reason, "The answer to this question requires...the services of a professional consultant." Yours is a project that's rather broad and seems to call out for a consultant to do the work or work with you. Not sure why someone thought the question deserves an upvote. Maybe they will answer for you. (1) I can point you to Variables[] for determining the variables in the equation the user types. (2) You have a parsing problem: Mathematica naturally interprets "final velocity" as "final" times "velocity". It would be an easier thing to program if you required Mma syntax. Nov 5 '21 at 13:23
• I can make the request specific. Given a relation with N variables X1.....XN, how can I make a calculator like emathhelps or WolframAlpha's Web Apps calculators to output a value? For a similar question see mathematica.stackexchange.com/questions/253772/…. Nov 5 '21 at 13:25
• You have to start somewhere. Try typing your ideas in Mathematica and ask specific questions. At the moment your post does not contain even a single line of code that we can work on. Nov 5 '21 at 13:27
Here's a quick and dirty version that I think should come close to what you're asking for. The handling of the variables and their localisation is not very sophisticated, but it should work for simple formulas:
Clear[a, b, c]
eq = c^2 == a^2 + b^2;
vars = ReduceFreeVariables[eq]
sol = "";
Manipulate[
Evaluate@Column@{HoldForm[Evaluate@eq], eq, Dynamic[sol]},
Evaluate@Grid[
Append[
{HoldForm[#],
InputField[
Dynamic[#,
Function[{val, expr},
sol = "";
If[val === Null, Clear[#], # = val]
]
], Number]} & /@ vars,
With[{vars = vars, eq = eq},
{
Button["Solve",
If[Count[vars, _Symbol] === 1,
sol = Flatten@Solve[eq],
sol = ""
],
ImageSize -> Automatic,
Method -> "Queued"
],
SpanFromLeft
}
]
]
]
]
To use it, give all input fields numerical values except for one. Then press solve.
Clear["Global*"]
\$Version
(* "12.3.1 for Mac OS X x86 (64-bit) (June 19, 2021)" *)
Enter equation to be used (equation must use Equal (==) rather than Set (=))
eqn = (Voltage == Current*Resistance);
vars = Variables[Level[eqn, {-1}]];
Manipulate[
Column[{
StringForm["Equation: ", eqn], "",
Reduce[eqn, var, domain],
Manipulate @@ {
Reduce[eqn, var, domain],
Sequence @@ ({#, 1} & /@ DeleteCases[vars, var]),
Paneled -> False,
AppearanceElements -> None}}],
Row[{
Control[{{var, vars[[1]], "Solve for"}, vars}],
Spacer[25],
Control[{{domain, Reals, "Domain"}, {PositiveReals, NonNegativeReals,
Reals, Complexes, PositiveIntegers, NonNegativeIntegers, Integers}}]}]]
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2022-01-27 14:17:26
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https://www.cedip.es/steel-tube/018d335e8c10960.html
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[email protected] | 50 Guohuai Road, Henan Province, China
We are a comprehensive steel machining service platform!
# Pressure acting on Underground Pipes
Earth Pressure acting on Underground Pipes Pressure due to soil and transport. The pressure caused by transport depends on the force (weight) on each wheel. The...Tag Search.
### Compari of earth pressure around pipe-roof Pressure acting on Underground Pipes
This study is to confirm the effect of pre-installed pipe-roof by measuring earth pressure acting on the underpass. In recently developed trenchless methods pre-inserted steel pipes before ground excavation to form pipe-roof are connected each other with re-bars and filled with mortar. In this study, focusing on the Upgraded Pipe Roof Structure method (UPRS) and Front-Jacking, earth pressure Pressure acting on Underground Pipes Earth Pressure acting on Underground PipesEarth Pressure acting on Underground Pipes Pressure due to soil and transport. The pressure caused by transport depends on the force (weight) on each wheel. The Pressure acting on Underground Pipes Tag Search. How does lateral pressure affect a concrete pipe?How does lateral pressure affect a concrete pipe?Lateral pressure causes bending moments in the pipe wall which act opposite to the bending moments resulting from vertical soil pressure. The moments produced by lateral soil pressure are therefore beneficial to the supporting strength of the pipe, as the larger bedding factor corresponds to a smaller required D load for a given installation.Recommendations for Design of Reinforced Concrete Pipe Pressure acting on Underground Pipes
### How is the pressure acting on a pipe?How is the pressure acting on a pipe?You can make ads in the Engineering ToolBox more useful to you! The pressure acting on an object in the ground - typical on the outside of a pipe can be calculated as ptransport = pressure caused by the transport load on surface of the soil (Pa)Earth Pressure acting on Underground Pipes How to calculate the pressure of a buried pipe?How to calculate the pressure of a buried pipe?The pressure acting on pipe at buried at depth 2 m and 2 m below groundwater level can be calculated as psoil = [ (1800 kg/m3) (9.81 m/s2) ((2 m) - (1 m)) ] + [ (1100 kg/m3) (9.81 m/s2) (1 m)] = 28449 Pa = 28.5 kPaEarth Pressure acting on Underground PipesAt-Rest Earth Pressure of Overconsolidated Collapsible Pressure acting on Underground Pipes
Oct 16, 2020Four pressure transducers (H1H4) were installed at strategic points on the wall to measure the earth pressure at these locations and accordingly the earth pressure distribution acting on the wall. Six pressure transducers (v1v6) were imbedded in the soil mass at 2 levels to measure the vertical stresses in the soil mass.
### Basement Waterproofing of New Structures
hydrostatic pressure head of 15-20 m. The swellable type of waterbars are smaller, in sizes of 5 mm x 10 mm or 10 mm x 10 mm which can be used for higher hydrostatic pressure heads of 50-100 m. The lowest level of basement floor slabs should be cast in bays or a series of continuous strips with transverse inducedCited by 4Publish Year 2019Author Qiang Ma, Zhun Ku, Henglin Xiaoearth pressure on buried pvc pipeplug flow modelling pressure pipespressure pipe flow calculationsoil pressure on buried pipesoil pressure on buried pipeburied pipe designA new model to predict soil pressure acting on deep burial Pressure acting on Underground PipesThis equation shows that the increase in normal stresses acting on the pipe due to soil dilation ($$\Delta \sigma_{n}$$) is proportional to the shear stiffness of the soil (G). Consequently, increasing the soil stiffness generally results in more pressure on the pipe. Effect of soil Domestic fuel supply pipes OFTEC consumer guidesWhere a fuel supply pipe passes through the wall of a building it should be run within a sleeve, such as a larger plastic pipe. Fuel supply pipes should not be run underground directly into the interior of a building, instead the pipe should rise externally to allow a remote acting fire valve to be fitted before it enters the building.
### Earth Pressure Distribution for Buried Pipe Bend Subject Pressure acting on Underground Pipes
Apr 26, 2012The behavior of a buried pipeline is significantly influenced by its interaction with the surrounding ground as well as the backfill material. The thrust force generated by the action of internal water pressure tends to move the bend of underground pipeline to the back side. This thrust force is supported by the passive soil pressure that affects the back ground.Earth Pressure acting on Underground Pipes Head and pressure in pumps Water Tech OnlineOct 13, 2010Underground clay pipes would carry the water by gravity to the different neighborhoods. The water would collect in fountains for the housewives to carry away daily in clay jars. Pressure acting on Underground Pipes Answer The pressure acting against the windows would be 2.6 pounds per square inch, or 6 feet ÷ 2.31 = 2.6 psi. The pump rep was right.
### Hydrostatic Pressure - Engineering ToolBox
Example - Pressure acting in water at depth 1 m . The density of water at 4 o C is 1000 kg/m 3. The pressure acting in water at 1 m can be calculated as. p = g h = (1000 kg/m 3) (9.81 m/s 2) (1 m) = 9810 Pa. Example - Pressure acting in water at depth 3 ft . The density of water at 32 o F is 1.940 slugs/ft 3. The pressure acting in water at 3 ft can be calculated asHydrostatic Pressure Cause of Basement Foundaton DamageUnderground water leaks (plumbing, HVAC systems, water pipes, city water mains, sprinklers, etc.) Poor concrete installation techniques (the concrete was improperly laid and/or contaminated with water right from the beginning). Concrete that wasnt allowed to dry before the flooring was added. Seaal variations in humidity levels.Lecture 4. Pipes Materials and LoadsFind the load transmitted to the pipe. Solution The load applied by the structure is 1340X1.22= 1635 kg The pressure applied to the soil above the pipe is P= 1635/0.91= 1795 kg/m The ratio of depth to the width is 1.83/1.22= 1.5 From table 2, the maximum proportion of the load reaching the pipe will be 0.51. Therefore the load reaching the pipe Pressure acting on Underground Pipes
### Loads on tunnels (1) - SlideShare
Apr 08, 2012Loads on tunnels (1) 1. Loads on Tunnels. 2. The most important potential loads acting on underground structures are earth/rock pressures and water pressure.. Live loads due to vehicle traffic on the surface can be safely neglected, unless the tunnel is a cut and cover type with a very small depth of overburden..M.R. AHMED Adjunct Professor McGill University Pressure acting on Underground PipesIn this study a laboratory setup that has been designed and built to measure the changes in earth pressure acting on a rigid pipe installed using the induced trench method is described.american concrete associationtype 3 bedding for pipecalculate material for "bedding" of pipe sandcalculate material for bedding of pipe sandconcrete pipe failure bedding materialconcrete pipe associationDesign Reinforced Concrete Pipe - Los Angeles County Pressure acting on Underground PipesThe weight of fluid, Wf in the pipe shall be considered in design based on a fluid weight of 62.4 lbs/ft3, unless otherwise specified. For Standard Installations, the fluid weight shall be supported by vertical earth pressure that is assumed to have the same distribution over the lower part of the pipe as given in Figure I-1 for earth load.
### basement waterproofing and finishingbasement waterproofing and mold removalbasement waterproofing and remodelingbasement waterproofing and repairbasement wall waterproofingbasement waterproof paintA new model to predict soil pressure acting on deep burial Pressure acting on Underground Pipes
In this paper, a new calculation model, modified from the other Terzaghi arching model was proposed to specifically predict the soil pressure acting on the deep burial jacked pipes. Values of crucial parameters of the height of the shearing bands, friction angle, friction coefficient, soil pressure ratio, silo width and soil cohesion were analyzed based on published tunnel research results and trap-door experiments.causes of indoor brust pipetypes of water pipe materialhow many water pipes burst in homes annwhat causes water pipes to burst in winteryelp reviews for plumbersberean baptist church galesville wiNumerical study of earth pressures on rigid pipes with Pressure acting on Underground PipesIt can be seen that TDA can effectively help to reduce the overburden pressure acting on the pipe crown. The inclusion of the TDA zone also produces a reduced earth pressure at the pipe springline compared to the theoretical value . At the pipe invert, the evaluated contact pressure is lower than the theoretical value .city of los angeles maximum bearing capamaximum allowable bearing capacity in fillbuilding construction for the fire servicecity of los angelescity of los angeles jobsMost Common Causes of Burst Pipes - Schuelke PlumbingPipe corrosion is common in copper-based water supply pipes. Pressure from External Forces. Water pipes can sometimes be subjected to external pressure. In most cases, pipes laid on the ground can be subjected to pressure from tree roots, passing cars, or even construction equipment excavating the ground. Such pressure normally tends to squeeze Pressure acting on Underground Pipes
### earth pressure on buried pvc pipelateral pressure calculatorlateral pressure calculationsloads on buried pipepressure thru a steel pipepressure of soilExplore further
Estimating earth loads on buried pipes under axial loading Pressure acting on Underground Pipeslink.springerTRUCK LOADS ON PIPE BURIED AT SHALLOW DEPTHSlminetSoil Pressure - an overview ScienceDirect TopicssciencedirectRecommended to you based on what's popular Model Tests of Earth Pressure on Buried Rigid Pipes and Pressure acting on Underground PipesBased on the hypothesis of Terzaghis underground cavern method, the earth pressure acting on the cavern is as follows where K is the lateral pressure coefficient; is the internal friction angle of soil; c is the cohesion of soil; is the unit weight of soil; H is the overlying soil thickness on crown of pipe; q is the upper load on backfill; and B 1 is the width of the loose zone.how to remove and cap old irrigation valvehow to replace a leaking irrigation sylinoid how to find irrigation leak with airhow does a sprinkler control valve work?how to automatic turn off irragation systehow to know if i have depressionReciprocating Pump - Basics, Definition, Parts, Working Pressure acting on Underground PipesReciprocating Pump Basic, Working Principle, Parts & Type. T he Reciprocating pump is a widely used positive displacement pump in many industries where large delivery pressure is required. In this kind of pump, the piston moves forward & backward and mechanical energy is converted into hydraulic energy. These pumps are the best choice among Pressure acting on Underground Pipeshydrostatic pressure test formulahydrostatic pressure testinghydrostatic pressure calculatorhydrostatic pressure equation cardiohydrostatic pressure medicahydrostatic pressure medicalLOADS AND SUPPORTING STRENGTHSpipe is installed on the original ground or compacted fill and then covered by an Pressure acting on Underground Pipes Magnitude of lateral pressure and the portion of the vertical height of the pipe over which it acts. Pressure acting on Underground Pipes Loads considered acting only at the top of the pipe.
### hydrostatic pressure under basement floorhydrostatic pressure of hearthydrostatic pressure of a hdpe pipehydrostatic pressure basementhydrostatic pressure in basementhydrostatic pressure insurance walkout baWhat Can Cause Fluctuations in Water Pressure?
Apr 08, 2018Air Trapped in Pipes. When air gets trapped in pipes, it can cause fluctuating, and spluttering water pressure as the air and water move through the pipes. Air trapped in pipes acts as a valve, causing water flow to stop and start in fits and bursts. Air can enter the pipes through a leaking suction line, damaged tank bladders, a faulty pump Pressure acting on Underground Pipeslifetme of reinforced concrete drain pipeservice life of reinforced concrete sidewalkservice life of reinforced concretecover over reinforced concrete pipewhat is the diameter of a reinforced concresafe load reinforced concrete pipe meaningWhat is a Pipe Expansion Joint and Why do I need one Pressure acting on Underground PipesExpansion Joints are used to absorb dimensional changes caused by thermal expansion or contraction of a pipeline, duct, or vessel while containing the system pressure. The flexible element of the expansion joint that expands or contracts to absorb thermal movement is called Bellows. It picture of drill headsuse of torsion snap jointsimage of a cantilever snapjointpicture of instrument case locksconnecticute directional drillingconnecticut directional drillingHow to Detect a Water Leak in the Irrigation SystemJul 05, 2021Wait several minutes, then check the needle. If the needle is still moving, then this time, you will need to check for water pressure and the sound of running pipes Turn the stations on again, one by one, starting with the one closest to the main pipe where water comes into your propertyusually located near the meter itself.
### piping invert elevationelectrical underground pipeunderground piping drawingsection for piping planright section for piping planpvc pipe for underground electrical27. Thrust Restraint Design for Buried Piping.
the pipe where changes in fluid velocity, changes in pipe size or changes in pipeline direction occur. This is generally at fittings such as plugs, caps, valves, tees, bends or reducers. 4) Thrust forces may also occur at the locations where new pipe is connected in-line to a different type of existing pipe with different sealing diameters.pressure of pressure vessel equationexternal pressure vessel calculationsexternal peer pressureasme pressure vessel failureexternal media pressurepipe for pressure vesselForces Exerted on a Sewer Sewage Waste ManagementSimilarly the internal pressure may be exerted by the sewage on outfall sewers which have to flow full under pressure. The internal pressure is invariably exerted by the sewage on the sewers which carry sewage under pressure, i.e., in the case of pressure mains or pressure sewers.steam pipe valve packing proceduresteam header expansion loopconstant support pipe hangerpipe packing methodsstainless steel expansion in a steam linecopper pipe wall supportThe importance of the annular gap for pipe jacking Pressure acting on Underground PipesDec 03, 2020Figure 6 Illustration of the permissible force according to pipe statics, the force actually acting on the jacking pipes of intermediate Station 4 and the permissible force according to OLC calculation based on the torsion/load history (source INKA Aachen). Problems of uplift during tunnelling underground water
### thrust restraint calculation dipraforsyth department of water & sewer standford uniflange restraining ac x dipthrust restraint calculatordipra restraint calculatordipra thrust restraintDesign Data 9 - Concrete Pipe
strength of the buried pipe, is dependent on two instal-lation characteristics 1. Width and quality of contact between the pipe and bedding. 2. Magnitude of lateral pressure and the portion of the vertical height of the pipe over which it acts. For the embankment condition, Spangler developed a general equation for the bedding factor, which Pressure acting on Underground Pipesthrust restraint design for ductile iron pipe thrust restraint for 2 inch pipesand silt soil designationrestraint joint calculatorpipe thrust restraint pipe supportfan thrust restraint pricingExternal Pressure Pressure Vessel EngineeringJul 05, 2012Vacuum + external pressure on half pipe, dimple and stayed surfaces Step 1 the external pressure is now 15+30 = 45 psi (vacuum +30 psi jacket pressure). The required thickness under the dimple jacket rises to 0.172 (Formula App 17-5 (2)). The water tower atmospheric pressure youtubehow does atmospheric pressure change wwork from pressurecalculating water pressur ephysics 2how to calculate atmoshric pressurewhat is hydrostatic pressureThrust Restraint Design Equations and Soil Parameters = Frictional resistance acting on the pipeline (acting on the full pipe diameter), (F sb) l = F sb on the large side of a reducer, f = Friction angle modifier coefficient H c = Mean depth from surface to pipe center line, ft K n = Trench compaction modifier K p = Rankin passive pressure coefficient L = Minimum restrained length for bends, ft L b
### what can cause low water pressurewhat would cause water pressure to spikehow to decrease water pressurewhat causes water hammerair trapped in water pipeair in water lines5.1 Water from Wells- Atmospheric Pressure at Work Pressure acting on Underground Pipes
Jun 23, 20215.1 Water from Wells- Atmospheric Pressure at Work. A water well is an excavation or structure created in the ground by digging, driving, boring, or drilling to access groundwater in underground aquifers. The well water is often drawn by a pump (Figure 5.1. 1 ). Unfortunately, it impossible to pump water from very deep in the ground with just Pressure acting on Underground Pipeswhat is head in a water pipe70psi 1250 gpm water sprinkler pumpdischarge and suction pressurepositive displacement pumps equation for positive displacement pumpsgallon in a m3Recommendations for Design of Reinforced Concrete Pipe Pressure acting on Underground PipesLateral pressure acting on the pipe will produce bending moments in the pipe wall which act opposite to those bending moments produced by vertical loads and therefore, will reduce the total bending moment within the pipe wall. The lateral pressure also produces an axial thrust component in the wall of the pipe where the maximum moment occurs Pressure acting on Underground PipesPiping Designers . com - Section - 15C Underground Piping Pressure acting on Underground PipesThis also allows multiple small drains (1/2" to 1" normally) to be centered onto one drain funnel . (I perally witnessed 5 each ½" drains routed to a single 6" drain funnel). A common "funnel size is 6" so a 6"x 4" or a 6"x 3" reducer is used. The 3" & 4" size are a common branch size, but don't get too hung-up if the size is a bit Pressure acting on Underground Pipes
### Pressure due to soil and transport. The pressure caused by transport depends on the force (weight) on each wheel. The Pressure acting on Underground PipesTag Search. More Pressure acting on Underground PipesEarth Pressure acting on Underground Pipes
Was this helpful?People also askWhat causes the pressure in an underground pipe?What causes the pressure in an underground pipe?ptransport = pressure caused by the transport load on surface of the soil (Pa) sw = density of soil below groundwater level (reduced due to Buoyancy of soil - typical value 1100 kg/m3) The pressure caused by transport depends on the force (weight) on each wheel.Earth Pressure acting on Underground PipesSteam distribution - Pipe expansion and supports in steam Pressure acting on Underground PipesSliding joint. These are sometimes used because they take up little room, but it is essential that the pipeline is rigidly anchored and guided in strict accordance with the manufacturers' instructions; otherwise steam pressure acting on the cross sectional area of the sleeve part of the joint tends to blow the joint apart in opposition to the forces produced by the expanding pipework (see Pressure acting on Underground Pipes
### THRUST RESTRAINT DESIGN FOR DUCTILE IRON PIPE
The internal hydrostatic pressure acts perpendicularly on any plane with a force equal to the pressure (P) times the area (A) of the plane. All components of these forces acting radially within a pipe are balanced by circumferential tension in the wall of the pipe.Trenching Without the Trench Hydraulics & PneumaticsSep 04, 2019The utility cable or pipe is attached to the free end of the reaming tool, and the machine begins pulling the drill pipe back out of the ground. As it pulls, the machine also rotates the drill pipe, and with it the reaming tool. The spinning reaming tool enlarges the diameter of the underground channel to accommodate the utility cable or pipe.What is Restrained and Unrestrained Pipes Part 1 What Pressure acting on Underground PipesThe second part is pipe shortening due to Hooks law. Pipe expansion from pressure load on end cap is L Pipe Length. E Modulus of Elasticity. Pipe cross-section area is. D Pipe Outer Diameter. t Pipe Wall Thickness. N Axial Force in the Pipe. Axial force N is equal to the force acting on cap. P Internal Pressure. Pipe Pressure acting on Underground Pipes
### [DOC]SECTION 33 30 00, SANITARY SEWER UTILITIES
Web viewPressure-Type Pipe Couplings. Tubular-Sleeve Couplings Couplings shall meet AWWA C219, with center sleeve, gaskets, end rings, and bolt fasteners. Metal, bolted, sleeve-type, reducing or transition couplings for joining underground pressure piping:
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2022-01-22 02:10:45
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https://math.stackexchange.com/questions/3144113/show-x-n-sqrtn-is-not-cauchy-sequence
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# Show $\{x_n = \sqrt{n}\}$ is not Cauchy sequence
Consider the sequence {$$x_n$$},$$x_n$$=$$\sqrt{n}$$
Show that $$\forall \varepsilon > 0, \exists n_0 \in \Bbb N$$ s.t. $$\forall n \geq n_0$$, |$$x_{n+1}-x_n$$|<$$\varepsilon$$.
This is what I have:
Let $$\varepsilon>0$$ and let $$n_0$$ = $$(\frac{1}{2\varepsilon})^2, \forall n \geq n_0$$. $$|\sqrt{n+1}-\sqrt{n}|$$. So, $$|\frac{(\sqrt{n+1}-\sqrt{n})(\sqrt{n+1}+\sqrt{n})}{(\sqrt{n+1}+\sqrt{n})}|$$.
Then, $$|\frac{1}{\sqrt{n+1}}$$ + $$\sqrt{n}|$$ $$\leq$$ $$|\frac{1}{\sqrt{n}+\sqrt{n}}|$$=$$|\frac{1}{2\sqrt{n}}|$$= $$\varepsilon$$.
Therefore, $$|x_{n+1}-x_n|<\varepsilon, \forall n \geq n_0$$
After I did all this it got me thinking can you prove {$$x_n$$} is not cauchy? if so how?
• You made a typo, $|\frac{1}{\sqrt{n+1}} + \sqrt{n}|$ probably needs to be $|\frac{1}{\sqrt{n+1} + \sqrt{n}}|$. Your proof is correct. Note that for Cauchy you need that for any $m,n\geq n_0$: $|x_n-x_m|<\epsilon$ which is not the case – Stan Tendijck Mar 11 at 19:32
Any Cauchy sequence converges. Since $$\sqrt{n}\to+\infty$$, it diverges, so it is not Cauchy.
Telling about the condition in question, we have $$\sqrt{n+1}-\sqrt{n}=\frac{1}{\sqrt{n+1}+\sqrt{n}}\to 0,$$ so it holds trivially by definition of a limit.
• You forgot "in a complete metric space" after "any Cauchy sequence converges." I am guessing that they have not proven that $\mathbb{R}$ is complete and they will have to prove the non-Cauchy property "by hand". – Jair Taylor Mar 11 at 19:57
• @JairTaylor, If the metric os not specified, usually one thinks about the Eucldean one, which is, of course, complete. In OP's question we have $|x_{n+1}-x_n|$, which clearly indicates the Euclidean metric. Please show me, where OP specifies another metric. – szw1710 Mar 11 at 23:43
• Of course, it is implied in this case the metric is Euclidean. But it is important to note that Cauchy sequences do not necessarily converge in other metrics. – Jair Taylor Mar 11 at 23:45
• More importantly, this answer relies on the completeness of (and construction of) $\mathbb{R}$ which is not trivial. But of course it is correct. – Jair Taylor Mar 11 at 23:47
You have a solid argument for the main part, aside from the typo $$|\frac1{\sqrt{n+1}}+\sqrt{n}|$$ in the second line (already noted in a comment).
After I did all this it got me thinking can you prove $$\{x_n\}$$ is not Cauchy? If so, how?
The definition of a Cauchy sequence refers not only to the difference between adjacent pairs of elements, but also the difference between pairs of elements any index distance apart - as long as they're both far enough out in the sequence.
Just eyeballing it, the square roots increase without bound; we should be able to find one that exceeds any particular target. So, then, given some $$m$$, can you find some larger $$n$$ with $$\sqrt{n}-\sqrt{m} > 1$$? A rule to do this would immediately contradict the Cauchy criterion for $$\epsilon=1$$, and show the sequence isn't Cauchy.
Don't worry about being terribly precise here. We don't need the smallest $$n$$, just anything that works.
• so if I chose n to be 1/4 or 1/8 would either of those work? – user597188 Mar 11 at 20:36
• Uh, what? $n$ is an integer. And, for the anti-Cauchy criterion we're trying to prove, it has to be greater than $m$. – jmerry Mar 11 at 21:00
• sorry I meant like n/2$\sqrt{m}$<1/4 or 1/8 – user597188 Mar 11 at 21:07
• I still doubt that's what you mean; there's no reason to divide $n$ and $m$. Now, in what I wrote, the $1$ is arbitrary. We could replace it by $1/4$, or by $40$. But, whatever we do, it has to be a constant, not depending on $m$ at all. – jmerry Mar 11 at 21:11
• So if I let $\epsilon$ =1/4 id have (m-n)/( $\sqrt{m}$ + $\sqrt{n}$) $\geq$ n/(2$\sqrt{m}$) then $\sqrt{m}$/2 - n/(2$\sqrt{m}$) > 1/2-n/(2$\sqrt{m}$) >1/2-1/4 > 1/4 which is what epsilon equals but how would I do it if I let epsilon=1? – user597188 Mar 11 at 21:18
Let $$\epsilon_0=\frac13$$. For all $$n\in\mathbb{N}$$ and $$p=n$$, $$|\sqrt{n+p}-\sqrt n|=(\sqrt{2}-1)\sqrt n\ge\sqrt 2-1>\epsilon_0.$$ Namely, $$\sqrt{n}$$ is not Cauchy.
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2019-06-24 13:21:43
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https://www.gamedev.net/forums/topic/619338-chaiscript/
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# ChaiScript
This topic is 2818 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Hey guys,
I have a question about ChaiScript. I've embedded it in my game and i have boost but when i compile it i get weird errors
||=== Pew Pew Adventure, Debug ===| ::~thread_specific_ptr()]+0x65)||undefined reference to _imp___ZN5boost6detail12set_tss_dataEPKvNS_10shared_ptrINS0_20tss_cleanup_functionEEEPvb'| )]+0x85)||undefined reference to _imp___ZN5boost6detail12set_tss_dataEPKvNS_10shared_ptrINS0_20tss_cleanup_functionEEEPvb'| ::get() const]+0xd)||undefined reference to _imp___ZN5boost6detail12get_tss_dataEPKv'| ||=== Build finished: 3 errors, 0 warnings ===| `
i used boost earlier in the game so it was already there, can anyone help?
• ### Game Developer Survey
We are looking for qualified game developers to participate in a 10-minute online survey. Qualified participants will be offered a \$15 incentive for your time and insights. Click here to start!
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2019-10-17 16:32:54
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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": 0.1780107468366623, "perplexity": 12564.997188009525}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "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-2019-43/segments/1570986675409.61/warc/CC-MAIN-20191017145741-20191017173241-00109.warc.gz"}
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http://math.stackexchange.com/questions/171972/how-to-prove-this-combinatorial-summation
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# How to prove this combinatorial summation?
How to prove this combinatorial summation?
I expanded $C(m, i)$ and $C(n-1, n-i)$ and clubbed them together but it didn't yield anything useful. Please show me the approach only.
Is this the Chu-Vandermonde identity?
-
I don't understand your notation. – user29999 Jul 17 '12 at 15:29
Yes, it is the Chu-Vandermonde identity. – Phira Oct 29 '12 at 21:10
Write in words what this means.
You have two collections. One of $m$ objects and another of $n$ objects. When you choose $n$ objects totally, then you would've chosen, say $i$ objects from the first $m$ and hence $n-i$ from the remaining $n-1$ elements.
Similarly choosing $i$ from the first $m$ and $n-i$ from the remaining $n-1$ gives a way of choosing $n$ objects totally!
-
The idea is the following: $C(m+n-1, n)$ is the number of ways to choose $n$ items from $m+n-1$ items. Well, you can do this by first picking $i$ items out of the first $m$ items ($C(m,i)$ ways to do this) and then choose $n-i$ items out of the remaining $n-1$ items. But of course $i$ could be anything between $1$ and $n$ (which leads me to think there is a typo in your question at the moment).
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2014-07-23 16:09:33
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https://papers.neurips.cc/paper/2020/hash/9239be5f9dc4058ec647f14fd04b1290-Abstract.html
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Authors
Nicolò Campolongo, Francesco Orabona
Abstract
In the setting of online learning, Implicit algorithms turn out to be highly successful from a practical standpoint. However, the tightest regret analyses only show marginal improvements over Online Mirror Descent. In this work, we shed light on this behavior carrying out a careful regret analysis. We prove a novel static regret bound that depends on the temporal variability of the sequence of loss functions, a quantity which is often encountered when considering dynamic competitors. We show, for example, that the regret can be constant if the temporal variability is constant and the learning rate is tuned appropriately, without the need of smooth losses. Moreover, we present an adaptive algorithm that achieves this regret bound without prior knowledge of the temporal variability and prove a matching lower bound. Finally, we validate our theoretical findings on classification and regression datasets.
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2021-05-16 02:42:45
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https://bcallaway11.github.io/2021/08/15/ife.html
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Sonia Karami and I just posted a new version of our paper Treatment Effects in Interactive Fixed Effects Models.
# Connection between Difference in Differences and Interactive Fixed Effects Models
A lot of my research has involved identifying treatment effect parameters in a difference in differences (DID) framework. For DID, the main identifying assumption is the parallel trends assumption:
Parallel Trends Assumption $\mathbb{E}[\Delta Y_t(0) | D=1] = \mathbb{E}[\Delta Y_t(0) | D=0]$
Parallel trends assumptions are very closely related to the following model for untreated potential outcomes:
$Y_{it}(0) = \theta_t + \eta_i + U_{it}$ where $$\theta_t$$ is a time fixed effect, $$\eta_i$$ is an individual fixed effect, and $$U_{it}$$ are idiosyncratic time varying unobservables.
An extended version of the parallel trends assumption is the following conditional parallel trends assumption
Conditional Parallel Trends Assumption $\mathbb{E}[\Delta Y_t(0) | \tilde{Z}, D=1] = \mathbb{E}[\Delta Y_t(0) | \tilde{Z}, D=0]$ which says that parallel trends holds after conditioning on $$\tilde{Z}$$. To give an example, the application in our paper is about job displacement and the outcome is an individual’s earnings. It seems likely that the path of untreated potential outcomes (how outcomes would change over time if an individual were not displaced from their job) likely depends on a person’s education, demographic characteristics, etc. If these are distributed differently across displaced workers and non-displaced workers (which is also likely), then conditioning on these sorts of variables before invoking parallel trends will be important.
This conditional parallel trends assumption is closely related to the following model for untreated potential outcomes $Y_{it}(0) = g_t(\tilde{Z}_i) + \eta_i + U_{it}$ where $$g_t$$ is a nonparametric, time-varying function of $$\tilde{Z}$$, and $$\eta_i$$ and $$U_{it}$$ are the same as before (the important thing here is the additive separability of $$\eta_i$$ which allows for it to be differenced out). It’s common to impose linearity for $$g_t$$ to get to $Y_{it}(0) = \tilde{Z}_i'\tilde{\delta}_t + \eta_i + U_{it}$ where we take $$\tilde{Z}_i$$ to include an intercept so that the time fixed effect is absorbed into $$\tilde{Z}_i'\delta_{\tilde{Z},t}$$ from here on out.
I have been a bit purposely vague about $$\tilde{Z}$$ above. What variables need to be conditioned on though is largely a theoretical exercise. The variable that I mentioned above (education and/or demographic characteristics) are commonly observed in many datasets, but one might also think that parallel trends only holds after additionally conditioning on ability’’ which is unlikely to be observed in most data.
Let’s partition $$\tilde{Z} = (Z,\lambda)$$ where $$Z$$ corresponds to the observed components of $$\tilde{Z}$$ and $$\lambda$$ corresponds to the unobserved components of $$\tilde{Z}$$. Similarly, let’s partition $$\tilde{\delta}_t = (\delta_t, F_t)$$ where $$\delta_t$$ corresponds to the elements in $$Z$$ and $$F_t$$ corresponds to the elements in $$\lambda$$. Plugging this back into the model for untreated potential outcomes above yields $Y_{it}(0) = Z_i'\delta_t + \lambda_i'F_t + \eta_i + U_{it}$ This is an interactive fixed effects model for untreated potential outcomes!
# Identification Challenges
Even if we like the interactive fixed effects model for untreated potential outcomes, it is still not clear if we can recover any causal effect parameters of interest under palatable identifying assumptions.
For one thing, like DID, we’d like to identify causal effect parameters when the number of time periods is small, and much of the interactive fixed effects literature involves arguments where the number of time periods goes to infinity.
To make things concrete, let’s consider the case with 3 time periods: $$t$$, $$t-1$$, and $$t-2$$. And let’s suppose that no one is treated until the last period. We also define $$D_i$$ as a variable that it is equal to one for individuals in the treated group (i.e., that become treated in the last period) and is equal to 0 otherwise. Like most of the literature on treatment effects with panel data, we’ll target identifying the average treatment effect on the treated (ATT) which is given by $ATT = \mathbb{E}[Y_t(1) - Y_t(0) | D=1]$ which is the difference between treated and untreated potential outcomes on average among individuals in the treated group. Given the interactive fixed effects model, notice that we can write
# The Rest of the Paper…
We have a number of extensions to these kind of results in the paper.
• Pretty much the same arguments apply in cases where there are more than one interactive fixed effect. The main additional requirement is that, for each interactive fixed effect, we need at least one covariate whose effect on untreated potential outcomes is time invariant
• We spend a lot of time thinking about practical issues such as weak instruments, not enough covariates with time invariant effects, and tests for covariates actually having time invariant effects. Except in one or two very pernicious cases, we think that our approach should either work or that one would be able to successfully detect that it is not working.
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2021-09-26 09:18:57
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https://mathoverflow.net/questions/157457/intermediate-submodels-which-do-not-satisfy-ac
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# Intermediate submodels which do not satisfy AC
The following is known:
Theorem. Suppose $V[G]$ is a generic extension of $V$ by a set forcing, and let $N$ be a model of $ZFC$ with $V\subseteq N\subseteq V[G].$ Then $N$ is a generic extension of $V$ by a set forcing, in particular $N=V[A],$ for some set of ordinals.
It seems that the above theorem is not true if $N$ does not satisfy $AC$. In fact the following abstract is given in a talk by James Cummings (see http://settheory.mathtalks.org/cmu-math-logic-seminar-tues-11-september/):
If $c$ is Cohen-generic over $L$, then there is a transitive class model $M$ of $ZF$ intermediate between $L$ and $L[c]$ which is not of the form $L(A)$ for any $A.$
Does anyone know a proof of this fact?
• The Bristol model, I see. Have you contacted James or Menachem? Asaf Karagila was working on an alternative approach for a while. – Andrés E. Caicedo Feb 13 '14 at 6:31
• @AsafKaragila: Dear Asaf, have you completed your notes on Bristol model? – Mohammad Golshani Nov 13 '14 at 5:24
To my knowledge there is no written proof of this fact. I have all the available notes, which include a very very scattered description of $V_{\omega+1}$ and $V_{\omega+2}$ of this model $M$, and a single lemma which is used to proceed through successor of singular cardinals.
I am working on rebuilding this model in a cleaner method, and I am relatively close to finishing (some technical constructions are needed to finish the outline, but the idea itself is completely finished).
With luck I might actually finish this soon, and I could write a reasonable outline announcement (and then a full detailed accounts of the construction).
I should probably add that I asked all the people involved in the construction of this model, The Bristol model, and what I was told by everyone of them is that it started as some general idea to play with, and by the time they realized someone should be writing things down they already did a lot of the work, so it didn't survive into the notes.
## Update (April 25, 2017):
• Great! I'll be waiting, then. (I have hopes of actually finishing today, but as every other day showed, it might not be the case.) – Asaf Karagila Feb 13 '14 at 8:43
• Wow. It only took me three years to finish this. Never say "finish this soon" on something complicated. The general proof is done, but I still need to write some additional consequences of the construction, and a nice blackboxed introduction to iterations of symmetric extensions. This, I hope, will take much much less than three years. But a few minutes ago I finished writing the actual proof. PHEW! I'll update my answer once I have posted the preprint on arXiv. – Asaf Karagila Mar 7 '17 at 13:34
• Mohammad, I posted the paper on arXiv. – Asaf Karagila Apr 25 '17 at 4:59
• For finishing my dissertation? Sure... :) – Asaf Karagila Apr 25 '17 at 16:41
• I read the introduction of the paper till now. You have said your strategy of the proof is different from the one suggested by the Bristol group. The idea presented by Bristol group also seems very interesting to me and somehow very strange. Do you possibly can give the basic idea of their proof in some details (or do you have any notes)? (maybe reading your paper gives the basic idea) – Mohammad Golshani Apr 26 '17 at 3:41
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2020-01-27 07:09:10
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https://msp.org/agt/2010/10-2/p04.xhtml
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#### Volume 10, issue 2 (2010)
Recent Issues
The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
The twisted Floer homology of torus bundles
### Yinghua Ai and Thomas D Peters
Algebraic & Geometric Topology 10 (2010) 679–695
##### Abstract
We prove an exact sequence for $\omega$–twisted Heegaard Floer homology. As a corollary, given a torus bundle $Y$ over the circle and a cohomology class $\left[\omega \right]\in {H}^{2}\left(Y;ℤ\right)$ which evaluates nontrivially on the fiber, we compute the Heegaard Floer homology of $Y$ with twisted coefficients in the universal Novikov ring.
##### Keywords
Floer homology, torus bundles
Primary: 57M27
Secondary: 53D40
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2018-07-18 18:34:11
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https://wiki.vsc.ac.at/doku.php?id=doku:cfd
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Engineering
Users sometimes find that their jobs take longer than the maximaum runtime permitted by the scheduler to complete. Providing that your model does not automatically re-mesh (for example, after a fracture), you may be able to make use of Abaqus’ built-in checkpointing function.
This will create a restart file (.res file extension) from which a job that is killed can be restarted.
1. Activate the restart feature by adding the line:
*restart, write
at the top of your input file and run your job as normal. It should produce a restart file with a .res file extension.
1. Run the restart analysis with
abaqus job=jobName oldjob=oldjobName ...
where oldJobName is the initial input file and newJobName is a file which contains only the line:
*restart, read
Example:
INPUT: dynam.inp
JOB SCRIPT: job.sh
INPUT FOR RESTART: dynamr.inp
• doku/cfd.txt
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2022-09-29 13:45:32
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https://www.sangakoo.com/en/unit/inverse-trigonometric-ratios-cosecant-secant-and-cotangent
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# Inverse trigonometric ratios: cosecant, secant and cotangent
In this section, we are going to define the inverse trigonometric ratios, this is, the inverse ratios of the sine, the cosine and the tangent. Given a triangle rectangle, we define the cosecant, the secant and the cotangent of an angle $$x$$ as the inverse ratios of the sine, the cosine and the tangent, respectively.
• $$\csc(x)$$: the cosecant is the inverse of the sine or, also, its multiplicative inverse: $$\csc(x)=\dfrac{1}{\sin(x)}=\dfrac{c}{a}$$$• $$\sec (x)$$: the secant is the inverse of the cosine or, also, its multiplicative inverse: $$\sec(x)=\dfrac{1}{\cos(x)}=\dfrac{c}{b}$$$
• $$\cot(x)$$: the cotangent is the inverse of the tangent or, also, its multiplicative inverse: $$\cot(x)=\dfrac{1}{\tan(x)}=\dfrac{b}{a}$$$Given the triangle of sides $$a = 3$$, $$b = 4$$ and $$c = 5$$, we are going to compute the trigonometric ratios associated with such a triangle. Then: $$\sin(x)= \dfrac{3}{5} \qquad \cos(x)=\dfrac{4}{5} \qquad \tan(x)=\dfrac{3}{4}$$$
The associated inverse trigonometric ratios are: $$\csc(x)= \dfrac{5}{3} \qquad \sec(x)=\dfrac{5}{4} \qquad \cot(x)=\dfrac{4}{3}$$$Given the triangle of sides $$a = 5$$, $$b = 12$$ and $$c = 13$$, compute its trigonometric ratios. $$\sin(x)= \dfrac{5}{13}= \qquad \cos(x)=\dfrac{12}{13} \qquad \tan(x)=\dfrac{5}{12}$$$
$$\csc(x)= \dfrac{13}{5} \qquad \sec(x)=\dfrac{13}{12} \qquad \cot(x)=\dfrac{12}{5}$$\$
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2023-02-01 06:19:13
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https://sites.uci.edu/morlighem/bedmachine-antarctica/
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# BedMachine Antarctica
Since 2014, we have been working on a self-consistent dataset of the Antarctic Ice Sheet based on the conservation of mass that is now freely available at NSIDC.
Note: keep in mind that not all of the bed is mapped using mass conservation (MC). If there is a fast flowing region that is currently not mapped with MC, let me know and I will try to add it in the next release. If you have ice thickness data that is not included, I would also be more than happy to add it to the mapping to further improve the topography.
## Description
The data are in one single file in NetCDF format (795 Mb) and all heights are in meters above mean sea level (the geoid used is provided in the NetCDF file). All the data use the same 450 m-resolution grid although the “true” resolution of the bedrock may vary depending on the method used to map the bed. This dataset uses data from 1993 to 2016 and has a nominal date of 2012 (same as REMA).
Antarctic mask The ice/land masks are from ADD rock outcrop, and the floating ice is derived from InSAR grounding lines (pers. comm.). 0 = ocean, 1 = ice-free land, 2 = grounded ice, 3 = floating ice, 4 = lake Vostok Surface elevation The surface dem is from REMA. Source Method used to calculate ice thickness: 0 = none, 1 = REMA/IBCSO, 2 = Mass conservation, 3 = interpolation, 4 = hydrostatic equilibrium, 5 = streamline diffusion, 6 = gravity, 7=seismic, 10+ = bathymetry data Ice thickness The ice thickness is inferred using mass conservation along the peryphery of the ice sheet and ordinary kriging in the interior. Bed topography The bed elevation is calculated by subtracting the ice thickness from the surface elevation data. Error map Ice thickness and bed topography error.
For the hydrostatic equilibrium calculation, we used a density of ice ρice=917 kg/m3, and an ocean water density of ρocean=1027 kg/m3 (following the densities used in Griggs & Bamber 2011 and Chuter & Bamber 2015).
As any model output, there are errors in these maps (there is an estimate included in the dataset). Feedback is more than welcome.
## Citation
Morlighem, M., Rignot, E., Binder, T. et al. Deep glacial troughs and stabilizing ridges unveiled beneath the margins of the Antarctic ice sheet. Nat. Geosci. (2019) doi:10.1038/s41561-019-0510-8
## Disclaimer
The ice thickness and bed topography are model outputs and are not free of error (especially in regions where ice thickness measurements are sparse). This dataset is a work in progress and we encourage users to send us feedback so that we keep improving it.
## Projection
The projection is Polar Stereographic South (71ºS, 0ºE), which corresponds to ESPG 3031
MATLAB now has an extensive library for NetCDF files. filename = 'BedMachineAntarctica-2019-09-04.nc'; x = ncread(filename,'x'); y = ncread(filename,'y'); bed = ncread(filename,'bed')'; %Do not forget to transpose (MATLAB is column oriented) %Display bed elevation imagesc(x,y,bed); axis xy equal; caxis([-1000 3000]);
## Converting heights to WGS84
All heights are referenced to mean sea level (using the geoid EIGEN-6C4). To convert the heights to heights referenced to the WGS84 ellipsoid, simply add the geoid height:
$$z_{ellipsoid}=z_{geoid} + geoid$$
## Surface height and firn depth correction
All the quantities provided in BedMachine are in ice equivalent. This affects primarily the upper surface of the ice, to which we have subtracted a firn depth correction to account for the presence of air in the firn layer. The ice thickness is also in ice equivalent. To recover the top of the surface dem from RAME in WGS84:
$$z_{REMA}= surface + firn + geoid$$
where “firn” is the firn depth correction, “surface” is the surface height, and “geoid” is the geoid height. All these quantities are provided in the netCDF file.
## Acknowledgements and References
This project is performed at the University of California Irvine under a contract with the National Aeronautics and Space Administration (Sea Level Rise Program #NNX14AN03G and MEaSURES-3) and the National Science Foundation (Thwaites #1739031).
The ice thickness data are from:
The bathymetry data are from:
The surface velocity data used by MC are from:
The surface mass balance is from RACMO 2.3 1 km:
The surface topography map is from:
• REMA
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2020-01-25 12:58:57
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https://www.physicsforums.com/threads/solving-ode-y-ye-x-y.351669/
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# Solving ODE y' = ye^(x+y)
1. Nov 4, 2009
### brandy
1. The problem statement, all variables and given/known data
dy/dx=y*e^(x+y)
solve for y
3. The attempt at a solution
move the y's over to the other side:
dy/(y*e^y)=e^x.dx
then you integrate and this is where i get screwed up.
i use inverse product rule where u=y and v'=e^y, and i also tried u=e^y and v'=y. but this didnt get me anywhere
so i did it again for the integral on the right hand side for each and it still didnt get me anywhere.
HELP!
also, i doubt if id be able to put it back into y= forms so yea could you help with that too? if not it doesnt really matter. primarily its just the integrating i want help with.
2. Nov 4, 2009
### Gib Z
Re: dy/dx=y*e^(x+y)
It's not solvable in terms of elementary functions, but can be done with a special Function. You may have seen the the more common problem $$\int \frac{e^x}{x} dx$$. It is defined to be equal to the Exponential Integral function. It's most common definition is $$Ei (x) = \int^x_{-\infty} \frac{e^t}{t} dt$$.
Can you see how the integral you have is a certain case of that function?
3. Nov 4, 2009
### brandy
Re: dy/dx=y*e^(x+y)
well yea its e^-t
but im a dummy, i have to solve something this in an exam.
i still dont know how to do it.
whats with the Ei(x) part? and how does this give you the integral
4. Nov 4, 2009
### Gib Z
Re: dy/dx=y*e^(x+y)
Basically the function you want to integrate, as well as the one I showed you with the e^x on the numerator, both can't actually be done by any normal methods! It has no simple answer, but since it comes up so often we just denote it with a shorter symbol because its useful! Think about it, using the Fundamental theorem of calculus, differentiate Ei (x), what do you get? =]
So now, express the Integral you have in terms of the Ei function.
5. Nov 5, 2009
### brandy
Re: dy/dx=y*e^(x+y)
blarg! i'm sorry, i still dont get it. i think i need a bigger hint as to how to relate it and then what to do from there. im sorry im so slow, i really am.
6. Nov 5, 2009
### Gib Z
Re: dy/dx=y*e^(x+y)
Its ok, many people seem perturbed by the idea of just "naming" a solution. The short story is, the integral you have to work out Can't be done in any normal way. So if you got that one in a test, you should just leave it because its not doable. They will probably make sure in the actual exam they give you possible ones.
7. Nov 5, 2009
### brandy
Re: dy/dx=y*e^(x+y)
oh wait, so if you differentiate Ei(x) then you get ex/x
but what about when its e-x/x
i'm not sure i understand how to relate it.
but you'd just write that the integral of ex/x=Ei(x)??? or = that thing you wrote. and would you keep it with respect to t or x.
8. Nov 5, 2009
### brandy
Re: dy/dx=y*e^(x+y)
and we will be getting that exact question in the test, i am 110% sure of this. so :S
9. Nov 5, 2009
### Gib Z
Re: dy/dx=y*e^(x+y)
Well, the integral you have isn't perfectly Ei(x), but Ei(-x). Can you see why?
10. Nov 5, 2009
### brandy
Re: dy/dx=y*e^(x+y)
yea i can see why.
so would it be
$$\int e^(-y) /y * dx$$
= Ei (-y) = $$\int$$ $$^{-y}_{-\infty}$$ et /t *dt]
sorry, i dont really know how to use the latex stuff, i have never really used them before.
11. Nov 5, 2009
### Gib Z
Re: dy/dx=y*e^(x+y)
Well not exactly =[ We're getting variables a bit mixed up here. Look at the definition of Ei i gave, x is a variable in the bounds, not the integrand.
So $$Ei (-x) = \int^{-x}_{-\infty} \frac{e^t}{t} dt$$
To get that to look like yours (remember indefinite integrals vary by additive constants) let u=-t and simplify.
12. Nov 5, 2009
### brandy
Re: dy/dx=y*e^(x+y)
huh? i didnt put it in the integrand. how can you simplfy that?
and would it become e^-u /-u becaues its e^t/t or because i have a negative x its e^-t /t and therefore it becomes e^u / -u
i'm so sorry, i apologise for my inept brain uut you are really helping me so thankyou. verily much
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2017-10-20 22:53:18
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http://mathhelpforum.com/calculus/224900-maximum-value-area.html
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# Thread: maximum value of area
1. ## maximum value of area
A rectangle with one side on the x-axis and one side on the line has its upper left vertex on the graph of y=x^2 For what value of x does the area of the rectangle attain its maximum value?
I know the answer is 4/3.
Do you solve this by rectangle approximation?
2. ## Re: maximum value of area
Originally Posted by Jonroberts74
A rectangle with one side on the x-axis and one side on the line has its upper left vertex on the graph of y=x^2 For what value of x does the area of the rectangle attain its maximum value?
I know the answer is 4/3.
Do you solve this by rectangle approximation?
No need for any approximations here. If I understand your setup you have a rectangle with vertices at
(0,0) (0,x2), (-x, x2), (-x,0)
this has area of -x3
As x -> -infinity this area grows w/o bound so there is no maximum.
Perhaps you left something out of the problem statement?
3. ## Re: maximum value of area
ah it should say with one side at the x-axis and one side at the line x = 2 and the upper left vertex on the graph y=x^2.
sorry
4. ## Re: maximum value of area
this is still infinite area as x -> -infinity
5. ## Re: maximum value of area
it doesn't give infinity as an answer, it is multiple choice with the answers
2, 4/3 , 1, 3/4 and 2/3
and according to the answer key the correct one is x=4/3
6. ## Re: maximum value of area
Originally Posted by Jonroberts74
it doesn't give infinity as an answer, it is multiple choice with the answers
2, 4/3 , 1, 3/4 and 2/3
and according to the answer key the correct one is x=4/3
Well it's pretty clear that if you have a rectangle with it's right side at x=2, and it's bottom at y=0, and let the left side go off to -infinity that you're going to have an infinite area rectangle. You can see that can't you?
Ok, I see it. x is restricted to x >= 0.
So what have you got. Your vertices are at (x,0), (x,x^2), (2,x^2), (2,0)
length is 2-x, width is x^2, area is (2-x)x^2
Use your calculus to find the maximum of this function. Take it's derivative and set it equal to 0 and solve for x.
One of these values is a maximum and one will be a minimum. Use the 2nd derivative to figure out which is which (though it should be pretty obvious from their values).
7. ## Re: maximum value of area
Hello, Jonroberts74!
A rectangle with one side on the x-axis and one side on the line $x=2$
has its upper left vertex on the graph of $y=x^2.$
For what value of $x$ does the area of the rectangle attain its maximum value?
Did you make a sketch?
Code:
| .
* | * .
| .
* | *-------*
* | *|:::::::|y
* | * |:::::::|
----------*--------*-------*---
| x : 2-x 2
|
The area of the rectangle is: . $A \;=\;y(2-x) \;=\;x^2(2-x)$
You must maximize the function: . $A \;=\;2x^2 - x^3$
Got it?
8. ## Re: maximum value of area
did you do that in a text editor? good lord.
9. ## Re: maximum value of area
got it, thank you!
10. ## Re: maximum value of area
Hi,
I'm with Soroban. You should sketch a picture. I enjoy drawing pictures with "modern" software. Two advantages are evident. One, the graphs can be accurate in the sense that the true shape of the graph is drawn. Before the advent of modern software, I didn't know what the graph of y = x2 really looks like. Secondly, in the static drawing attached, it comes from a program that allows me to have a slider for x. I can then dynamically change x and see the various rectangles; also this allows me to check and see if I have found the maximum area.
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2017-08-22 16:55:37
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https://nrich.maths.org/2397/clue
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### I'm Eight
Find a great variety of ways of asking questions which make 8.
### Let's Investigate Triangles
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
### Noah
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
# Hundred Square
##### Age 5 to 7 Challenge Level:
Can you imagine the square on the back? Where will its $1$ be? Where will its $10$ be?
So what will be on the back of the $20$ in the $100$ square in the picture? The $30$? Does this help with the $100$?
You could print off the $100$ square, or draw your own, and write just, for example, $1-10$ on the back of it to get you started. Can you see where $11-20$ would be? Perhaps this helps to predict the other numbers.
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2019-10-21 13:28:36
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https://zbmath.org/?q=ci%3A3344010
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Closed graph theorems for bornological spaces.(English)Zbl 1376.46005
For bornological vector spaces over the field $$K$$, where $$K=\mathbb{R}$$ or $$K=\mathbb{C}$$, F. Gach [Acta Math. Univ. Comen., New Ser. 75, No. 2, 209–218 (2006; Zbl 1164.46301)] has presented a theorem that includes two classical results: M. De Wilde’s [Bull. Soc. R. Sci. Liège 40, 116–118 (1971; Zbl 0216.40603)] closed graph theorem for webbed locally convex spaces, and a bornological closed graph theorem of N. Popa [C. R. Acad. Sci., Paris, Sér. A273, 294–297 (1971; Zbl 0217.44401)]. In the paper under review, the theorem of Gach is extended to the non-archimedean setting.
The author first gives an introductory overview of bornological vector spaces over a complete non-trivially valued field $$K$$. In a separated convex bornological vector space $$\left( F,\mathcal{B}\right)$$ over such a field $$K$$, a pair $$\left( \mathcal{V},b\right)$$, where $$\mathcal{V}: \bigcup _{k\in\mathbb{N}}\mathbb{N}^{k}\rightarrow\mathcal{P}\left( F\right)$$ and $$b: \mathbb{N}^{\mathbb{N}}\rightarrow\left\{ \left| K^{\times}\right| \right\} ^{\mathbb{N}}$$ (here, $$\left| K^{\times}\right| :=\left\{ \left| r\right| \mid r\in K\diagdown\left\{ 0\right\} \right\}$$), is called a bornological web if the following conditions hold:
(1)
the image of $$\mathcal{V}$$ consists of disks,
(2)
$$\mathcal{V}\left( \varnothing\right) =F,$$
(3)
$$\mathcal{V}\left( n_{0},\dots,n_{k} \right)$$ is absorbed by $$\bigcup_{n\in\mathbb{N}}\mathcal{V}\left( n_{0},\dots,n_{k},n\right)$$ for each $$\left( n_{0},\dots,n_{k}\right) \in$$ $$\bigcup_{k\in\mathbb{N}}\mathbb{N}^{k},$$
(4)
for every $$s:\mathbb{N\rightarrow N}$$, the series $$\sum_{k\in\mathbb{N}}\lambda\left( s\right) _{k}x_{k}$$ (with $$\lambda\left( s\right) _{k}\in K$$) converges bornologically in $$F,$$ whenever $$x_{k}\in\mathcal{V}\left( s\left( 0\right) ,\dots,s\left( k\right) \right)$$ and $$\left| \lambda\left( s\right) _{k}\right| =b\left( s\right) _{k}$$.
Then $$\left( \mathcal{V},b\right)$$ determines on $$F$$ a convex linear bornology, $$\mathcal{B}_{\left( \mathcal{V},b\right) }$$, and $$\left( F,\mathcal{B} _{\left( \mathcal{V},b\right) }\right)$$ is called a webbed convex bornological space. The main result of the paper is the following.
Theorem 2.11. Let $$E$$ and $$F$$ be separated convex bornological vector spaces, where $$E$$ is complete and $$F$$ is endowed with a bornological web $$\left( \mathcal{V},b\right)$$. Then every linear map $$f: E\rightarrow F$$ with bornologically closed graph is bounded with respect to the given bornology on $$E$$, and $$\mathcal{B}_{\left( \mathcal{V},b\right) }$$ on $$F$$.
As consequences of this theorem, the author obtains generalized versions both of the closed graph theorems of Popa and De Wilde cited above. For the last one, the field $$K$$ is supposed to be spherically complete.
MSC:
46A17 Bornologies and related structures; Mackey convergence, etc. 46A30 Open mapping and closed graph theorems; completeness (including $$B$$-, $$B_r$$-completeness) 46J05 General theory of commutative topological algebras 46A08 Barrelled spaces, bornological spaces 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis
Full Text:
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2022-12-09 02:46:08
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https://www.jepusto.com/tags/meta-analysis/
|
# meta-analysis
Power for Meta-Analysis of Dependent Effects
## Single case design research in Special Education: Next generation standards and considerations
Single case design has a long history of use for assessing intervention effectiveness for children with disabilities. Although these designs have been widely employed for more than 50 years, recent years have been especially dynamic in terms of …
## Power approximations for overall average effects in meta-analysis of dependent effect sizes
Meta-analytic models for dependent effect sizes have grown increasingly sophisticated over the last few decades, which has created challenges for a priori power calculations. We introduce power approximations for tests of average effect sizes based …
## Investigating narrative performance in children with developmental language disorder: A systematic review and meta-analysis
__Purpose__: Speech-language pathologists (SLPs) typically examine narrative performance when completing a comprehensive language assessment. However, there is significant variability in the methodologies used to evaluate narration. The primary aims …
## Multi-level meta-analysis of single-case experimental designs using robust variance estimation
Single-case experimental designs (SCEDs) are used to study the effects of interventions on the behavior of individual cases, by making comparisons between repeated measurements of an outcome under different conditions. In research areas where SCEDs …
## Meta-Analysis with robust variance estimation: Expanding the range of working models
In prevention science and related fields, large meta-analyses are common, and these analyses often involve dependent effect size estimates. Robust variance estimation (RVE) methods provide a way to include all dependent effect sizes in a single …
## Cluster wild bootstrapping to handle dependent effect sizes in meta-analysis with a small number of studies
The most common and well-known meta-regression models work under the assumption that there is only one effect size estimate per study and that the estimates are independent. However, meta-analytic reviews of social science research often include …
## Examining the effects of social stories on challenging behavior and prosocial skills in young children: A systematic review and meta-analysis
Social stories are a commonly used intervention practice in early childhood special education. Recent systematic reviews have documented the evidence-base for social stories, but findings are mixed. We examined the efficacy of social stories for …
## Variance component estimates in meta-analysis with mis-specified sampling correlation
$\def\Pr{{\text{Pr}}} \def\E{{\text{E}}} \def\Var{{\text{Var}}} \def\Cov{{\text{Cov}}}$ In a recent paper with Beth Tipton, we proposed new working models for meta-analyses involving dependent effect sizes. The central idea of our approach is to use a working model that captures the main features of the effect size data, such as by allowing for both between- and within-study heterogeneity in the true effect sizes (rather than only between-study heterogeneity).
## Implications of mean-variance relationships for standardized mean differences
I spend more time than I probably should discussing meta-analysis problems on the R-SIG-meta-analysis listserv. The questions that folks pose there are often quite interesting—especially when they’re motivated by issues that they’re wrestling with while trying to complete meta-analysis projects in their diverse fields.
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2023-02-04 09:47:47
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http://billpringle.com/wrp/webtools.html
|
Bill Pringle - Bill@BillPringle
# Web Tools Package
This page describes the web tools package developed by Bill Pringle. This package allows the user to create web sites quickly and easily, so that all the pages have a consistent look and feel. This package can generate web pages for a wide variety of web sites.
The main element of this package is the bld_page program, which translates text files into HTML (web) pages. This is done by copying the input file and expanding any macros it encounters. Furthermore, certain pre-defined macros are called at certain times to create the beginning and end of the page. Users may define the code to be expanded for each of the macros, which controls the look and feel of the web site.
## Set Up Web Server
The first thing we will do is to install a web server on your computer. This is not absolutely necessary for these demo pages, but will be needed if you begin to add features to your pages.
The package we will be installing is called xampp and can be downloaded from here. Follow the installation instructions,and when done, you can resume reading this tutorial.
Assuming you installed the xampp package in the default location, when you are done, you should see a directory C:\xampp. The subdirectory C:\xampp\htdocs is the root directory of your web server. This means you can create several web sites on your local computer by creating subdirectories for each site under C:\xampp\htdocs.
## Set Up Files and Directories
We are now ready to create our first web site. Let's look at a short example to illustrate the use of the webtools package. The bld_page program reads files from an input directory, converts the input file to an HTML (web) file, and writes the resulting page to an output directory. By default, the input directory is called in and the output directory is called out.
To get started, download the Bld Page package, which contains a subset of the webtools package, and unzip it to the C:\xampp\htdocs folder.
This will create the directories listed below, as well as the input pages that are described after that. If you want to enter everything yourself, then unzip the package into a different directory, and then copy the files you need into the directory you created.
When you are done with this step, you should have the following files and directories:
C:\xampp\htdocs\Web
This is the root directory of the web site.
C:\xampp\htdocs\Web\bld_page.exe
This is the program that will create the web pages.
C:\xampp\htdocs\Web\bld_dir.bat
This script is the one you will run to generate your web pages.
C:\xampp\htdocs\Web\include\include.txt
This is the macro definition file.
You will need to edit this file to insert your own name and e-mail address.
C:\xampp\htdocs\Web\in
This is where you will create the input files for your web site.
If you unzipped the bld_page package into your web directory, there should be three test pages, index.html, page2.html, and page3.html. They should be the same as the instructions below.
C:\xampp\htdocs\Web\out
This is where your web site pages will be created. There will be one output file created for each file in your input directory.
C:\xampp\htdocs\Web\out\my.css
This file controls the look and feel of your web pages. It is called a Cascading Style Sheet, and you can read more about it later, but for now, just leave it alone.
## Create Web Page Files
Next you want to set up the files you will need to build your web site. We will use the default macros from the webtools package, and create a small set of files to start with. Once you get the initial web site created, you can start adding your own content by filling in the web page files.
Double-click on C:\xampp\htdocs\Web\include\include.txt. This should bring the include file in notepad. If you have a favorite text editor, use it to edit the include file.
There are several places in the include file containing your-name and your-email-addr. Change these to your actual name and e-mail address. Save the file.
You are ready to create your first web page. When you unzipped the bld_page file, you already created the web pages described below. You can create them yourself and overwrite the pages that were downloaded, or simply examine the downloaded files to follow the tutorial. (I find that I learn better if I create the files myself rather than just reading, but whatever works for you is fine.)
Assuming you want to create your own web pages, you will need a text editor (like notepad). If you have a text editor that you like, then you can use that. Using whatever text editor you want, enter the following text:
My Web Site
>Normal
This is my first web page.
>NormNext
>NormEnd
Save this file as C:\xampp\htdocs\Web\in\index.html.
We will create two more pages that will be used for additional major categories. Links to these pages will appear on the top of all the pages on your web site.
Major Category 2
>Normal
>NormEnd
Save this file as C:\xampp\htdocs\Web\in\page2.html.
The last page has some extra macros that we will explain in more detail later on. For now, simply create this page:
Major Category 3
>Normal
>NormEnd
>Normal
>NormEnd
>Normal
>NormEnd
Save this file as C:\xampp\htdocs\Web\in\page3.html
If you unzipped the bld_page package into your C:\xampp\htdocs\Web directory, this page will have some additional text as well as some pictures. If you are entering the pages by hand, just do the above text, and then look at the provided page3.html to see what else you can do.
## Build Web Pages
You are now ready to build your web pages. Using your windows explorer, double-click on the bld_dir.bat script file in the C:\xampp\htdocs\Web directory. This will run the bld_page program to read the files in your input directory and create your web pages in the output directory.
After the program finishes, use your windows explorer to look at the C:\xampp\htdocs\Web\out directory. You should see output files with the same names as those found in your input directory (index.html, page2.html, and page3.html). However, the files in the output directory are actual HTML pages, while those in the input directory are used by the bld_dir.bat command to create the output HTML pages.
http://localhost/Web/out/
This should cause the web site you just created to be displayed inside your browser. Although you probably use Internet Explorer, there are significant advantages to using Firefox instead. Regardless of which browser you use, you should see something like the following in your browser:
If you have changed the C:\xampp\htdocs\Web\include\include.txt file and inserted your actual name and e-mail address, you should see your name along the top of the home page, with links marked Home, Page 2, and Page 3. If you click on those three links, you will see that the corresponding web pages are displayed. Congratulations! You have just created a web site! Of course, it isn't on the Internet yet, but you will be able to view it from your own computer.
If you compare your input files to the web pages they create, you can get an overview of the process. The first line of the input file is both the title of the page and the top header as well. If you look at the top of the browser, you will see that it has the same thing as the header at the top of the page. You will also notice lines that start with a greater than sign (>). These are macro commands. Each time the bld_page program encounters a macro, it substitutes the macro definition found in the include file (C:\xampp\htdocs\Web\include\include.txt), inserting the macro arguments where specified. The sample pages don't use any macros with arguments, but they will be discussed later.
Another advantage of this approach is that it provides the functionality of what is called a Content Manager, something that large commercial web sites pay lots of money for, without the overhead of needing a database. A content manager allows you to develop a template for your web pages, and then insert content into the appropriate sections for each page. This means that all the pages on the site have common elements, which helps make the web site look professional.
Most content managers use a database to store all the information needed for the web pages, and then builds each web page when the user visits the page. The bld_page program uses the macros you have defined (or the default macros if you haven't made any changes) to create a consistent look and feel for all the web pages. And since the bld_page program creates the actual HTML pages, you don't need a database. And best of all, you don't have to pay for it!
You can experiment by changing the content of the pages, running bld_pages again, and see the results. Don't make any changes to the macros just yet; we will cover that topic later. Once you are ready, the next section will teach you some of the commands that you can insert on your pages to make them look the way you want.
## Bld_Page Macros
There are a number of macros in the macro definition file (C:\xampp\htdocs\Web\include\include.txt), and you can even add new ones once you are more familiar with how the package works. A macro definition begins with a greater-than sign (>) followed by the name of the macro. Everthing that follows up to a line containing only a greater-than sign is the definition of that macro.
To understand macros, you need some understanding of HTML, which is the language used to create web pages. HTML consists of different kinds of elements, like paragraphs, headers, hyperlinks, etc. These elements are identified with tags, which indicates the nature of the element. A tag consists of a tag name surrounded by angle brackets, some text which is the content of the element, and a closing tag which looks like the open tag, except that there is a slash in front of the tag name. (There is a lot more to HTML, but that is enough for now.)
For example, the tag for a paragraph is the "p" tag, which looks like this: <p>. This tag marks the start of a paragraph. Everything that appears between the start tag and its closing tag (</p>) is considered a paragraph.
Tags can have attributes, which can be used to change how the tag is handled. The two attributes that all tags can have are id and class. The values of these attributes must be a string that starts with a letter and has only letters or digits. Most of the time you won't actually specify these attributes, but you will see them in the macro definitions. For a further discussion of these attributes, see the macro definition for Top Banner.
The id attribute identifies the specific tag. There can only be one tag with a specific id attribute; it must be unique. The class attribute defines a sub-class of the tag, which often changes the way that the element will appear.
Now that you understand a little about HTML, look at the top of the macro definition file, where you can find the macros for Normal, NormNext, and NormEnd:
>Normal
<p>
>
>NormNext
</p><p>
>
>NormEnd
</p>
>
You can see from the above definitions that the Normal macro inserts a paragraph tag (<p>) into the page. The NormNext inserts a closing paragraph tag (</p>) and an open paragraph tag, while the NormEnd tag inserts a closing paragraph tag.
This means that the Normal macro starts a paragraph. The NormNext closes the previous paragraph and starts a new one. And finally, the NormEnd closes the current paragraph and doesn't start a new one.
This is why when you want to write a block of text on your web page, you should start out with the Normal macro. Each time you want to start a new paragraph, you use the NormNext macro. And when you are done with the block of text, you finish up with a NormEnd tag. If you forget the Normal tag or the NormEnd tag, your web page will have an error in it. Sometimes the browser will still be able to display the web page, but you should try to make sure your page doesn't have any errors. Part of the problem is that different browsers on different systems might display pages with errors differently. If you want to be sure that everyone can read your web pages, you should find and get rid of any errors that appear.
If you look at the pages you created for your first web site, you will notice that you have already been using macros. If a line starts with a greater-than sign (>), it means that it is a macro line. Right after the greater-than sign will be the name of the macro. So, when you typed the line ">Normal", you were using a macro.
If the macro takes any arguments, they should appear after the macro name, separated by vertical bars (|). The SubLink macro on page3.html used arguments. If you look at the definition for that macro, and then compare what you entered and what the web page contains, you will get a better understanding of how macros with arguments work.
There are also some macros that are called automatically at certain times, such as the start of a page or the end of a page. This means you should never enter these macros in any of your pages, since that will call the macro twice, which will probably mess up your page.
Here is a list of the macros you will find in the default include file. If a macro takes any arguments, they will be indicated in the list below:
### Paragraph Macros
These macros define paragraphs of text. In general, there is one macro that begins a block of text, and another that ends the block. If more than one paragraph appears in the block, a macro defines where the new paragraphs are located.
For example, on the input file index.html you will see the Normal macro start the block, the NormNext macro create new paragraphs, and finally the NormEnd macro to terminate the block of text.
>Normal
This begins normal text. This macro starts the first paragraph of each section.
>NormNext
This macro should be used after the Normal macro each time you want to start a new paragraph.
>NormEnd
This macro signals the end of the text that was started by the Normal macro. If you want to start text after this macro, you will need to use another Normal command.
This macro should also be used to terminate other sets of paragraphs, such as those created by the Note macro.
>NormRight
This macro can be used anywhere that the NormNext macro can be used. The paragraph that this macro defines will be right justified, and italicied.
>NormCenter
This macro can be used anywhere that the NormNext macro can be used. The paragraph that this macro defines will be centered, and italicied.
>Note
This macro can be used anywhere that the Normal macro can be used. The paragraph that this macro defines will be in bold red letters.
>NoteNext
This macro can be used anywhere that the NormNext macro can be used. The paragraph that this macro defines will be in bold red letters.
>NoteEnd
This macro can be used to terminate a series of Note paragraphs. You could actually use the NormEnd and NoteEnd macros interchangeably.
>Indent
This macro can be used anywhere that the Normal macro can be used. The paragraph that this macro defines will be indented from the left margin.
>IndentNext
This macro can be used anywhere that the NormNext macro can be used. The paragraph that this macro defines will be indented from the left margin.
>IndentEnd
This macro can be used anywhere that the NormEnd macro can be used. In fact, you can use this macro and NormEnd interchangeably.
>StandOut|text
This macro will cause the text argument to appear in red bold text. It can be placed in the middle of a paragraph if you don't want the entire paragraph to be bold.
For example:
>Normal
>StandOut|Note:
This is important
>NormEnd
will produce:
Note: This is important
^Macros
These macros can be used to create hyper-links to other locations within the page, or even other web sites.
Each page will have two menus: a global menu that appears exactly the same on all of the pages, and a sub-menu that contains links to the sections of each page. The global menu is defined within the TopBanner macro. The same global menu appears on each page. The submenu is generated by the bld_page program by creating an index to each subsection defined for the current page using the SubLink macro. Page 3 contains SubLink macros. Look at the input file and the web page to see how they work.
>Top
This macro will insert a link to the top of the page. If you have a long page, you might want to insert these at the end of various sections.
>HRef|url|text|trailer
This macro will create a link that will cause the browser to jump to the specified destination.
For example,
Find it on
will produce:
>HRefWin|url|text|trailer|window
This macro works the same as the HRef macro, except that the browser will open the designation in a new window, named window. This is useful if you don't want the user to leave your site, so you open up the new window.
This macro will create a sub-section for your page. A link to this subsection will appear in the subsection menu of the page. Look at the page3.html input and output files to see how this macro works. The id value must be a unique string that starts with a letter and has only letters and numbers (no spaces). The text field is what will appear on the page with a tag type tag (usually h2, which is a level 2 header.) If text is long, you will want to supply a shorter string (short) that will appear along the left side of the page. You probably shouldn't experiment with href and win until you learn a lot more about HTML.
Each SubLink macro will create a new link on the left side of the page. These links don't move when you scroll down the page, so if you have too many subsections, they won't fit on the page. If you experiment a bit, you will be able to figure out the optimum number of SubLink macros to use.
>Image|image|width|title|win
This macro lets you add pictures to your web site. Normally, these pictures are placed in a subdirectory called images, but they could be anywhere. If your site has a lot of pictures, then you might want to have several directories for pictures.
The image argument is the location of the picture, while width is how wide you want the picture (it is best to use a percentage). The title argument will be used as a caption, as well as the tool-tip for the image. (If you hover the mouse over the image, then the title will appear in a small rectangle.) Finally, the win argument is optional, but can be used to specify the name of the window for the picture. The default window is img, which means that if you click on a new image, it will replace whatever picture was already in that window. If you want the user to have several windows of pictures, you can give each image its own window name.
For example, if you have an image foobar.jpg and you would like it to take up half the page. You could do something like this:
>Image|images/foobar.jpg|50%|This is my picture
>MailMe|trailer
This macro inserts a link that will cause an e-mail to be sent to you. You first need to replace the string your-email-addr in the macro with your e-mail address.
The trailer string is optional. If present, it will appear directly after the link without any space.
For example:
If you have any questions,
>MailMe|.
Will produce:
If you have any questions, send e-mail to your-email-addr.
Notice that the period isn't part of the link. If you put the period on the next line, a space would appear before the period.
This macro will create a link that will send e-mail to the specified email-addr with a subject line of subject. The optional trailer string will appear directly after the link, without any spaces.
^Macros
### Page Macros
These macros affect the page layout, and are automatically called by the bld_page program. This means that you will not want to insert these macros in any of your pages, but you might want to customize these macros to produce the look and feel that you want. You must be very careful when making any changes to the macros. It won't take much to totally mess up your pages if you make the wrong change. You probably want to make a copy of the include file before you start making any changes. That way, if something goes wrong, you can restore the last working version.
>PageStart|title
This macro is called to start a new page. The argument, title is the first line of the file. You probably don't want to change this macro.
If the second line of the file isn't a blank line, the bld_page program will copy all the non-blank lines until a blank line is found. These lines are inserted into the header section of the page. You should not try this unless you understand HTML.
>PageHdr|title
This macro is called start the body of the page. It terminates the header section and starts the body section. The default macro definition will call the TopBanner macro to create a banner across the top of the page. The page header will consist of the title argument, which is the first line of the file.
>TopBanner
This macro is called by the PageHdr macro in the default macro definitions. This macro is not called by bld_page directly, so if you change the PageHdr macro definition, you can eliminate this macro if you want. (You can also change the definition of this macro to be empty, which would do the same thing.)
This is one macro that you will want to change, since it generates the global menu for all pages.
Here is the original definition for this macro:
>TopBanner
<div id="beg">
<p class="larger">your-name</p>
<p>
|
>HRef|index.html|Home
|
>HRef|page2.html|Page 2
|
>HRef|page3.html|Page 3
|
</p>
</div>
>
Before talking about the changes you will want to make, I will explain about the id and class attributes in this macro. The div tag allows you to group a collection of elements together. In this case, the entire top banner is grouped into a single division called beg, as specified by the id attribute. Since this is the first thing on the page, if you want to go to the top of the page, you can jump to this division. If you look at the Top macro, you will see that it inserts a hyperlink to #top, which will be this division. (If a link starts with a pound sign (#), that indicates that the link is located on the current page.)
Notice that the next line has a p tag with class="larger" attribute. This means that this isn't a normal paragraph, but a special paragraph of the larger class. The my.css file contains instructions to the browser that a larger type paragraph should be displayed with larger characters. That is why your name or your site title appears bigger than the menu directly beneath it. Unless you want to have a lot of links within your pages, or do something special without using the macros, you probably will never need to use either the id or class attributes.
Now that you understand a little bit about tag attributes, let's talk about the changes you will want to make to this macro:
• Change the string your-name to either your name, or the name you want to give to the site.
• Customize the HRef links of the global menu. Rather than page2.html and page3.html, you probably want to create pages with names that better describe the sections of your site.
For example, let's say that you want to call your web site Bill's Web Site, and create sections for music, books, and pictures. Your TopBanner macro could look like this:
>TopBanner
<div id="beg">
<p class="larger">Bill's Web Site</p>
<p>
|
>HRef|index.html|Home
|
>HRef|music.html|Music
|
>HRef|books.html|Books
|
>HRef|pics.html|Pictures
|
</p>
</div>
>
You would then create input files music.html, books.html, and pics.html for those sections of your web site.
If you are brave, you can make even further changes to this macro. For example, suppose you don't want to have the name of your site at the top of the page. You could remove the line:
<p class="larger">Bill's Web Site</p>
and the title will go away after you re-build the web pages.
This macro is called once the content of the page is finished, and the page sub-menu is about to be created. This macro is usually used to generate any trailer that is to appear on all the pages. The default macros do this by calling the Trailer macro. You probably don't want to change this macro.
>Trailer
This macro is not called by bld_page directly, but by the default version of the SubMenuStart macro. If you remove that call, then you can remove this macro.
You will want to modify this macro. The initial value of this macro is:
>Trailer
<p class="trailer">
© 2007
</p>
>
The above macro inserts a copyright notice with your name as a hyper link that will send you e-mail. You will want to make the following changes to this macro:
• Change the date to the current year
• Put in your actual name
• Make any other changes to the content of the trailer you might want
This macro is called for each SubLink macro that is found in the input file. The macro will create a new entry in the sub-menu list. You should not try to change this macro unless you really know what you are doing.
This macro is called after all the sub-menu items have been created. You should have no reason to change this macro.
>PageEnd
This macro is called at the very end of the page, and supplies the closing lines.
If you are using Google Analytics, you can add the JavaScript code in this macro before the </body> tag.
^Macros
## Making Changes to your Pages
Whenever you make any changes to the input files, you have to double-click on the bld_pages script to run the bld_page program, and re-create new web pages. After the program finishes, look at the web pages and see if the changes look the way you wanted them. If not, make more changes and generate the web pages again. Keep this up until you are happy with your changes. Remember to refresh your browser to see the changed pages.
It is best to make one set of changes at a time rather than a bunch of changes before rebuilding the web pages. That way, if something goes wrong, you have a better idea of where the problem is. For example, if you made only one change, then that change is what introduced the error. If, however, you made a bunch of changes, it will be a lot harder to find out what went wrong. Until you get comfortable with the process, making one change at a time will seem time consuming, but it will make fixing errors much easier. In summary, you will do the following steps over and over again until you are done with all your changes:
• Make a small number of changes
• Run the bld_pages program to re-generate your web pages
|
2018-06-22 22:16:50
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https://math.stackexchange.com/questions/3259920/how-to-write-the-adjoint-application-defined-by-a-matrix
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How to write the adjoint application defined by a matrix?
I'm having a hard time understanding the problem that asks to write the adjoint application $$f_A$$ defined by $$A:\begin{bmatrix}a & b \\ c & d\end{bmatrix}$$ with respect to the euclidean product. Any tips?
• Are we talking about finite-dimension vector spaces? – Sam Skywalker Jun 12 at 15:15
• Yes, precisely two-dimensions vector space. – Kevin Jun 12 at 15:16
• With dot product I mean that the vector space is defined by the euclidean product. – Kevin Jun 12 at 15:27
Bear in mind that a matrix stands for a linear map between two $$\mathbb F$$-vector spaces over the field $$\mathbb F$$. Since it is a square matrix and our dimension is two, we can assume that both spaces are the same, so $$A:V\to V$$.
The dual space of $$V$$, which we denote by $$V^*$$, is the space of linear maps from $$V$$ to the field $$\mathbb F$$. This is again a vector space and its dimension is that of $$V$$.
We can regard the dot product as a rule that associates to each vector $$v\in V$$ a linear map the following way: $$<\cdot,\cdot>: V\to V^*;\quad v\mapsto .$$
Recall that $$:V\to \mathbb F$$ is a linear map that eats vectors and gives scalars.
The transpose matrix of $$A$$, $$A^ t$$ is the finite-dimensional version of the adjoint. In this case, $$A^t$$ is the dual map of $$A$$. If you let $$A^t$$ act on a basis of the dual space $$V^*$$ (see the discussion on the dot product two paragraphs above), you get a basis of $$V^{**}$$, which is canonically isomorphic to $$V$$, our original vector space.
Do not hesitate to reply if you need further help.
• Thank you very much! :) – Kevin Jun 12 at 20:52
The adjoint of $$A$$ is the transpose of $$C$$, that is, the $$n×n$$ matrix whose $$(i,j)$$ entry is the $$(j,i)$$ cofactor of $$A$$
$${\displaystyle \operatorname {adj} (\mathbf {A} )=\mathbf {C} ^{\mathsf {T}}=\left((-1)^{i+j}\mathbf {M} _{ji}\right)_{1\leq i,j\leq n}.}$$ Where $$M_{ij}$$ is minor of A.
$${\displaystyle \mathbf {A} ={\begin{pmatrix}{a}&{b}\\{c}&{d}\end{pmatrix}}}$$ Then $${\displaystyle \operatorname {adj} (\mathbf {A} )={\begin{pmatrix}{d}&{-b}\\{-c}&{a}\end{pmatrix}}}$$.
• Is this what you are looking for? – Vineet Jun 12 at 16:04
• I am pretty sure he wants the other kind of adjoint, since he is saying "with respect to the euclidean product". – darij grinberg Jun 12 at 16:28
• Yes, that one with euclidean product. I'm new to linear algebra, thanks! – Kevin Jun 12 at 16:42
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2019-06-24 17:31:03
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http://mathoverflow.net/api/userquestions.html?userid=3521&page=1&pagesize=10&sort=views
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2013-05-21 18:22:00
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http://xvisionx.com/error-function/how-to-compute-error-bars.html
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Home > Error Function > How To Compute Error Bars
# How To Compute Error Bars
## Contents
The standard answer for how to compute anything numerical in Python is "Look in SciPy." However, this person didn't want to take on the dependence on SciPy. Prudnikov, A.P.; Brychkov, Yu.A.; and Marichev, O.I. Translate erfError functioncollapse all in page Syntaxerf(X) exampleDescriptionexampleerf(X) represents the error function of X. Gaussian Quadrature is an accurate technique –Digital Gal Aug 28 '10 at 1:25 GQ is nice, but with (a number of) efficient methods for computing $\mathrm{erf}$ already known, I http://xvisionx.com/error-function/compute-complementary-error-function.html
The pairs of functions {erff(),erfcf()} and {erfl(),erfcl()} take and return values of type float and long double respectively. xrealnumber 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt Privacy Policy Terms of use FAQ Contact us © 2016 CASIO COMPUTER CO., LTD. Numerical Methods That Work, 2nd printing. Craig, A new, simple and exact result for calculating the probability of error for two-dimensional signal constellaions, Proc. 1991 IEEE Military Commun. navigate to this website
## How To Compute Error Bars
Julia: Includes erf and erfc for real and complex arguments. Generated Wed, 05 Oct 2016 09:46:17 GMT by s_hv1002 (squid/3.5.20) If you size it properly, then the function will appear constant with respect to your machine precision outside of this interval. The (Laplace) continued fraction tends to be slightly easier to handle than the asymptotic series for medium-to-large arguments. –J.
For complex, the Faddeeva package provides a C++ complex implementation. M. is the double factorial: the product of all odd numbers up to (2n–1). Complementary Error Function Calculator Jason Merrill 13 April 2015 at 21:27 This is nice, thanks for writing this up.If you're using this routine, one thing to watch out for is large relative error when |x|
J. Retrieved 2011-10-03. ^ Chiani, M., Dardari, D., Simon, M.K. (2003). Level of Im(ƒ)=0 is shown with a thick green line. Because these numbers are not symbolic objects, you get the floating-point results:A = [erf(1/2), erf(1.41), erf(sqrt(2))]A = 0.5205 0.9539 0.9545Compute the error function for the same numbers converted to symbolic objects.
The Q-function can be expressed in terms of the error function as Q ( x ) = 1 2 − 1 2 erf ( x 2 ) = 1 2 Erfc Function Supancic, "On Bürmann's Theorem and Its Application to Problems of Linear and Nonlinear Heat Transfer and Diffusion," The Mathematica Journal, 2014. I've seen variations on this question come up in several different contexts lately, including questions about computing the normal distribution function, so I thought I'd write up a solution.Here's a Python add
if abs(x) < 1e-3:
return 1.1283791670955126*x
The constant is a decimal expansion of 2/sqrt(π).
## How To Calculate Error Function In Casio Calculator
Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian Do whatever you'd like.Here is some similar stand-alone code, also in the public domain. How To Compute Error Bars Is "The empty set is a subset of any set" a convention? Inverse Error Function Calculator Google search: Google's search also acts as a calculator and will evaluate "erf(...)" and "erfc(...)" for real arguments.
But if you're an engineer who has never heard of the error function but needs to use it, it may take a while to figure out how to handle negative inputs.One Analytic Theory of Continued Fractions. Similarly, the En for even n look similar (but not identical) to each other after a simple division by n!. The error function is related to the cumulative distribution Φ {\displaystyle \Phi } , the integral of the standard normal distribution, by[2] Φ ( x ) = 1 2 + 1 Complementary Error Function Table
R. (March 1, 2007), "On the calculation of the Voigt line profile: a single proper integral with a damped sine integrand", Monthly Notices of the Royal Astronomical Society, 375 (3): 1043–1048, For , (11) (12) Using integration by parts gives (13) (14) (15) (16) so (17) and continuing the procedure gives the asymptotic series (18) (19) (20) (OEIS A001147 and A000079). Similarly, (8) (OEIS A103979 and A103980). The error and complementary error functions occur, for example, in solutions of the heat equation when boundary conditions are given by the Heaviside step function.
After division by n!, all the En for odd n look similar (but not identical) to each other. Error Function Excel erf(-x) = -erf(x). See also Related functions Gaussian integral, over the whole real line Gaussian function, derivative Dawson function, renormalized imaginary error function Goodwin–Staton integral In probability Normal distribution Normal cumulative distribution function, a
## comm., Dec.15, 2005).
1. This directly results from the fact that the integrand e − t 2 {\displaystyle e^{-t^ 8}} is an even function.
2. The evaluation is called many times.
3. Fortran 77 implementations are available in SLATEC.
4. The inverse complementary error function is defined as erfc − 1 ( 1 − z ) = erf − 1 ( z ) . {\displaystyle \operatorname ζ 4 ^{-1}(1-z)=\operatorname
5. Definite integrals involving include Definite integrals involving include (34) (35) (36) (37) (38) The first two of these appear in Prudnikov et al. (1990, p.123, eqns. 2.8.19.8 and 2.8.19.11), with ,
An example on a Linux machine: bash$cat erf.i %module erf #include double erf(double); bash$ swig -o erf_wrap.c -python erf.i bash$gcc -o erf_wrap.os -c -fPIC -I/usr/include/python2.4 erf_wrap.c bash$ gcc -o Also, this may be a better question for stack overflow instead, since it's more of a computer science thing. –Jon Bringhurst Jul 20 '10 at 20:26 @Jon: Nope, I'm The formula appears as 1 - (a1t1 + a2t2 + a3t3 + a4t4 + a5t5)exp(-x2), which is absolutely correct. Error Function Matlab Practice online or make a printable study sheet.
A Course in Modern Analysis, 4th ed. Sequences A000079/M1129, A001147/M3002, A007680/M2861, A103979, A103980 in "The On-Line Encyclopedia of Integer Sequences." Spanier, J. For more information, see Tall Arrays.TipsYou can also find the standard normal probability distribution using the Statistics and Machine Learning Toolbox™ function normcdf. New York: Dover, pp.297-309, 1972.
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2017-10-21 06:32:48
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http://math.stackexchange.com/questions/375112/calculate-expectancy-of-poisson-distribution-with-poisson-parameter
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# Calculate Expectancy of Poisson distribution with Poisson parameter
The problem:
Let X have the Poisson distribution with parameter $\lambda$, where $\lambda >0$.
Calculate E[X!] for every possible value of $\lambda$,
So what I got so far:
$$E[X!] = \sum_0^\infty\frac{i!\cdot e^{-\lambda}\cdot\lambda^i}{i!} = e^{-\lambda} \sum_0^\infty\lambda^i=\frac{1}{e^\lambda\cdot(1-\lambda)}$$
Is this correct?
Help will be much appreciated.
Thanks!
-
Well it holds for $\lambda < 1$ I believe... – homiee Apr 28 '13 at 11:11
yes that's correct – roger Apr 28 '13 at 11:17
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2015-04-19 02:02:17
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https://labs.tib.eu/arxiv/?category=cond-mat.dis-nn
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• ### Covering Problems and Core Percolations on Hypergraphs(1605.00897)
Covering problems are classical computational problems concerning whether a certain combinatorial structure 'covers' another. For example, the minimum vertex covering problem aims to find the smallest set of vertices in a graph so that each edge is incident to at least one vertex in that set. Interestingly, the computational complexity of the minimum vertex covering problem in graphs is closely related to the core percolation problem, where the core is a special subgraph obtained by the greedy leaf removal procedure. Here, by generalizing the greedy leaf removal procedure in graphs to hypergraphs, we introduce two generalizations of core percolation in graphs to hypergraphs, related to the minimum hyperedge cover problem and the minimum vertex cover problem on hypergraphs, respectively. We offer analytical solutions of these two core percolations for random hypergraphs with arbitrary vertex degree and hyperedge cardinality distributions. We also compute these two cores in several real-world hypergraphs, finding that they tend to be much smaller than their randomized counterparts. This result suggests that both the minimum hyperedge cover problem and the minimum vertex cover problem in those real-world hypergraphs can actually be solved in polynomial time. Finally, we map the minimum dominating set problem in graphs to the minimum hyperedge cover problem in hypergraphs. We show that our generalized greedy leaf removel procedure significantly outperforms the state-of-the-art method in solving the minimum dominating set problem.
• ### The hipster effect: When anticonformists all look the same(1410.8001)
In such different domains as neurosciences, spin glasses, social science, economics and finance, large ensemble of interacting individuals following (mainstream) or opposing (hipsters) to the majority are ubiquitous. In these systems, interactions generally occur after specific delays associated to transport, transmission or integration of information. We investigate here the impact of anti-conformism combined to delays in the emergent dynamics of large populations of mainstreams and hipsters. To this purpose, we introduce a class of simple statistical systems of interacting agents composed of (i) mainstreams and anti-conformists in the presence of (ii) delays, possibly heterogeneous, in the transmission of information. In this simple model, each agent can be in one of two states, and can change state in continuous time with a rate depending on the state of others in the past. We express the thermodynamic limit of these systems as the number of agents diverge, and investigate the solutions of the limit equation, with a particular focus on synchronized oscillations induced by delayed interactions. We show that when hipsters are too slow in detecting the trends, they will consistently make the same choice, and realizing this too late, they will switch, all together to another state where they remain alike. Similar synchronizations arise when the impact of mainstreams on hipsters choices (and reciprocally) dominate the impact of other hipsters choices, and we show that these may emerge only when the randomness in the hipsters decisions is sufficiently large. Beyond the choice of the best suit to wear this winter, this study may have important implications in understanding synchronization of nerve cells, investment strategies in finance, or emergent dynamics in social science, domains in which delays of communication and the geometry of information accessibility are prominent.
• ### Suppression and Revival of Weak Localization through Control of Time-Reversal Symmetry(1411.1671)
We report on the observation of suppression and revival of coherent backscattering of ultra-cold atoms launched in an optical disorder and submitted to a short dephasing pulse, as proposed in a recent paper of T. Micklitz \textit{et al.} [arXiv:1406.6915]. This observation, in a quasi-2D geometry, demonstrates a novel and general method to study weak localization by manipulating time reversal symmetry in disordered systems. In future experiments, this scheme could be extended to investigate higher order localization processes at the heart of Anderson (strong) localization.
• ### MBL-mobile: Quantum engine based on many-body localization(1707.07008)
Many-body-localized (MBL) systems do not thermalize under their intrinsic dynamics. The athermality of MBL, we propose, can be harnessed for thermodynamic tasks. We illustrate this ability by formulating an Otto engine cycle for a quantum many-body system. The system is ramped between a strongly localized MBL regime and a thermal (or weakly localized) regime. The difference between the energy-level correlations of MBL systems and of thermal systems enables mesoscale engines to run in parallel in the thermodynamic limit, enhances the engine's reliability, and suppresses worst-case trials. We estimate analytically and calculate numerically the engine's efficiency and per-cycle power. The efficiency mirrors the efficiency of the conventional thermodynamic Otto engine. The per-cycle power scales linearly with the system size and inverse-exponentially with a localization length. This work introduces a thermodynamic lens onto MBL, which, having been studied much recently, can now be considered for use in thermodynamic tasks.
• ### Complex Networks from Classical to Quantum(1702.08459)
Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information physics is setting the stage for a theory of complex systems with quantum information-inspired methods. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have been proposed to offer enhancement for several network problems. Here we review the results at the cutting edge, pinpointing the similarities and the differences found at the intersection of these two fields.
• ### Random Close Packing and the Hard Sphere Percus-Yevick Theory(1703.09903)
The Percus-Yevick theory for monodisperse hard spheres gives very good results for the pressure and structure factor of the system in a whole range of densities that lie within the liquid phase. However, the equation seems to lead to a very unacceptable result beyond that region. Namely, the Percus-Yevick theory predicts a smooth behavior of the pressure that diverges only when the volume fraction $\eta$ approaches unity. Thus, within the theory there seems to be no indication for the termination of the liquid phase and the transition to a solid or to a glass. In the present article we study the Percus-Yevick hard sphere pair distribution function, $g_2(r)$, for various spatial dimensions. We find that beyond a certain critical volume fraction $\eta_c$, the pair distribution function, $g_2(r)$, which should be positive definite, becomes negative at some distances. We also present an intriguing observation that the critical $\eta_c$ values we find are consistent with volume fractions where onsets of random close packing (or maximally random jammed states) are reported in the literature for various dimensions. That observation is supported by an intuitive argument. This work may have important implications for other systems for which a Percus-Yevick theory exists.
• ### Backward Simulation of Stochastic Process using a Time Reverse Monte Carlo method(1708.08045)
The "backward simulation" of a stochastic process is defined as the stochastic dynamics that trace a time-reversed path from the target region to the initial configuration. If the probabilities calculated by the original simulation are easily restored from those obtained by backward dynamics, we can use it as a computational tool. It is shown that the naive approach to backward simulation does not work as expected. As a remedy, the Time Reverse Monte Carlo method (TRMC) based on the ideas of Sequential Importance Sampling (SIS) and Sequential Monte Carlo (SMC) is proposed and successfully tested with a stochastic typhoon model and the Lorenz 96 model. TRMC with SMC, which contains resampling steps, is shown to be more efficient for simulations with a larger number of time steps. A limitation of TRMC and its relation to the Bayes formula are also discussed.
• ### Matter wave speckle observed in an out-of-equilibrium quantum fluid(1606.01589)
We report the results of a direct comparison of a freely expanding turbulent Bose-Einstein condensate and the propagation of an optical speckle pattern. We found remarkably similar statistical properties underlying the spatial propagation of both phenomena. The calculated second-order correlation together with the typical correlation length of each system is used to compare and substantiate our observations. We believe that the close analogy existing in between an expanding turbulent quantum gas and a traveling optical speckle, might burgeon into an exciting new research field investigating disordered quantum matter.
• ### Singular Spectrum and Recent Results on Hierarchical Operators(1705.04884)
We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical operators and matrices. We proceed to contrast the localizing effect of the hierarchical structure in the deterministic setting with previous results and conjectures in the random setting. Furthermore, we survey stronger localization statements truly exploiting the disorder for the hierarchical Anderson model and report recent results concerning the spectral statistics of the ultrametric random matrix ensemble.
• ### Extremes of $2d$ Coulomb gas: universal intermediate deviation regime(1710.06222)
In this paper, we study the extreme statistics in the complex Ginibre ensemble of $N \times N$ random matrices with complex Gaussian entries, but with no other symmetries. All the $N$ eigenvalues are complex random variables and their joint distribution can be interpreted as a $2d$ Coulomb gas with a logarithmic repulsion between any pair of particles and in presence of a confining harmonic potential $v(r) \propto r^2$. We study the statistics of the eigenvalue with the largest modulus $r_{\max}$ in the complex plane. The typical and large fluctuations of $r_{\max}$ around its mean had been studied before, and they match smoothly to the right of the mean. However, it remained a puzzle to understand why the large and typical fluctuations to the left of the mean did not match. In this paper, we show that there is indeed an intermediate fluctuation regime that interpolates smoothly between the large and the typical fluctuations to the left of the mean. Moreover, we compute explicitly this "intermediate deviation function" (IDF) and show that it is universal, i.e. independent of the confining potential $v(r)$ as long as it is spherically symmetric and increases faster than $\ln r^2$ for large $r$ with an unbounded support. If the confining potential $v(r)$ has a finite support, i.e. becomes infinite beyond a finite radius, we show via explicit computation that the corresponding IDF is different. Interestingly, in the borderline case where the confining potential grows very slowly as $v(r) \sim \ln r^2$ for $r \gg 1$ with an unbounded support, the intermediate regime disappears and there is a smooth matching between the central part and the left large deviation regime.
• ### Probing many-body localization in a disordered quantum magnet(1707.04952)
Jan. 16, 2019 cond-mat.dis-nn
Quantum states cohere and interfere. Quantum systems composed of many atoms arranged imperfectly rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent clusters of spins by driving the system beyond its linear response regime at a single frequency and measuring the resulting "hole" in the overall linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the disordered Ising magnet, $\mathrm{LiHo_{0.045}Y_{0.955}F_4}$, the quality factor $Q$ for spectral holes can be as high as 100,000. We tune the dynamics of the quantum degrees of freedom by sweeping the Fano mixing parameter $q$ through zero via the amplitude of the ac pump as well as a static external transverse field. The zero-crossing of $q$ is associated with a dissipationless response at the drive frequency, implying that the off-diagonal matrix element for the two-level system also undergoes a zero-crossing. The identification of localized two-level systems in a dense and disordered dipolar-coupled spin system represents a solid state implementation of many-body localization, pushing the search forward for qubits emerging from strongly-interacting, disordered, many-body systems.
• ### The localization transition in SU(3) gauge theory(1706.03562)
Jan. 3, 2019 hep-ph, hep-lat, cond-mat.dis-nn
We study the Anderson-like localization transition in the spectrum of the Dirac operator of quenched QCD. Above the deconfining transition we determine the temperature dependence of the mobility edge separating localized and delocalized eigenmodes in the spectrum. We show that the temperature where the mobility edge vanishes and localized modes disappear from the spectrum, coincides with the critical temperature of the deconfining transition. We also identify topological charge related close to zero modes in the Dirac spectrum and show that they account for only a small fraction of localized modes, a fraction that is rapidly falling as the temperature increases.
• ### Spontaneous synchrony in power-grid networks(1302.1914)
An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that are determinants of spontaneous synchronization. Our analysis gives rise to an approach to specify parameter assignments that can enhance synchronization of any given network, which we demonstrate for a selection of both test systems and real power grids. Because our results concern spontaneous synchronization, they are relevant both for reducing dependence on conventional control devices, thus offering an additional layer of protection given that most power outages involve equipment or operational errors, and for contributing to the development of "smart grids" that can recover from failures in real time.
• ### Renormalization-group theory of the abnormal singularities at the critical-order transition in bond percolation on pointed hierarchical graphs(1710.04014)
We study the singularity of the order parameter at the transition between a critical phase and an ordered phase of bond percolation on pointed hierarchical graphs. In pointed hierarchical graphs, the renormalization group (RG) equation explicitly depends on the bare parameter, which causes the phase transitions that correspond to the bifurcation of the RG fixed point. We derive the relation between the type of this bifurcation and the type of the singularity of the order parameter. In the case of a saddle node bifurcation, the singularity of the order parameter is power-law or essential one depending on the fundamental local structure of the graph. In the case of pitchfork and transcritical bifurcations, the singularity is essential and power-law ones, respectively. These becomes power-law and discontinuous ones, respectively, in the absence of the first-order perturbation to the largest eigenvalue of the combining matrix, which gives the growth rate of the cluster size. We also show that the first-order perturbation vanishes if the relevant RG parameter is unique and the backbone of the pointed hierarchical graph is simply connected via nesting subunits.
• ### Feedback through graph motifs relates structure and function in complex networks(1605.09073)
In physics, biology and engineering, network systems abound. How does the connectivity of a network system combine with the behavior of its individual components to determine its collective function? We approach this question for networks with linear time-invariant dynamics by relating internal network feedbacks to the statistical prevalence of connectivity motifs, a set of surprisingly simple and local statistics of connectivity. This results in a reduced order model of the network input-output dynamics in terms of motifs structures. As an example, the new formulation dramatically simplifies the classic Erdos-Renyi graph, reducing the overall network behavior to one proportional feedback wrapped around the dynamics of a single node. For general networks, higher-order motifs systematically provide further layers and types of feedback to regulate the network response. Thus, the local connectivity shapes temporal and spectral processing by the network as a whole, and we show how this enables robust, yet tunable, functionality such as extending the time constant with which networks remember past signals. The theory also extends to networks composed from heterogeneous nodes with distinct dynamics and connectivity, and patterned input to (and readout from) subsets of nodes. These statistical descriptions provide a powerful theoretical framework to understand the functionality of real-world network systems, as we illustrate with examples including the mouse brain connectome.
• ### A homotopic mapping between current-based and conductance-based synapses in a mesoscopic neural model of epilepsy(1510.00427)
Changes in brain states, as found in many neurological diseases such as epilepsy, are often described as bifurcations in mesoscopic neural models. Nearly all of these models rely on a mathematically convenient, but biophysically inaccurate, description of the synaptic input to neurons called current-based synapses. We develop a novel analytical framework to analyze the effects of a more biophysically realistic description, known as conductance-based synapses. These are implemented in a mesoscopic neural model and compared to the standard approximation via a single parameter homotopic mapping. A bifurcation analysis using the homotopy parameter demonstrates that if a more realistic synaptic coupling mechanism is used in this class of models, then a bifurcation or transition to an abnormal brain state does not occur in the same parameter space. We show that the more realistic coupling has additional mathematical parameters that require a fundamentally different biophysical mechanism to undergo a state transition. These results demonstrate the importance of incorporating more realistic synapses in mesoscopic neural models and challenge the accuracy of previous models, especially those describing brain state transitions such as epilepsy.
• ### Resolution of the exponent puzzle for the Anderson transition in doped semiconductors(1710.01742)
Dec. 4, 2018 quant-ph, cond-mat.dis-nn
The Anderson metal-insulator transition (MIT) is central to our understanding of the quantum mechanical nature of disordered materials. Despite extensive efforts by theory and experiment, there is still no agreement on the value of the critical exponent $\nu$ describing the universality of the transition --- the so-called "exponent puzzle". In this work, going beyond the standard Anderson model, we employ ab initio methods to study the MIT in a realistic model of a doped semiconductor. We use linear-scaling DFT to simulate prototypes of sulfur-doped silicon (Si:S). From these we build larger tight-binding models close to the critical concentration of the MIT. When the dopant concentration is increased, an impurity band forms and eventually delocalizes. We characterize the MIT via multifractal finite-size scaling, obtaining the phase diagram and estimates of $\nu$. Our results suggest an explanation of the long-standing exponent puzzle, which we link to the hybridization of conduction and impurity bands.
• ### The Layered Structure of Tensor Estimation and its Mutual Information(1709.10368)
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using a new type of interpolation method developed in [1]. We then show how to harness the structure in "layers" of tensor estimation in order to obtain a formula for the mutual information for the order 3 problem from the knowledge of the formula for the order 2 problem, still using the same kind of interpolation. Our proof technique straightforwardly generalizes and allows to rigorously obtain the mutual information at any order in a recursive way.
• ### Time-dependent Real-space Renormalization-Group Approach: application to an adiabatic random quantum Ising model(1708.05948)
Nov. 26, 2018 cond-mat.dis-nn
We develop a time-dependent real-space renormalization-group approach which can be applied to Hamiltonians with time-dependent random terms. To illustrate the renormalization-group analysis, we focus on the quantum Ising Hamiltonian with random site- and time-dependent (adiabatic) transverse-field and nearest-neighbour exchange couplings. We demonstrate how the method works in detail, by calculating the off-critical flows and recovering the ground state properties of the Hamiltonian such as magnetization and correlation functions. The adiabatic time allows us to traverse the parameter space, remaining near-to the ground state which is broadened if the rate of change of the Hamiltonian is finite. The quantum critical point, or points, depend on time through the time-dependence of the parameters of the Hamiltonian. We, furthermore, make connections with Kibble-Zurek dynamics and provide a scaling argument for the density of defects as we adiabatically pass through the critical point of the system.
• ### The Morphospace of Consciousness(1705.11190)
We construct a complexity-based morphospace to study systems-level properties of conscious & intelligent systems. The axes of this space label 3 complexity types: autonomous, cognitive & social. Given recent proposals to synthesize consciousness, a generic complexity-based conceptualization provides a useful framework for identifying defining features of conscious & synthetic systems. Based on current clinical scales of consciousness that measure cognitive awareness and wakefulness, we take a perspective on how contemporary artificially intelligent machines & synthetically engineered life forms measure on these scales. It turns out that awareness & wakefulness can be associated to computational & autonomous complexity respectively. Subsequently, building on insights from cognitive robotics, we examine the function that consciousness serves, & argue the role of consciousness as an evolutionary game-theoretic strategy. This makes the case for a third type of complexity for describing consciousness: social complexity. Having identified these complexity types, allows for a representation of both, biological & synthetic systems in a common morphospace. A consequence of this classification is a taxonomy of possible conscious machines. We identify four types of consciousness, based on embodiment: (i) biological consciousness, (ii) synthetic consciousness, (iii) group consciousness (resulting from group interactions), & (iv) simulated consciousness (embodied by virtual agents within a simulated reality). This taxonomy helps in the investigation of comparative signatures of consciousness across domains, in order to highlight design principles necessary to engineer conscious machines. This is particularly relevant in the light of recent developments at the crossroads of cognitive neuroscience, biomedical engineering, artificial intelligence & biomimetics.
• ### Out-of-equilibrium dynamical mean-field equations for the perceptron model(1710.04894)
Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.
• ### Moments of the inverse participation ratio for the Laplacian on finite regular graphs(1506.02048)
Nov. 14, 2018 math-ph, math.MP, cond-mat.dis-nn
We investigate the first and second moments of the inverse participation ratio (IPR) for all eigenvectors of the Laplacian on finite random regular graphs with $n$ vertices and degree $z$. By exactly diagonalizing a large set of $z$-regular graphs, we find that as $n$ becomes large, the mean of the inverse participation ratio on each graph, when averaged over a large ensemble of graphs, approaches the numerical value $3$. This universal number is understood as the large-$n$ limit of the average of the quartic polynomial corresponding to the IPR over an appropriate $(n-2)$-dimensional hypersphere of $\mathbb{R}^n$. For a large, but not exhaustive ensemble of graphs, the mean variance of the inverse participation ratio for all graph Laplacian eigenvectors deviates from its continuous hypersphere average due to large graph-to-graph fluctuations that arise from the existence of highly localized modes.
• ### Monte Carlo simulation of charge transport in disordered organic systems using buffer lattice at boundary(0909.1481)
In this article, we present an alternative method for simulating charge transport in disordered organic materials by using a buffer lattice at the boundary. This method does not require careful tracking of carrier's hopping pattern across boundaries. Suitability of this method is established by reproducing the field dependence of mobility, carrier relaxation and carrier diffusion in disordered organic systems obtained by simulating the charge transport for the full length of the systems along the field direction without and boundary condition. The significance of the buffer lattice is emphasized by simulating field dependence of mobility without using a buffer lattice, which results in negative field dependence of mobiltiy (NFDM) at low field regime due to the extra bias the carrier gains from the neglected hops and boundaries along field direction.
• ### Crossover from impurity-controlled to granular superconductivity in (TMTSF)2ClO4(1709.03361)
Using a proper cooling procedure, a controllable amount of non-magnetic structural disorder can be introduced at low temperature in (TMTSF)2ClO4. Here we performed simultaneous measurements of transport and magnetic properties of (TMTSF)2ClO4 in its normal and superconducting states, while finely covering three orders of magnitude of the cooling rate around the anion ordering temperature. Our result reveals, with increasing density of disorder, the existence of a crossover between homogeneous defect-controlled d-wave superconductivity and granular superconductivity. At slow cooling rates, with small amount of disorder, the evolution of superconducting properties is well described with the Abrikosov-Gorkov theory, providing further confirmation of non-s-wave pairing in this compound. In contrast, at fast cooling rates, zero resistance and diamagnetic shielding are achieved through a randomly distributed network of superconducting puddles embedded in an normal conducting background and interconnected by proximity effect coupling. The temperature dependence of the AC complex susceptibility reveals features typical for a network of granular superconductors. This makes (TMTSF)2ClO4 a model system for granular superconductivity where the grain size and their concentration are tunable within the same sample.
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2020-01-29 20:06:51
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https://en.wikiversity.org/wiki/Portal:Radiation_astronomy
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This image is a composite of several types of radiation astronomy: radio, infrared, visual, ultraviolet, soft and hard X-ray. Credit: NASA.
Radiation astronomy is astronomy applied to the various extraterrestrial sources of radiation, especially at night. It is also conducted above the Earth's atmosphere and at locations away from the Earth, by satellites and space probes, as a part of explorational (or exploratory) radiation astronomy.
Seeing the Sun and feeling the warmth of its rays is probably a student's first encounter with an astronomical radiation source. This will happen from a very early age, but a first understanding of the concepts of radiation may occur at a secondary educational level.
Radiation is all around us on top of the Earth's crust, regolith, and soil, where we live. The study of radiation, including radiation astronomy, usually intensifies at the university undergraduate level.
And, generally, radiation becomes hazardous, when a student embarks on graduate study.
Cautionary speculation may be introduced unexpectedly to stimulate the imagination and open a small crack in a few doors that may appear closed at present. As such, this learning resource incorporates some state-of-the-art results from the scholarly literature.
The laboratories of radiation astronomy are limited to the radiation observatories themselves and the computers and other instruments (sometimes off site) used to analyze the results.
There is "a correlation between the arrival directions of cosmic rays with energy above 6 x 1019 electron volts and the positions of active galactic nuclei (AGN) lying within ~75 megaparsecs."
Some low energy cosmic rays originate or are associated with solar flares. Even these cosmic rays have too high an energy to originate from the solar photosphere. The coronal cloud in close proximity to the Sun may be a source or create them as it bombards the chromosphere from above.
"In particular we recognize a first trace of Vela, brightest gamma and radio galactic source, and smeared sources along Galactic Plane and Center [as a source of ultra high energy cosmic rays (UHECR)]." Read more...
Selected lecture
This is an image of Johannes Vermeer's The astronomer. Credit: www.essentialvermeer.com : Home : Info : Pic.
Radiation astronomy entities, radiation entities, are any astronomical persons or things that have separate and distinct existences in empirical, objective or conceptual reality.
Some of them, like the astronomers of today, or at any time in the past, are relatively known. But there are many entities that are far less known or understood, such as the observers of ancient times who suggested that deities occupied the sky or the heavens. Likewise, these alleged deities may be entities, or perhaps something a whole lot less.
Astronomical X-ray entities are often discriminated further into sources or objects when more information becomes available, including that from other radiation astronomies.
A researcher who turns on an X-ray generator to study the X-ray emissions in a laboratory so as to understand an apparent astronomical X-ray source is an astronomical X-ray entity. So is one who writes an article about such efforts or a computer simulation to possibly represent such a source.
"The X-ray luminosity of the dominant group [an entity] is an order of magnitude fainter than that of the X-ray jet."[1]
## References
1. A. Finoguenov, M.G. Watson, M. Tanaka, C.Simpson, M. Cirasuolo, J.S. Dunlop, J.A. Peacock, D. Farrah, M. Akiyama, Y. Ueda, V. Smolčič, G. Stewart, S. Rawlings, C.vanBreukelen, O. Almaini, L.Clewley, D.G. Bonfield, M.J. Jarvis, J.M. Barr, S. Foucaud, R.J. McLure, K. Sekiguchi, E. Egami (April 2010). "X-ray groups and clusters of galaxies in the Subaru-XMM Deep Field". Monthly Notices of the Royal Astronomical Society 403 (4): 2063-76. doi:10.1111/j.1365-2966.2010.16256.x. Retrieved 2011-12-09.
Selected theory
This animation depicts the collision between our Milky Way galaxy and the Andromeda galaxy. Credit: Visualization Credit: NASA; ESA; and F. Summers, STScI; Simulation Credit: NASA; ESA; G. Besla, Columbia University; and R. van der Marel, STScI.
Most of the mathematics needed to understand the information acquired through astronomical radiation observation comes from physics. But, there are special needs for situations that intertwine mathematics with phenomena that may not yet have sufficient physics to explain the observations. Both uses constitute radiation mathematics, or astronomical radiation mathematics, or a portion of mathematical radiation astronomy.
Astronomical radiation mathematics is the laboratory mathematics such as simulations that are generated to try to understand the observations of radiation astronomy.
The mathematics needed to understand radiation astronomy starts with arithmetic and often needs various topics in calculus and differential equations to produce likely models.
Selected topic
## Backgrounds
This graph shows the power density spectrum of the extragalactic or cosmic gamma-ray background (CGB). Credit: pkisscs@konkoly.hu.
In the figure at right, CUVOB stands for the cosmic ultraviolet and optical background.
The diffuse extragalactic background light (EBL) is all the accumulated radiation in the Universe due to star formation processes, plus a contribution from active galactic nuclei (AGNs). This radiation covers the wavelength range between ~ 0.1-1000 microns (these are the ultraviolet, optical, and infrared regions of the electromagnetic spectrum). The EBL is part of the diffuse extragalactic background radiation (DEBRA), which by definition covers the overall electromagnetic spectrum. After the cosmic microwave background, the EBL produces the second-most energetic diffuse background, thus being essential for understanding the full energy balance of the universe.
Selected X-ray astronomy article
This is an artist's impression of an X-ray Binary. Credit: ESA, NASA, and Felix Mirabel (French Atomic Energy Commission and Institute for Astronomy and Space Physics/Conicet of Argentina).
An X-ray binary is a class of binary star that is luminous in X-rays.
The X-rays are produced by matter falling from one component, called the donor (usually a relatively normal star) to the other component, called the accretor, which is compact: a white dwarf, neutron star, or black hole. The infalling matter releases gravitational potential energy, up to several tenths of its rest mass, as X-rays. (Hydrogen fusion releases only about 0.7 percent of rest mass.)
Objects
Selected image
The Chandra X-ray Observatory has imaged the center of the Andromeda galaxy. Like the Milky Way, Andromeda's galactic center appears to harbor an X-ray source characteristic of a black hole of a million or more solar masses. Seen above, the false-color X-ray picture shows a number of X-ray sources, likely X-ray binary stars, within Andromeda's central region as yellowish dots. The blue source located right at the galaxy's center is coincident with the position of the suspected massive black hole. While the X-rays are produced as material falls into the black hole and heats up, estimates from the X-ray data show Andromeda's central source to be very cold - only about million degrees, compared to the tens of millions of degrees indicated for Andromeda's X-ray binaries. Credit: S. Murray, M. Garcia, et al., Authors & editors: Robert Nemiroff (MTU) & Jerry Bonnell (USRA), NASA Technical Rep.: Jay Norris.
Selected lesson
## First cyan source in Caelum
This is an image of NGC 1679 in Caelum. It is a spiral galaxy located two degrees south of Zeta Caeli. Credit: NASA/ESA (Wikisky).
The first cyan source in Caelum is unknown.
This is a lesson in map reading, coordinate matching, and searching. It is also a project in the history of cyan astronomy looking for the first astronomical cyan source discovered in the constellation of Caelum.
Nearly all the background you need to participate and learn by doing you've probably already been introduced to at a secondary level.
Some of the material and information is at the college or university level, and as you progress in finding cyan sources, you'll run into concepts and experimental tests that are an actual search.
To succeed in finding a cyan source in Caelum is the first step. Next, you'll need to determine the time stamp of its discovery and compare it with any that have already been found. Over the history of cyan astronomy a number of sources have been found, many as point sources in the night sky. These points are located on the celestial sphere using coordinate systems. Familiarity with these coordinate systems is not a prerequisite. Here the challenge is geometrical, astrophysical, and historical.
NGC 1679 in the image at left appears to contain some cyan, probably as a result of a mixture of light blue and yellow.
Selected quiz
## Cosmic ray astronomy quiz
The cosmic-ray telescope collects data on the composition of the cosmic ray particles and their energy ranges. Credit: NASA.
Cosmic-ray astronomy is a lecture as part of the radiation astronomy course on the principles of radiation astronomy.
You are free to take this quiz based on cosmic-ray astronomy at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{principles of radiation astronomy}} template. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!
Selected laboratory
## Cosmogony laboratory
This is an image of Chaos magnum from a book. Credit: Sailko.
This laboratory is an activity for you to create a universe. While it is part of the astronomy course principles of radiation astronomy, it is also independent.
Some suggested primordial entities to consider are electromagnetic radiation, neutrinos, mass, time, Euclidean space, Non-Euclidean space, dark matter, dark energy, purple phantoms, and spacetime.
More importantly, there are your primordial entities.
And, yes, you can create a universe from a peanut butter and jelly sandwich if you wish to.
You may choose to define your primordial entities or not.
Usually, research follows someone else's ideas of how to do something. But, in this laboratory you can create these too.
This is an astronomy cosmogony laboratory, but you may create what an astronomy, a cosmogony, or a laboratory is.
Yes, this laboratory is structured. And, you are providing it. Or, not, an unstructured universe is okay too.
I will provide an example of a cosmogony. The rest is up to you.
Questions, if any, are best placed on the discussion page. Please put your laboratory results, you'd like evaluated, on the laboratory's discussion page.
Selected problems
## Angular momentum and energy
This diagram describes the relationship between force (F), torque (τ), momentum (p), and angular momentum (L) vectors in a rotating system. 'r' is the radius. Credit: Yawe.
Angular momentum and energy are concepts developed to try to understand everyday reality.
An angular momentum L of a particle about an origin is given by
${\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} }$
where r is the radius vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product (r · p sin θ). Theta is the angle between r and p.
Please put any questions you may have, and your results, you'd like evaluated, on the problem set's discussion page.
Enjoy learning by doing!
Selected X-ray astronomy pictures
Classified as a Peculiar star, Eta Carinae exhibits a superstar at its center as seen in this image from Chandra. The new X-ray observation shows three distinct structures: an outer, horseshoe-shaped ring about 2 light years in diameter, a hot inner core about 3 light-months in diameter, and a hot central source less than 1 light-month in diameter which may contain the superstar that drives the whole show. The outer ring provides evidence of another large explosion that occurred over 1,000 years ago. Credit: Chandra Science Center and NASA.
Fields
Related portals
Wikimedia
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Content by Subject
Arts · Humanities · Mathematics · Medicine · Science · Social Sciences · Technology
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2019-10-13 21:31:38
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https://demo7.dspace.org/items/a8799b4d-0253-4618-933c-5197ead3716e
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## Evolution of structures in two particle correlations in RHIC Cu+Cu collisions as a function of centrality and momentum
De Silva, L. C.
##### Description
Two particle correlation measurements in heavy ion collisions at RHIC have shown an extended near side correlation in $\Delta\eta$ relative to p+p for both, momentum triggered and untriggered analyses. This phenomenon is also known as the "ridge". An investigation into the momentum and centrality dependence of two particle correlations is presented for Cu+Cu 200 GeV collisions from the STAR experiment. We extract the amplitude, $\Delta\eta$ and $\Delta\phi$ widths from the near side correlation structure, and show how its parameters depend on centrality and the lower transverse momentum cut-off. Implications for the origin of the ridge will be discussed.
Comment: DPF-2009 conference held at, Wayne State University, Detroit, MI. 5 pages and 7 figures
##### Keywords
Nuclear Experiment
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2022-12-05 00:45:47
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https://stacks.math.columbia.edu/tag/00ME
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Lemma 10.98.1. Suppose that $R \to S$ is a local homomorphism of Noetherian local rings. Denote $\mathfrak m$ the maximal ideal of $R$. Let $M$ be a flat $R$-module and $N$ a finite $S$-module. Let $u : N \to M$ be a map of $R$-modules. If $\overline{u} : N/\mathfrak m N \to M/\mathfrak m M$ is injective then $u$ is injective. In this case $M/u(N)$ is flat over $R$.
Proof. First we claim that $u_ n : N/{\mathfrak m}^ nN \to M/{\mathfrak m}^ nM$ is injective for all $n \geq 1$. We proceed by induction, the base case is that $\overline{u} = u_1$ is injective. By our assumption that $M$ is flat over $R$ we have a short exact sequence $0 \to M \otimes _ R {\mathfrak m}^ n/{\mathfrak m}^{n + 1} \to M/{\mathfrak m}^{n + 1}M \to M/{\mathfrak m}^ n M \to 0$. Also, $M \otimes _ R {\mathfrak m}^ n/{\mathfrak m}^{n + 1} = M/{\mathfrak m}M \otimes _{R/{\mathfrak m}} {\mathfrak m}^ n/{\mathfrak m}^{n + 1}$. We have a similar exact sequence $N \otimes _ R {\mathfrak m}^ n/{\mathfrak m}^{n + 1} \to N/{\mathfrak m}^{n + 1}N \to N/{\mathfrak m}^ n N \to 0$ for $N$ except we do not have the zero on the left. We also have $N \otimes _ R {\mathfrak m}^ n/{\mathfrak m}^{n + 1} = N/{\mathfrak m}N \otimes _{R/{\mathfrak m}} {\mathfrak m}^ n/{\mathfrak m}^{n + 1}$. Thus the map $u_{n + 1}$ is injective as both $u_ n$ and the map $\overline{u} \otimes \text{id}_{{\mathfrak m}^ n/{\mathfrak m}^{n + 1}}$ are.
By Krull's intersection theorem (Lemma 10.50.4) applied to $N$ over the ring $S$ and the ideal $\mathfrak mS$ we have $\bigcap \mathfrak m^ nN = 0$. Thus the injectivity of $u_ n$ for all $n$ implies $u$ is injective.
To show that $M/u(N)$ is flat over $R$, it suffices to show that $I \otimes _ R M/u(N) \to M/u(N)$ is injective for every ideal $I \subset R$, see Lemma 10.38.5. Consider the diagram
$\begin{matrix} & & 0 & & 0 & & 0 & & \\ & & \uparrow & & \uparrow & & \uparrow & & \\ & & N/IN & \to & M/IM & \to & M/(IM + u(N)) & \to & 0 \\ & & \uparrow & & \uparrow & & \uparrow & & \\ 0 & \to & N & \to & M & \to & M/u(N) & \to & 0 \\ & & \uparrow & & \uparrow & & \uparrow & & \\ & & N \otimes _ R I & \to & M \otimes _ R I & \to & M/u(N)\otimes _ R I & \to & 0 \end{matrix}$
The arrow $M \otimes _ R I \to M$ is injective. By the snake lemma (Lemma 10.4.1) we see that it suffices to prove that $N/IN$ injects into $M/IM$. Note that $R/I \to S/IS$ is a local homomorphism of Noetherian local rings, $N/IN \to M/IM$ is a map of $R/I$-modules, $N/IN$ is finite over $S/IS$, and $M/IM$ is flat over $R/I$ and $u \bmod I : N/IN \to M/IM$ is injective modulo $\mathfrak m$. Thus we may apply the first part of the proof to $u \bmod I$ and we conclude. $\square$
Comment #3817 by Alapan Mukhopadhyay on
In the diagram $\frac{M}{IN+u(N)}$ is to be replaced by $\frac{M}{IM+u(N)}$.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
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2019-05-20 06:31:06
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http://connection.ebscohost.com/c/articles/47388517/product-intuitionistic-fuzzy-bck-algebras
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TITLE
# Product of Intuitionistic Fuzzy Bck-Algebras
AUTHOR(S)
PUB. DATE
March 2009
SOURCE
Advances in Fuzzy Mathematics;2009, Vol. 4 Issue 1, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
The purpose of this paper is to introduce the notion of product of two intuitionistic fuzzy sets in BCK-algebras and we provide some results on it.
ACCESSION #
47388517
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2018-06-20 11:10:39
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https://www.rdocumentation.org/packages/rmarkdown/versions/2.2/topics/rmd_metadata
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0th
Percentile
Rmd files include a metadata section (typically located at the top of the file) that can specify (among other things) the title, author, and date of the document. Metadata adheres to the YAML format and is delimited by lines containing three dashes (---). Here is an example metadata section:
---
title: "Crop Analysis Q3 2013"
author: Martha Smith
date: October 23rd, 2013
---
Note that the title field is quoted. This is because titles often contained embedded colons (:) and colons followed by a space need to be quoted in YAML.
Details
When title, author, and date metadata is provided it's used to automatically create a title section within output documents. If you don't want this section included in your document then you should remove the corresponding metadata fields.
When generating PDF and Beamer output there are also a number of other metadata fields that can be included to customize the appearance and theme of PDF output. For more details see the documentation for pdf_document and beamer_presentation.
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2020-07-10 16:43:54
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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": 0.28214994072914124, "perplexity": 3303.6285052799453}, "config": {"markdown_headings": false, "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/1593655911092.63/warc/CC-MAIN-20200710144305-20200710174305-00489.warc.gz"}
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http://www.bondeconomics.com/2018/04/can-we-falsify-models-with-time-varying.html
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## Sunday, April 29, 2018
### Can We Falsify Models With Time-Varying Parameters?
In a previous article, I argued that having unknown fixed parameters within many economic models does not create much in the way of uncertainty: just extend the range of historical data available, and we can pin down the parameter values. This article covers a related case: what if we allow parameters to vary with time? This possibility will make it impossible to make reliable forecasts with the model. However, such models have another defect: they can be fitted to practically any data set, making the model non-falsifiable. This can be illustrated by thinking about the simplest model of stock index returns. My argument that the apparent success of mainstream macro modelling techniques relies on the use of such non-falsifiable models.
## Introduction
In previous articles (first in series), I discussed the concept of forecastability: is it possible to forecast the future outputs of a mathematical model, based on a past history of public information? (The definition needs to distinguish between the information available to the forecaster versus all the information in the model.) It should be emphasised that this is a property of mathematical models; whether it extends to the real world depends upon whether we believe a particular model is a good representation of reality.
The normal justification of using mathematical economic models is that we can use them to make forecasts, and so one might assume that the model being forecastable is a useful property. My view is that we actually want the opposite: since real world forecasting exercises tend to fail in particular ways, we want models that are similarly hard to forecast. For example, the Quantity Theory of Money provides a straightforward model that is easily forecast. And in the real world, the Quantity Theory of Money is easily rejected empirically (by those of us who do not want to come up with stories to manipulate the data so that they fit the desired theory).
## What are Parameters?
When doing mathematics, we need to be careful of what definitions we use. One can legitimately use the same English word in different ways, so long as you make it clear what definition you use. My intuition for parameters comes from engineering, and they would normally be fixed constants. (A better term for my intuition is coefficient.)
If we start with linear systems theory, we are interested in the evolution of a set of state variables, which we stack into a vector denoted $x$ by tradition. If we confine ourselves to the set of linear, time-invariant, finite dimensional systems, the state dynamic equation is of the form:
$$x(t+1) = A x(t) + B u(t),$$
where $x$ is the state, $u$ is a vector of input variables, while $A$ and $B$ are fixed matrices of the appropriate size. (In economics, the models are often of the form $x(t) = Ax(t-1) + Bu(t)$, that is, there is no lag from the output to the state variable.) The elements of $A$ and $B$ are fixed parameters.
For example, a simple compound growth system with a growth rate of 1% is given by:
$$x(t+1) = 1.01 x(t) + u(t)$$
(with $x,u$ being single-dimensional time series). In this case, the $A$ matrix just has one element ($a_{1,1}$), which has a fixed value of 1.01.
Importantly, with a linear system, we cannot have the dynamic equation contain expressions where the state variables multiply each other (or other complex expressions). There is a strict division between fixed parameters (the $A, B$ matrices above) and state variables, which vary over time.
In economic models, we have complicated systems where we do have state variables interacting in a nonlinear way. For example, if we return to model SIM (which I discussed in the previous article; see the references therein), the consumption function depends on multiplying income and wealth by the alpha parameters (which are the propensity to consume out of income and wealth). If those parameters are fixed (as I assumed in the previous article), we end up with a linear time invariant system. However, one could imagine a specification of the model where the alpha parameters themselves change as a function of time. They are elevated to being state variables, and we have a nonlinear system. As a result, the intuition for economists for what constitutes a parameter would be variables that are not economic time series, which are either fixed coefficients or allowed to vary.
(In my Python sfc_models framework, all variables are assumed to be time series; the only fixed parameters would be the ones that are hard-coded as constants.)
As I noted in the previous article, forecasting the output of a linear system with fixed parameters is straightforward (assuming that key variables are directly measured, which is the usual condition). Things are very different if we allow for time-varying parameters.
## Simplest Stock Market Model
If we denote the total return index for a stock market as $x$, the simplest possible stock market model is:
$$x(t+1) = a(t)x(t),$$
(where $a(t)$ can be thought of as $1 + r(t)$, with $r$ the one-period return).
So long as the total return index stays away from zero, this model can reproduce any observed time history for returns. (If the total return index goes to zero, it stays there, according to this model.)
This is not a useful model for reality, but the question is: why?
The first thing to examine is forecastability. If we assume that the time series $a$ is not public information, the model is non-forecastable. This fits with the empirical results regarding market efficiency, with the simplest version is that it is hard to forecast stock market returns.
The next thing to think about is statistical tests. However, so long as our data set does not have the stock index going to zero and then bouncing back, this model can easily reproduce any historical time series. (One could imagine a stock index disappearing because of a war or similar calamity, and then a new set of equities arising thereafter. From the perspective of the original owners, the new index would be a separate entity.) In other words, it will always pass statistical tests of validity. This is one reason I do not see a blind reliance on statistical tests as being best practices for assessing the usefulness of models.
Instead, the reason why this is a bad model seems to be that it provides no useful information (other than the assumption that stock markets will not go to zero and then rise). It is too flexible: it can fit any observed data set.
In communication systems theory, the notion of information is quantifiable: it is related to a stream of bytes you are sending down some channel. Unfortunately, in this context, the statement that a model does not convey useful information does not appear to be directly quantifiable. However, we might be able to capture the idea by comparing the model to other models. Is it possible to find a class of models coming from a smaller set of models that also can be fit to historical data? In this case, we could have models with stochastic volatility, which also can be fit to historic data, but cannot reproduce the full set of behaviour shown by assuming no restrictions on period returns.
Alternatively, one might see that the model is so flexible that it can be fit to the output of a wide variety of models that have theoretical content that contradicts that of the model in question. In this case, one could argue that the model cannot falsified, as it can be fit to a almost any plausible set of data.
## Mainstream Macro
The problem with mainstream macroeconomic theory is that it is too heavily reliant upon time-varying parameters, such as the natural rate of unemployment or the natural interest rate (or whatever fad terms have replaced those names for the concepts). The models appear to offer some information about future developments in the economy, but not a lot: since those key parameters cannot be directly measured, nor forecast.
The way to test this is see whether mainstream economic techniques could be fit to other classes of models, particularly those that rely on different underlying assumptions (e.g., stock-flow consistent models). Given the flexibility of the natural interest rate in adapting to real-world data, I see such a fit being achieved.
In other words, the statistical tests used to "prove" that the policy rate drives activity in the real world could be applied to models in which we know the policy rate has no such effect. This is theoretically awkward, to say the least.
## Concluding Remarks
Allowing for drift in key parameters is one way to make model behaviour more interesting. The cost is that the model may end up offering no theoretical content, and being unable to be rejected empirically.
(c) Brian Romanchuk 2018
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2019-09-18 20:59:42
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https://www.r-bloggers.com/2019/01/waterinfo-downloading-tidal-data-to-understand-the-behaviour-of-a-migrating-eel/
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[This article was first published on rOpenSci - open tools for open science, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
Do you know what that sound is, Highness? Those are the Shrieking Eels — if you don’t believe me, just wait. They always grow louder when they’re about to feed on human flesh. If you swim back now, I promise, no harm will come to you. I doubt you will get such an offer from the Eels.
Vizzini, The Princess Bride
European eels (Anguilla anguilla) have it tough. Not only are they depicted as monsters in movies, they are critically endangered in real life. One of the many aspects that is contributing to their decline is the reduced connectivity between their freshwater and marine habitats. Eels are catadromous: they live in freshwater, but migrate to the Sargasso Sea to spawn, a route that is blocked by numerous human structures (shipping locks, sluices, pumping stations, etc.). Pieterjan Verhelst studies the impact of these structures on the behaviour of eels, making use of the fish acoustic receiver network that was established as part of the Belgian LifeWatch observatory. This animated video gives a quick introduction to his research and the receiver network:
In this blog post, we’ll explore if the migration of one eel is influenced by the tide. It’s a research use case for our R package wateRinfo, which was recently peer reviewed (thanks to reviewer Laura DeCicco and editor Karthik Ram for their constructive feedback!) and accepted as a community-contributed package to rOpenSci.
### Meet Princess Buttercup
Pieterjan provided us the tracking data for eel with transmitter A69-1601-52622. Let’s call her Princess Buttercup, after the princess that almost got eaten by the Shrieking Eels in the classic and immensly quotable movie The Princess Bride.
eel <- read_csv(here("data", "eel_track.csv"))
Her tracking data consists of the residence time interval (arrival until departure) at each receiver station that detected her along the Scheldt river. It also contains the calculated residencetime (in seconds), as well as the station name, latitude and longitude.
date receiver latitude longitude station arrival departure residencetime
2016-10-19 VR2W-112297 51.00164 3.85695 s-Wetteren 2016-10-19 23:44:00 2016-10-19 23:48:00 240
2016-10-19 VR2W-112287 51.00588 3.77876 s-2 2016-10-19 16:07:00 2016-10-19 19:12:00 11100
2016-10-20 VR2W-122322 51.02032 3.96965 s-2a 2016-10-20 13:18:00 2016-10-20 13:23:00 300
2016-10-20 VR2W-122322 51.02032 3.96965 s-2a 2016-10-20 02:21:00 2016-10-20 02:29:00 480
2016-10-20 VR2W-115438 51.01680 3.92527 s-Wichelen 2016-10-20 01:01:00 2016-10-20 01:09:00 480
2016-10-20 VR2W-122322 51.02032 3.96965 s-2a 2016-10-20 05:52:00 2016-10-20 06:00:00 480
Using the latitude, longitude and total residencetime for each station, we can map where Princess Buttercup likes to hang out:
### Moving up and down the Scheldt river
To get a better sense of her journey along the river, we add a distance_to_sea (in meters) for the stations, by joining the tracking data with a distance reference file 1. We can now plot her movement over time and distance:
Princess Buttercup’s signal was picked up by receivers in Merelbeke (near Ghent) shortly after she was captured and released there on October 11. She resided in a 40 km stretch of the river (between Wetteren and Sint-Amands) for about a month before migrating towards the sea and starting the long journey towards the Sargasso Sea. The periodic movement pattern up and down the river during the second half of November is of particular interest: it looks like tidal frequency 2. It would be interesting to compare the movement pattern with real water level data from the Scheldt river… which is where our wateRinfo package comes in.
### Getting tidal data with the wateRinfo package
Waterinfo.be, managed by the Flanders Environment Agency (VMM) and Flanders Hydraulics Research, is a website where one can find real-time water and weather related environmental variables for Flanders (Belgium), such as rainfall, air pressure, discharge, and water level. The website also provides an API to download time series of these measurements as open data, but compositing the download URL with the proper system codes can be challenging. To facilitate users in searching for stations and variables, subsequently downloading data of interest and incorporating waterinfo.be data access in repeatable workflows, we developed the R package wateRinfo to do just that. See the package documentation for more information on how to install and get started with the package.
Timeseries in waterinfo.be (identified by a ts_id) are a combination of a variable, location (station_id) and measurement frequency (15min by default). For example:
library(wateRinfo)
get_stations("water_level") %>%
select(ts_id, station_id, station_name, parametertype_name) %>%
ts_id station_id station_name parametertype_name
92956042 39483 Kieldrecht/Noordzuidverbinding H
31683042 21995 Leuven/Dijle1e arm/stuw K3 H
20682042 20301 StMichiels/Kerkebeek/Rooster H
96495042 10413 Oudenburg/Magdalenakreek H
25074042 20788 Schulen/Inlaat A/WB_Schulensbroek H
2006042 10432 Merkem/Steenbeek H
At the time of writing (see this issue), the stations measuring water levels in the Scheldt tidal zone are not yet included by the API under the core variable water_level and are thus not yet available via get_stations("water_level"). We therefore rely on a precompiled list of tidal time series identifiers (tidal_zone_ts_ids):
tidal_zone_ts_ids <- read_csv(here("data", "tidal_zone_ts_ids.csv"))
From which we select the 10-min frequency tidal timeseries in the Scheldt river:
ts_id station_id station_name portal_bekken
55419010 0430087 Sint-Amands tij/Zeeschelde Beneden-Scheldebekken
55565010 0430029 Tielrode tij/Durme Beneden-Scheldebekken
55493010 0430081 Temse tij/Zeeschelde Beneden-Scheldebekken
54186010 0419418 Dendermonde tij/Zeeschelde Beneden-Scheldebekken
54493010 0430078 Hemiksem tij/Zeeschelde Beneden-Scheldebekken
55355010 0430091 Schoonaarde tij/Zeeschelde Beneden-Scheldebekken
53989010 0419484 Antwerpen tij/Zeeschelde Beneden-Scheldebekken
54606010 0430071 Kallosluis tij/Zeeschelde Beneden-Scheldebekken
56088010 0430062 Prosperpolder tij/Zeeschelde Beneden-Scheldebekken
54936010 0430068 Liefkenshoek tij/Zeeschelde Beneden-Scheldebekken
55059010 0430242 Melle tij/Zeeschelde Beneden-Scheldebekken
This wateRinfo vignette shows how to download data for multiple stations at once using wateRinfo and dplyr. We use a similar approach, but instead of manually providing the start and end date, we get these from Princess Buttercup’s tracking data:
tidal_data <-
tidal_zone_ts_ids %>%
group_by(ts_id) %>%
do(get_timeseries_tsid(
.$ts_id, from = min(eel$date), # Start of eel tracking data
to = max(eel\$date), # End of eel tracking data
datasource = 4
)) %>%
# Join data back with tidal_zone_ts_id metadata
ungroup() %>%
left_join(tidal_zone_ts_ids, by = "ts_id")
In just a few lines of code, we downloaded the tidal data for each measurement station for the required time period. ????
The water level is expressed in mTAW (meter above mean sea level) 3. Let’s plot the data for a station (here Dendermonde in November 2016) to have a look:
We now have all the pieces to verify if Princess Buttercup was surfing the tide back and forth.
### Is Princess Buttercup surfing the tide?
Let’s add the tidal data to Princess Buttercup’s journey plot we created before. The first step is to join the tidal data with the same distance reference file to know the distance from each tidal station to the sea:
tidal_data <-
tidal_data %>%
left_join(
distance_from_sea %>% select(station, distance_from_sea, municipality),
by = c("station_name" = "station")
) %>%
filter(station_name != "Hemiksem tij/Zeeschelde") # Exclude (probably erroneous) data from Hemiksem
To avoid visual clutter, we’ll use ridges (from ggridges) to display the tidal data for each station over time:
Looking at the plot, Princess Buttercup seems to be “lazy” and drift with the tide. Rising water levels push her upstream, while decreasing water levels bring her closer to sea again. On November 22 (see also previous plot), she embarks on her migration for real.
### Conclusion
In this blogpost we used the wateRinfo package to gain some insight in the movement/migration behaviour of an individual eel. We hope the package can support many more research questions and that you have fun storming the castle.
### Acknowledgements
Waterinfo.be data is made available by the Flanders Environment Agency, Flanders Hydraulics Research, Agentschap Maritieme Dienstverlening & Kust and De Vlaamse Waterweg. The fish acoustic receiver network, as well as the work by Stijn and Peter, is funded by FWO as part of the Flemish contribution to LifeWatch. The animated video on eel research was funded by the Flanders Marine Institute (VLIZ), coordinated by Karen Rappé and Pieterjan Verhelst, animated by Steve Bridger, and narrated by Bryan Kopta.
1. To represent the data along a straight line (y-axis), we calculated the distance along the river from each station to a reference station close to the sea (ws-TRAWL), using a costDistance function. See this script for more the details on the calculation.
2. The Scheldt is under tidal influence from its river mouth all the way to Ghent (160km upstream) where it is stopped by sluices. The tide goes much further than the freshwater-saltwater boundary of the river.
3. TAW means Tweede Algemene Waterpassing, a reference height for Belgium.
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2021-04-20 01:41:30
|
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https://academy.vertabelo.com/course/postgresql-common-functions/date-time-functions/date-and-time-data-types-in-postgresql/using-date-and-time-with-constant-values
|
Deals Of The Week - hours only!Up to 80% off on all courses and bundles.-Close
Introduction
Dealing with dates
Working with time
Date and time data types in PostgreSQL
19. Using date and time with constant values
Extracting dates and times
Intervals
Timezone conversion
Format date and time
Current date and time data
Summary
## Instruction
Did you spot the mistake in the table? The timestamp data type is very precise in defining a point in time. This is why using the equal sign (=) with this data type isn't a good idea. Two of these values may differ by a single nanosecond, which means the equality condition wouldn't be satisfied.
Nevertheless, you can use comparisons (e.g., >, <, !=, etc.) with timestamp data. This will work when you're comparing two columns or when you're comparing one column against a constant value.
Do we have to be precise when providing a constant value? Not really. Take a look:
SELECT id,
launched_timestamp
FROM aircraft
WHERE launched_timestamp > '2015-01-01';
As you can see, we compared a timestamp with a simple date. How is this possible? Well, our database converted the date we provided to a timestamp by adding as many zeros as necessary. For instance, '2015-01-01' will become '2015-01-01 00:00:00' and '2014-02-12 12:00' will become '2014-02-12 12:00:00'. Convenient, isn't it?
## Exercise
Find the ID number and withdrawn date for all aircraft discontinued after October 14, 2015.
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2022-10-02 06:03:26
|
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https://math.stackexchange.com/questions/181556/given-lattice-g-parameters-of-torus-r2-g
|
# Given lattice G; parameters of torus R^2/G?
This should be a simple, known result, but I can't seem to find it.
Given a lattice $\Gamma = m\mathbb{Z} \times n\mathbb{Z}$, $\mathbb{R}^2/\Gamma$ is topologically a torus. For suitable $m$ and $n$ (say $m$ big enough and $n$ small enough), this torus can be embedded in $\mathbb{R}^3$ by the parametrization
$$x(\theta,\phi) = ((R+r\cos\theta)\cos\phi,(R+r\cos\theta)\sin\phi,r\sin\theta).$$
Without loss of generality, we can take $n = 1$ and $m > 1.$ Given $m$ and $1$, what are the values of $R$ and $r$?
If we consider the topological construction, we can say that we identify the long edges so that the small circle of the obtained cylinder has radius $n/2\pi$. However, identifying the remaining sides will create stretching so that we can no longer say the radius is $m/2\pi$.
Alternatively, we have a torus in $S^3$ given by $$x(\theta,\phi) = (\sin\rho\cos\theta,\sin\rho\sin\theta,\cos\rho\cos\phi,\cos\rho\sin\phi),$$ where $\rho$ is a parameter that allows us to determine a torus with any ratio of radii. Is it true that $m/n = \sin\rho$ (or something like that)? Seems so; how can I show it?
I have a conjecture that $R = \sqrt{m^2 + n^2}$ but don't know how to show it.
The point is to identify any torus in $\mathbb{H}/SL_2(\mathbb{Z})$ with a parametrization so that I may find the area and volume and the energy of a certain functional (Willmore). Does anyone know perhaps simpler ways of determining area and volume given a point in the typical fundamental domain of the modular surface?
• If you look at the diagonal of the unit rectangle, the length you get when you map that diagonal into your parametrization of the torus (i.e. the curve $\psi(t) = x(t,t)$), $$\int_0^{2\pi} \| \psi'(t) \| dt = r \int_0^{2\pi} \sqrt{1 + \left( R/r + \cos t \right)^2 } \, dt.$$ So once the ratio $R/r$ is fixed, the length of that curve and the length of the diagonal are proportional when $r$ varies, up to that ugly integral constant. So I think your conjecture only holds in some cases but I can't tell which. – Patrick Da Silva Aug 12 '12 at 5:40
• If you mean conformal embedding then math.stackexchange.com/questions/152156 is relevant. That basically describes the case $n=1$ and $m \in \mathbb{N}_{\geq 1}$. The $k$ in the first answer is indeed a covering degree as suggested (i.e. corresponds to $m$ here). This is explained in the comments. – WimC Aug 12 '12 at 6:17
• @WimC Thanks for the link, I haven't found the answer there but maybe I'm reading wrong. I don't mean conformal embeddings, I mean any torus that can be embedded (so basically, $m$ such that there are no self-intersections). This should be possible, no? Perhaps a different question, then: given an embedding, $(R,r)$, what is the value of $m$ such that the lattice $\R^2/\Gamma$ corresponds to my torus? – snar Aug 12 '12 at 7:33
• @snarski To answer that you'll have to be very specific about what you mean by "corresponds". – WimC Aug 12 '12 at 7:53
• @snarski: You have not made clear whether you want just an embedding, a conformal embedding, an equal area embedding, or an isometric embedding, and whether the embedding should be into ${\mathbb R}^3$ or ${\mathbb R}^4$. – Christian Blatter Sep 11 '12 at 8:22
Here's an idea : The area of the rectangle is $mn$ and the area of the torus is $(2\pi r)(2\pi R)$. Since a line along the inner circle has length $m$, the radius $r$ is $m/2\pi$, so that the area of the torus is now $m (2 \pi R)$. This suggests $n = R/2\pi$. Do you agree? I think it does make sense, because arguably this thing should be symmetric in $m$ and $n$, since there is no preference of $n$ over $m$ in the quotient $\mathbb R^2 / G$. I assumed in all this that the donut-shaped torus had the same area as the original area of the rectangle, which is plausible since you don't want to stretch it too much anyway.
• I think there are many ways to geometrically do the second gluing, hence many possible values for $R$... – Patrick Da Silva Aug 12 '12 at 6:04
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2019-09-18 11:45:21
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http://planetmath.org/multivariatedistributionfunction
|
# multivariate distribution function
A function $F:\mathbb{R}^{n}\to[0,1]$ is said to be a multivariate distribution function if
1. 1.
$F$ is non-decreasing in each of its arguments; i.e., for any $1\leq i\leq n$, the function $G_{i}:\mathbb{R}\to[0,1]$ given by $G_{i}(x):=F(a_{1},\ldots,a_{i-1},x,a_{i+1},\ldots,a_{n})$ is non-decreasing for any set of $a_{j}\in\mathbb{R}$ such that $j\neq i$.
2. 2.
$G_{i}(-\infty)=0$, where $G_{i}$ is defined as above; i.e., the limit of $G_{i}$ as $x\to-\infty$ is $0$
3. 3.
$F(\infty,\ldots,\infty)=1$; i.e. the limit of $F$ as each of its arguments approaches infinity, is 1.
Generally, right-continuty of $F$ in each of its arguments is added as one of the conditions, but it is not assumed here.
If, in the second condition above, we set $a_{j}=\infty$ for $j\neq i$, then $G_{i}(x)$ is called a (one-dimensional) margin of $F$. Similarly, one defines an $m$-dimensional ($m) margin of $F$ by setting $n-m$ of the arguments in $F$ to $\infty$. For each $m, there are $\binom{n}{m}$ $m$-dimensional margins of $F$. Each $m$-dimensional margin of a multivariate distribution function is itself a multivariate distribution function. A one-dimensional margin is a distribution function.
Multivariate distribution functions are typically found in probability theory, and especially in statistics. An example of a commonly used multivariate distribution function is the multivariate Gaussian distribution function. In $\mathbb{R}^{2}$, the standard bivariate Gaussian distribution function (with zero mean vector, and the identity matrix as its covariance matrix) is given by
$F(x,y)=\frac{1}{2\pi}\int_{-\infty}^{x}\int_{-\infty}^{y}\operatorname{exp}% \big{(}{-\frac{s^{2}+t^{2}}{2}}\big{)}dsdt$
B. Schweizer and A. Sklar have generalized the above definition to include a wider class of functions. The generalization has to do with the weakening of the coordinate-wise non-decreasing condition (first condition above). The attempt here is to study a class of functions that can be used as models for distributions of distances between points in a “probabilistic metric space”.
## References
• 1 B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Dover Publications, (2005).
Title multivariate distribution function MultivariateDistributionFunction 2013-03-22 16:33:50 2013-03-22 16:33:50 CWoo (3771) CWoo (3771) 7 CWoo (3771) Definition msc 60E05 msc 62E10 Copula multivariate cumulative distribution function joint distribution function margin
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2018-06-18 15:33:31
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https://www.umu.se/en/events/equivalence-between-cauchy-riemann--planar-elastostatic-equation_11595419/
|
# Equivalence between Cauchy-Riemann & planar elastostatic equation
Wed
18
May
Wednesday 18 May, 2022 at 15:15 - 16:00
MIT.A.356
Abstract: In many engineering fields, such as e.g. the study of machine elements and the design of bridges, it is vital to have a clear sense of the distribution of internal forces in the structure at hand. If the domain of interest is planar, such as the cross-section of a beam or a cog, one commonly resorts to the field of planar elasticity theory. In particular, if the problem is time-independent we use the elastostatic equation whose solution yields the deformation and thereby the stress distribution in the domain.
The equation is most commonly solved using numerical methods. However, due to this method breaking down in concave geometries, it is vital to have some exact solutions to use for e.g. benchmarking. Kolosov and Mushkelisvhili first popularized these at the turn of the last century, where they used complex potential methods to construct solutions. We shall follow this work spiritually and prove that the elasticity equation is equivalent to the inhomogeneous Cauchy-Riemann equation. With this equivalence in place, we can use well-known solutions for the complex problem to construct physical solutions.
Event type: Seminar
Speaker
Andreas Granath
Teaching assistant
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2022-05-20 13:52:02
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|
https://economics.stackexchange.com/questions/30509/forecasting-volatility-through-garch-and-egarch-models
|
# Forecasting Volatility through GARCH and EGARCH models
I am at a final stage of my dissertation but I am a bit confused. I am trying to forecast volatility by using returns through GARCH(1,1) and EGARCH(1,1) models.
I use daily prices of indexes to generate returns, however, I am unsure if I should use either one of the formulas for the return series:
$$r_{t}=100*\frac{\ln(p_{t}}{p{t}-1)}$$ or simply $$r_{t}=\ln(\frac{pt}{p_{t}-1})$$
My professor asked me to keep all my results to 2 d.p. Therefore when I specify my mean equations for the models (using equation 2, for intercepts I get 0.00 (0.00) (error term in parenthesis). However, if I use equation 1, my coefficients for intercepts are nicer since they are obviously multiplied by 100 and take the form of 0.05 (0.01).
The reason why I am wondering is that when I read through the journals on volatility forecasting everyone uses equation 2. Will appreciate any help and advice! - Confused Student
|
2020-08-11 16:15:21
|
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https://linearalgebras.com/tag/wedderburns-theorem
|
If you find any mistakes, please make a comment! Thank you.
## A finite unital ring with no zero divisors is a field
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.21 Solution: [We will assume Wedderburn’s Theorem.] Let $R$ be a finite ring (not necessarily commutative) with…
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2022-11-29 08:01:38
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https://forum.allaboutcircuits.com/threads/digitally-controlled-voltage-with-feedback.121101/
|
Digitally controlled voltage with feedback.
coinmaster
Joined Dec 24, 2015
502
I'm trying to create a digitally controlled voltage which I will end up using for a software controlled voltage divider for a high voltage circuit control around 600v.
For now I am trying to get it to work on 5v.
This is the general idea
I want precise output voltages so I want to negate any non-linearities in the transistor with digital feedback from a voltage sense IC or something.
So basically I'll tell the controller that I want x voltage on the output and if the voltage on the output reads more or less than that voltage then it will self correct.
This is the code I'm using right now
C:
// the setup routine runs once when you press reset:
void setup() {
// initialize serial communication at 9600 bits per second:
Serial.begin(9600);
pinMode(13,OUTPUT);
}
// the loop routine runs over and over again forever:
void loop() {
digitalWrite(13, HIGH);
// Reads potentiometer voltage to get a reference number used for intended output voltage
// Takes analogRead value and turns it into the intended voltage reference number
float ReferenceNumber = reference * (5.0 / 1023.0);
// Translation from intended voltage number to analogWrite voltage
float output=ReferenceNumber*(225/5.0);
// output to transistor base
analogWrite(9,output);
// reads the output voltage for feedback control
// If the output voltage is greater or less than the intended voltage then the opto-isolator bias will be adjusted.
if (feedback*(255/1023.0) > output ) {
output = -1 ;}
if (feedback*(255/1023.0) < output ) {
output = +1 ;}
//Prints the output voltage
Serial.println(feedback* (5.0 / 1023.0));
}
I'm using a potentiometer to adjust the reference voltage and then I'm converting the reverence voltage number into analogWrite voltage which is then read by analogRead at the output and the output is adjusted based on whether the output is lower or higher than the reference number.
It works but it is not stable, it fluctuates all over within a volt or more.
Is there some problem in the concept of my code or something?
I only started learning digital electronics and coding a couple days ago.
Moderators note: changed code tags to C
Last edited by a moderator:
Alec_t
Joined Sep 17, 2013
11,817
R9/C1 introduce a considerable delay between the commanded voltage output and the AnalogRead value that you want. I don't see any delay routines to allow for that?
coinmaster
Joined Dec 24, 2015
502
What do you mean? How is my RC filter delaying the output voltage?
Also I changed the code and switched the supply pins on the arduino and this is the result
http://imgur.com/RSRyUwz
The stability is much better but the accuracy is off. Perhaps the ADC does not have a high enough resolution?
This is the code I am now using
C:
int PWMout = 9; // Ouput PWM pin
int output = 255; //Start PWM at 255 as this is zero voltage output, because the circuit is a shunt regulator.
// the setup routine runs once when you press reset:
void setup() {
// initialize serial communication at 9600 bits per second:
Serial.begin(9600);
pinMode(13, OUTPUT);
pinMode(A0, INPUT);
pinMode(A1, INPUT);
pinMode(PWMout, OUTPUT);
}
// the loop routine runs over and over again forever:
void loop()
{
digitalWrite(13, HIGH);
// Reads potentiometer voltage to get a reference number used for intended output voltage
// Takes analogRead value and turns it into the intended voltage reference
float ReferenceVoltage = reference * (5.0 / 1023.0);
// reads the feedback output voltage for feedback control
float FeedbackVoltage = feedback * (5.0 / 1023.0);
// If the feedback voltage is greater than the reference then the PWM needs to be increased to increase shunt current.
if (FeedbackVoltage > ReferenceVoltage )
{
output = +1 ;
}
// If the feedback voltage is less than the reference then the PWM needs to be decreased to decrease shunt current.
if (FeedbackVoltage < ReferenceVoltage )
{
output = -1 ;
}
// Check output value and limit maximum and minimum
if (output >= 255)
{
output = 255;
}
if (output <= 0 )
{
output = 0;
}
// Print variables
analogWrite(PWMout, output);
//Prints the voltages
Serial.print("Reference ");
Serial.print(ReferenceVoltage);
Serial.print("/tFeedbackVoltage ");
Serial.print(FeedbackVoltage);
Serial.print("/tPWMout ");
Serial.println(output);
}
Last edited:
dannyf
Joined Sep 13, 2015
2,197
it fluctuates all over within a volt or more.
it is very hard to stablize a mixed signal control loop.
The universal trick is to lower the gain - but it comes with its bag of negativity as well.
dannyf
Joined Sep 13, 2015
2,197
You are doing "on/off" control - may not be the best approach.
I would try this:
1) measure the analog output (middle of R5/R7);
2) if it is great than your desired output, increment output; else decrement output; update pwm duty cycle
3) go back to 1).
You can adjust the stepping of the increments / decrements.
coinmaster
Joined Dec 24, 2015
502
You are doing "on/off" control - may not be the best approach.
I would try this:
1) measure the analog output (middle of R5/R7);
2) if it is great than your desired output, increment output; else decrement output; update pwm duty cycle
3) go back to 1).
You can adjust the stepping of the increments / decrements.
Um, is that not what I am doing now? Check out my last post.
Also I changed it to
C:
if (FeedbackVoltage > ReferenceVoltage )
{
output++ ;
}
// If the feedback voltage is less than the reference then the PWM needs to be decreased to decrease shunt current.
if (FeedbackVoltage < ReferenceVoltage )
{
output--;
}
and the result is the same, whether I use +1 or ++
The error margin is pretty much eliminated after changing the supply pin and refining the code. The main issue is accuracy http://imgur.com/L3D2Ygz I'm assuming this is a resolution issue? The aruino only has 8 bits ADC.
Last edited:
Alec_t
Joined Sep 17, 2013
11,817
How is my RC filter delaying the output voltage?
The R9/C1 time constant is 100mS, so a voltage change at the Arduino output will not appear across C1, and hence at the 'Voltmeter' node, immediately.
dannyf
Joined Sep 13, 2015
2,197
Code:
[LIST=1]
[*]// If the feedback voltage is greater than the reference then the PWM needs to be increased to increase shunt current.
[*] if (FeedbackVoltage > ReferenceVoltage )
[*] {
[*] output = +1 ;
[*] }
[*]
[*] // If the feedback voltage is less than the reference then the PWM needs to be decreased to decrease shunt current.
[*] if (FeedbackVoltage < ReferenceVoltage )
[*] {
[*] output = -1 ;
[*] }
[/LIST]
That's what you wrote.
|
2021-01-27 20:53:58
|
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|
https://www.cs.cornell.edu/courses/cs3110/2021sp/textbook/interp/simpl_typesystem.html
|
# A Type System for SimPL
Recall the syntax of SimPL:
e ::= x | i | b | e1 bop e2
| if e1 then e2 else e3
| let x = e1 in e2
bop ::= + | * | <=
Let's define a type system ctx |- e : t for SimPL. The only types in SimPL are integers and booleans:
t ::= int | bool
To define |-, we'll invent a set of typing rules that specify what the type of an expression is based on the types of its subexpressions. In other words, |- is an inductively-defined relation, as you learned about in CS 2800. So, it has some base cases, and some inductive cases.
## Base Cases
An integer constant has type int in any context whatsoever, a Boolean constant likewise always has type bool, and a variable has whatever type the context says it should have. Here are the typing rules that express those ideas:
ctx |- i : int
ctx |- b : bool
{x : t, ...} |- x : t
## Inductive Cases
Let. As we already know from OCaml, we type check the body of a let expression using a scope that is extended with a new binding.
ctx |- let x = e1 in e2 : t2
if ctx |- e1 : t1
and ctx[x -> t1] |- e2 : t2
The rule says that let x = e1 in e2 has type t2 in context ctx, but only if certain conditions hold. The first condition is that e1 has type t1 in ctx. The second is that e2 has type t2 in a new context, which is ctx extended to bind x to t1.
Binary operators. We'll need a couple different rules for binary operators.
ctx |- e1 bop e2 : int
if bop is + or *
and ctx |- e1 : int
and ctx |- e2 : int
ctx |- e1 <= e2 : bool
if ctx |- e1 : int
and ctx |- e2 : int
If. Just like OCaml, an if expression must have a Boolean guard, and its two branches must have the same type.
ctx |- if e1 then e2 else e3 : t
if ctx |- e1 : bool
and ctx |- e2 : t
and ctx |- e3 : t
|
2021-07-28 19:36:17
|
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|
http://www.math.nsc.ru/publishing/DAOR/content/2012/01en/01-258.html
|
EN|RU Volume 19, No 1, 2012, P. 33-40 UDC 519.718 S. M. Grabovskaya About the reliability of nonbranching programs in the basis of a generalized conjunction Abstract: The problem of synthesis of nonbranching programs with conditional stop-operator is considered in a full finite basis which contains functions of the form $x_1\cdot x_2$, $\overline x_1\cdot x_2$ or $\overline x_1\cdot\overline x_2$. All functional operators are supposed to be prone to output inverse failures with probability $\varepsilon\in(0,1/2)$ and conditional stop-operators are absolutely reliable. Any Boolean function is proved to be realized by a nonbranching program with unreliability no more then $\varepsilon+59\varepsilon^2$ at $\varepsilon\in(0,1/960]$. Ill. 1, bibliogr. 4. Keywords: Boolean function, nonbranching program, conditional stop-operator, synthesis, reliability. Grabovskaia Svetlana Mikhailovna 1 1. Penza State University, 40 Krasnaya str., 440026 Penza, Russia e-mail: swetazin@mail.ru © Sobolev Institute of Mathematics, 2015
|
2018-10-21 02:43:35
|
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|
https://www.physicsforums.com/threads/capacitor-and-resistor-in-a-flowing-liquid.156335/
|
# Capacitor and resistor in a flowing liquid
1. Feb 14, 2007
### Saketh
1. The problem statement, all variables and given/known data
A parallel-plate capacitor with cross-sectional area S and plate separation d is put into a stream of conducting liquid with resistivity $\rho$. The liquid moves parallel to the plates with a constant velocity v, and the whole system is located in a uniform magnetic field of induction B, vector $\textbf{B}$ being parallel to the plates and perpendicular to the stream direction. The capacitor plates are interconnected by means of an external resistance R. What amount of power is generated in that resistance?
2. Relevant equations
$$\rho J = E$$
Maxwell's equations
3. The attempt at a solution
I have no intuitive grasp of what's going on in this problem. My first guess was that the charges in the fluid are being pushed by the magnetic field, but what does that have to do with the current flowing through the resistor? I'm not sure why current is flowing through the resistor at all.
I can't really show work because I'm not sure where to start. Once I figure out what's going on, I can do the rest of this problem myself.
Last edited: Feb 14, 2007
2. Feb 14, 2007
### Staff: Mentor
Cool question. It's related to the field of magnetohydrodynamics:
http://en.wikipedia.org/wiki/Magnetohydrodynamics
You are correct that the moving charges in the fluid will experience a force perpendicular to the magnetic field. This will effectively pump charges from one capacitor plate to the other, which will create a voltage which causes a current through the external resistor.
So if you can calculate what the plate-to-plate flux of charges is due to the force from the magnetic field, then you will be able to calculate the current flow through the resistor. The only thing I'm not sure about is whether you need to also account for a reverse leakage current back through the conductive liquid (as appearing like another resistor in parallel with the explicit load resistor)..... I'm not sure about that aspect without giving it more thought.
3. Feb 14, 2007
### Saketh
If the magnetic field is exerting a force on the charges, I thought that the fluid would be moving upwards, in which case it would not be moving parallel to the plates as said earlier.
This confuses me. How can the charges move from one plate to the other when the magnetic force will push them in an arc?
My guess is that the resistance of the liquid is negligible because it acts as a "current source" instead of a pure "voltage source." But I am the one who's confused about this question, so take that with a grain of salt.
4. Feb 14, 2007
### Staff: Mentor
The "conducting liquid" is flowing straight through the capacitor, I would think, under the influence of some hydraulic pressure source. The fact that the free conductors in the fluid are experiencing forces orthogonal to the fluid flow should not alter the fluid's direction substantially. The fluid flowing is what moves the conductors along perpendicular to the B field, which is what imparts a force on them to make them tend to flow from plate-to-plate.
I guess I'd start by ignoring the fluid aspect of the question, and just think about the charges as being free and flowing in a stream. I'd just think about the electrons and ignore the fact that there are matching protons somewhere in the soup to keep everything electrically neutral.
I'm not sure about the next steps, but I think I would assume that a voltage difference develops across the plates, which generates an opposing E field to the B field Lorentz force, in order for the current flow to reach equilibrium. I think that it is the balance between the E and B field forces on the electrons which will result in a steady upward motion of the electrons instead of a curved trajectory like they would follow in the absence of the capacitor plates.
Maybe explore that angle some -- see if you can get to where the electrons are travelling upward at some angle, and calculate the net flux of electrons between the plates from that. Fun problem.
5. Feb 14, 2007
### Saketh
Yes, it is a fun problem. It's from the Irodov book -- 3.265, to be exact.
I'll think about it more tomorrow, and report back if I have any breakthroughs.
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2017-06-25 02:17:14
|
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|
https://bitbucket.org/luensdorf/simpy-immediate-process
|
# SimPy
SimPy is a process-based discrete-event simulation framework based on standard Python. Its event dispatcher is based on Python’s generators and can also be used for asynchronous networking or to implement multi-agent systems (with both, simulated and real communication).
Processes in SimPy are simple Python generator functions and are used to model active components like customers, vehicles or agents. SimPy also provides various types of shared resources to model limited capacity congestion points (like servers, checkout counters and tunnels). From version 3.1, it will also provide monitoring capabilities to aid in gathering statistics about resources and processes.
Simulations can be performed “as fast as possible”, in real time (wall clock time) or by manually stepping through the events.
Though it is theoretically possible to do continuous simulations with SimPy, it has no features that help you with that. On the other hand, SimPy is overkill for simulations with a fixed step size where your processes don’t interact with each other or with shared resources — use a simple while loop in this case.
The SimPy distribution contains tutorials, in-depth documentation, and a large number of examples.
SimPy is released under the MIT License. Simulation model developers are encouraged to share their SimPy modeling techniques with the SimPy community. Please post a message to the SimPy-Users mailing list.
## A Simple Example
One of SimPy's main goals is to be easy to use. Here is an example for a simple SimPy simulation: a clock process that prints the current simulation time at each step:
>>> import simpy
>>>
>>> def clock(env, name, tick):
... while True:
... print(name, env.now)
... yield env.timeout(tick)
...
>>> env = simpy.Environment()
>>> env.process(clock(env, 'fast', 0.5))
<Process(clock) object at 0x...>
>>> env.process(clock(env, 'slow', 1))
<Process(clock) object at 0x...>
>>> env.run(until=2)
fast 0
slow 0
fast 0.5
slow 1
fast 1.0
fast 1.5
## Installation
SimPy requires Python 2.7, 3.2, PyPy 2.0 or above.
You can install SimPy easily via pip:
$pip install -U simpy You can also download and install SimPy manually: $ cd where/you/put/simpy/
$python setup.py install To run SimPy’s test suite on your installation, execute: $ python -c "import simpy; simpy.test()"
Of course, you can keep working with SimPy 2:
\$ pip install "simpy>=2.3,<3"
## Getting started
If you’ve never used SimPy before, the SimPy tutorial is a good starting point for you. You can also try out some of the Examples shipped with SimPy.
## Documentation and Help
You can find a tutorial, examples, topical guides and an API reference, as well as some information about SimPy and its history in our online documentation. For more help, contact the SimPy-Users mailing list. SimPy users are pretty helpful. You can, of course, also dig through the source code.
If you find any bugs, please post them on our issue tracker.
Enjoy simulation programming in SimPy!
|
2018-03-21 05:46:31
|
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|
http://motls.blogspot.com/2011/09/ten-new-things-modern-physics-has.html?m=1
|
## Saturday, September 03, 2011
### Ten new things modern physics has learned about time
Note that it may take half a minute for your browser to display various formulae in $$\LaTeX$$ that are included in the text below.
Here is a somewhat balanced, completed, and corrected version of a Cosmic Variance (CV) summary:
1. Time is just another, imaginary dimension of space: this is the basic insight of Albert Einstein's theory of relativity. Just like the distances $$ds$$ in 3D space are given by the Pythagorean theorem involving coordinate differences, $ds^2 = dx^2+dy^2+dz^2,$ the squared invariant separation in the spacetime - a space enhanced by time - is given by the same Pythagorean theorem where time enters just like space, is converted via $$c$$, the speed of light, and appears with the opposite sign: $ds^2 = -c^2 dt^2+dx^2+dy^2+dz^2.$ Note that $$-dt^2$$ may be written as $$+(i\cdot dt)^2$$, i.e. the minus sign may be converted to a plus sign if we use a new imaginary spatial coordinate $$x_4 = ic\,dt$$.
Simultaneity of two events depends on the observer (differently moving observers slice the spacetime in different directions); the moving clocks may be shown to tick slower relatively to a static observer by the factor of $$\sqrt{1-v^2/c^2}$$ (twin paradox etc.); according to general relativity, spacetime gets curved so the speed of clocks' ticking depends on the gravitational potential. A theory that can't explain that space and time are close cousins (i.e. that can't reproduce the Lorentz symmetry) is incompatible with the fundamental knowledge we have about Nature. CV largely ignored relativity in its description of time; the exception is CV #3, "everyone observes time differently".
2. The question about the existence of the past depends on our definition of existence: the discussions whether "the past exists" (or, more precisely, for experts, "the past light cone exists") depend on what we mean by the verb "exist" and whether the verb "exist" is allowed to have a grammatically unusual tense that unifies the present tense and the past tense, i.e. the past and the present. So one shouldn't make a big deal out of the "eternalism vs presentism" debates: they're just battles about what terminology should be used. CV #2 discusses this point but incorrectly includes the future which is addressed in the following point.
3. The future doesn't exist at the present regardless of any definitions: the information about the events that will occur in the future is strictly non-existent at the present; according to the free-will theorem by Conway and Kochen, building on general postulates of quantum mechanics, the quantum mechanically random outcomes of the experiments/events are only decided at the "right time" and can't be pre-determined; as long as we admit that the experimeters have a free will, all other quantum objects have to have a free will as well so their outcomes can't be functions of the data (hypothetical "hidden variables") that exist in the past light cone. CV #2 is invalid because it claims that the future exists at the present - a proposition that violates the rules of quantum mechanics: we may speculate about the future but all currently unknown facts about the future will only be decided in the future.
4. Some units of time are better than others: in technical terms, there is no symmetry of Nature that would allow you to slow processes down by a factor $$k$$ and expect that all these processes will continue unchanged. For example, the duration of one period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom is always equal to 1/9,192,631,770 of a second and one can't construct any "mutation of the caesium 133 atom" in which the denominator would be different. This important observation - contradicting a widespread myth on a scale invariance of the laws of Nature and underlying a key concept of modern quantum field theory developed in the 1970s by Ken Wilson et al. and known as the "Renormalization Group" (different time scales are associated with different "effective" laws of physics) - is being ignored by CV. The same comment applies to space as well, as guaranteed by TRF #1: the size of the atoms can't be "inflated" or "shrunk", either. So situations morally resembling the picture below are forbidden by the laws of Nature:
5. Among conserved quantities, time has a special relationship with energy: again, this key insight of physics of time - which holds both in classical physics and quantum physics - is being ignored by CV. Emmy Noether has shown that each conservation law may be attributed to a symmetry of Nature and vice versa. The time-translational symmetry of the laws of Nature (saying that the phenomena proceed identically at time $$t$$ and at a later time $$t+\Delta t$$) implies the conservation of energy and vice versa. Noether's deep time-energy relationship may be also used to show that in quantum mechanics, the evolution in time is "generated" by a particular operator called the Hamiltonian - which is just a fancy technical name for the total energy of the system (or, especially, the linear operator in quantum mechanics that represents it). In particular, systems with a totally well-defined energy have their wave function depending on time as $$\exp(Et/i\hbar)$$. Because energy is related to time in this intimate way, temperature (the average energy per one degree of freedom, with some proper refinements and in some units) is related to time as well. In quantum physics (especially when it's studied by Richard Feynman's path integral), absolute temperature $$T$$ may be visualized as a periodic imaginary time $$\tau=it$$ with a period obeying $$k_{{\rm Boltzmann}}T = \hbar / \Delta \tau$$.
6. All physical systems with many degrees of freedom inevitably possess a future-time asymmetry, the so-called logical arrow of time: in any physical description of anything as well as the reality itself, one must always be able to say that among two causally related events A, B, one of them is the consequence of the other or that it has evolved from the other. If the influence existed in both directions, one would produce closed time-like curves (including the paradox in which one may kill his granddad before he met his grandmother). Without a loss of generality, B has evolved out of A. In other words, we say that B belongs to the future light cone of A; A is an event in the past and B is an event in the future. The relation of A, B is completely asymmetric and implies very different ways how to derive probabilities of various properties of A and B from one another. In particular, direct probabilistic formulae for properties of B exist as functions of properties of A - these calculations are known as predictions; on the other hand, one needs to choose a priori arbitrary "prior probabilities" and perform a "retrodiction" - a form of Bayesian inference - if he wants to derive properties of A out of the properties of B. Such a retrodiction never works too well because macroscopic phenomena (i.e. laws of their evolution) are irreversible. This insight implies that CV #2 and CV #9 are wrong.
7. The logical arrow of time implies the asymmetry of all macroscopic processes, i.e. the thermodynamic arrow of time and other arrows of time: one may mathematically prove the so-called H-theorem which is a rigorous quantitative version of the "second law of thermodynamics" which says that "the entropy (the quantity describing the amount of disorder of a system) never decreases by a macroscopic amount as time increases". As a result, the proof of the H-theorem - first presented by Ludwig Boltzmann - identifies the direction of the "logical arrow of time" mentioned in TRF #6 with the direction of time in which the entropy increases. People are aging and the heat always goes from a warmer body to a cooler one; these are two well-known and typical examples of the second law of thermodynamics. There are millions of others: eggs break but don't unbreak, and so on. The second law applies not only globally but it also constrains arbitrary small regions of spacetime as long as the number of degrees of freedom is large in this region and as long as the interactions between them are fast enough; this fact invalidates most of the propositions in CV #9. The laws of physics allow ingenious surgeries that will make one feel younger, or cloning which may start a life from the beginning; but they do not allow to run a macroscopic process backwards so that one would be getting gradually younger in the same (mirror) way as he is getting older. Many things should be said about the second law of thermodynamics and the thermodynamic arrow of time. For example, it doesn't contradict the emergence of more organized and more symmetric structures (higher forms of life etc.) or the existence of fridges: both fridges and organisms are optimized to reduce their own entropy accompanied by the pumping of an even larger entropy to their environment. The ability to reduce one's own entropy is indeed a typical sign of life, in an almost direct contradiction with CV #8 that says that "purpose of life" is to increase the entropy. "A purpose of life" is to locally decrease the entropy which is pretty unusual among the natural phenomena.
8. An exact time-reversing symmetry which holds in Nature is called CPT and only applies to the microscopic laws: the weak nuclear force implies that the phenomena which are just reverted in time (future exchanged with the past: the T operation) do not proceed identically as the original ones. However, one may prove and Wolfgang Pauli and others have proved in the 1950s that if you combine the T reversal with parity P (the map $$(x,y,z)\to(-x,-y,-z)$$ and with the charge conjugation C (the replacement of particles by their antiparticles and vice versa: this C comes pretty naturally together with T because particles moving backwards in time - with the opposite sign of energy - become antiparticles), we get a symmetry called CPT that is the exact symmetry of the laws of Nature because it may be identified with a kind of rotation of the (Euclideanized) spacetime by 180 degrees - which is guaranteed to be a symmetry by TRF #1. However, this symmetry only has a "straightforward interpretation" in the case of microscopic processes in which all the information about the future and the past is determined so the map between the past and the future is one-to-one; whenever there is some incomplete information about the past or about the future (or both), and there is always some incomplete information when the number of degrees of freedom is large (much greater than one: and this claim is true both in classical and quantum physics), the logical arrow of time from TRF #6 implies that the probabilities in the future and in the past have to be treated differently (one averages, with some subjective prior probabilities, the probabilities over different initial states; but one sums over all final states and this summing has no subjective component). Much like in TRF #7, this guarantees that the macroscopic processes proceed so that the entropy increases; however, the CPT-reversed processes in which the entropy decreases by $$-\Delta S < 0$$ are less likely than the original processes by the factor of $$\exp(-\Delta S / k_{{\rm Boltzmann}})$$, as explained many times on this blog. For a finite entropy difference and assuming the $$k_{{\rm Boltzmann}}\to 0$$ limit, the entropy-decreasing transitions quickly become impossible.
9. To properly understand the psychological perception of time, one needs to analyze the functions of the brain: this doesn't really belong to "physics proper" but the brain or the mind isn't the exact copy of the spacetime; it is a device that collects impulses from the past and produces an image. It takes almost 0.1 second for us to realize that we have seen or otherwise witnessed something: see CV #4. Brains may be fooled to have a flawed idea about the past (known as the "memory"): see CV #5. Also, I don't quite understand what's the point of CV #6 but it would clearly belong to this item, too. Sean Carroll has dedicated way too much space to these psychological speculations because he has returned from an interdisciplinary conference in which many neuroscientists as well as vacuous philosophical babblers apparently tried to hype their occasionally unphysical musings. I think that one point is enough to summarize them - and I chose the summary that says that one must be careful about the inner workings of the brain if he wants to make any valid statements about time that depend on human (or other) psychology.
10. When times become as short as the Planck time, $$10^{-43}$$ seconds, time develops some wholly unfamiliar properties: quantum gravity allows one to calculate (and Max Planck was able to compute as early as 100 years ago) that there is something special going on at durations that are as short as the Planck time, $$t_{\rm Planck} = \sqrt{\hbar G/c^5}$$, which is a function of the most universal constants of physics only. The geometry of spacetime can no longer be imagined to be a simple pseudo-Euclidean geometry when the separations in time become this short. The Planck time is the shortest time at which our intuition about time (which is continuous, causal, in principle accurately determined, and locally isomorphic to $${\mathbb R}$$) remains marginally valid. "Shorter times" don't really exist in a conventional sense; alternatively, totally new phenomena allowing us to connect the past and future etc. in novel ways (quantum foam and other classes of unusual phenomena, including processes involving strings, branes, and topology change) take over when you try to access shorter times than the Planck time. Also, the Planck time is the (very ephemeral) lifetime after which the smallest black hole (marginally) worth its name evaporates by the Hawking radiation. Quantum gravity i.e. string/M-theory has to be properly understood (by you or by the whole mankind) to say anything sensible yet nontrivial about these extremely short periods of time (especially about the first moments after the Big Bang; the last moments of an evaporating black hole; or the vicinity of the singularities of larger black holes: unluckily enough, these 3 examples are among the least understood short-distance questions in string theory). This point - which is the only point of "truly contemporary physics" in this list - is ignored by CV, too. Time may be "emergent", as hinted by CV #1, and the Planck time regime may make such an emergent description of time more important. Emergent and fundamental descriptions may also be equivalent to each other. However, the equivalence of time and space as described in TRF #1 has to be valid at all times and all descriptions which is a huge constraint on possible candidate theories of physics - and candidate theories of time. This constraint immediately invalidates, among many other hypotheses, all hypotheses in which time is universally discrete or quantized or in which the spacetime curvature requires many degrees of freedom to be excited ("entropic gravity").
Let me mention that I don't believe that CV #10 ("each life lasts 1 billion heartbeats") has a broader range of validity that goes well beyond the organisms we know on Earth or that would hold very accurately. It's an OK observation that larger animals live longer but have slower heartbeats: one hearbeat brings you about 1 ppb closer to the death. However, pretty ordinary intelligent structures such as computers live for much longer a time than 1 billion cycles of the microprocessor (which would be less than a second). ;-)
I am sure that hypothetical extraterrestrial life forms (assuming that they exist) may be "hybrids" of our biological organisms or computers, or even more accurately and flawless computers than ours, so they may have a very different number of heatbeats per lifetime.
If you look at the list of points at CV, several points are valid (#3, #4, #5, #6, #7), one point is almost completely vacuous or "undecided" (#1), three points are wrong or at least their major propositions are wrong (#2, #8, #9), and one of them is just a very inaccurate phenomenological observation about a limited number of life forms on Earth (#10). Moreover, most of the points that are valid (#3, #4, #5, #6, #7) are morally redundant and overexpose a very small subset of scientific questions that have very little to do with physics.
Most of the points about time that I found totally paramount for the description of time as understood by contemporary physics (TRF #1, #4, #5, #6, #8, #10) were completely or almost completely omitted by the Cosmic Variance. This much for the scientific consensus. It's kind of remarkable that a famous cosmology blogger picks less than one-half of the important insights that physics has made about time; and in those that he did pick, about one-half is fundamentally invalid or at least vacuous.
1. Lubos:I am sure that hypothetical extraterrestrial life forms (assuming that they exist) may be "hybrids" of our biological organisms or computers, or even more accurately and flawless computers than ours, so they may have a very different number of heatbeats per lifetime.
We do not have to go to far from what is known, to conclude that the life span of any of the species on earth varies according to those heart beats measured in time:)
I appreciate your explanations on time and maybe you can talk more on what Sean Carroll states there about Einstein. They are quite selective there about comments, so I have been blocked.
Sean Carroll:As Einstein put it, “It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.”
Getting introduced by Grossman's to views on Riemann were liberating for Einstein as well as moving all of us to non euclidean views of reality?
Would you agree?
Best,
2. In 1952, in his book Relativity, in discussing Minkowski's Space World interpretation of his theory of relativity, Einstein writes:
Since there exist in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.
Einstein writes a letter to Besso's family in regards to Bessopreceding him in death ........for us physicists believe the separation between past, present, and future is only an illusion, although a convincing one."
Best,
3. The future doesn't exist at the present regardless of any definitions...
Isn't it true that given any event X in spacetime, any other event outside the future lightcone is, in some observer's frame, either simultaneous with X or in the past of X? Therefore, given a (infinite) hypersurface of simultaneity to some observer, what is unambiguously the future lies only in the intersection of all the future lightcones emanating from that surface, which is the empty set?
4. No, Arun, what lies unambiguously in the future of a given event/point in spacetime is this point's future light cone, not an empty set. (Yes, the intersection of all your bizarre collection of light cones is an empty set but it has no relevance for the original question - and by the way, your question is unrelated to my original statement, too.)
5. The future doesn't exist at the present regardless of any definitions...
Luboš - I'll try asking in another way. If events A and B are simultaneous as per some observer, and events B and C are simultaneous as per some other observer, and if C is in the future of A, then in what sense does C not exist when A occurs?
Either I have to take into account all the simultaneity reports of all observers, or of none of them.
That would be the solipsist approach that the only things which have existed or exist are those that are in my past light cone. The laws of physics don't stop working at my horizon, though. I need a way of talking about whether things that have wandered out of my past light cone still are, were, will be.
6. Let me try it another way, tell me if you agree.
Talking of future, present, past is misleading. I should talk only about knowable things and predictions, where I mean by knowable, everything inside my past light cone; and predictions everything outside my past light cone.
Anything I say about events outside my past light cone is a prediction, even though in my global coordinate system, it might lie in the past. In particular, the existence of a good part of the rulers and clocks that make up my global coordinate system is a prediction. That the far-away "now" event X will eventually enter my past light cone at which event I will find X to be coeval with the event 12:00 PM GMT, 2011-09-06, is a prediction (or a fundamental postulate about the nature of Lorentzian space).
I don't like the word "knowable" much, perhaps there is a better term for the knowable region - which is the region from which the results of a measurement could have reached my worldline.
7. Dear Arun,
what you try to paint as "solipsism" is exactly the right answer. Only the past light cone "exists now".
The events that are spacelike-separated from the event "I, now" can't have influenced me yet which is why I can't even know whether these spacelike separated regions exist or not. The vacuum could have decayed over there, a fact that will only arrive here later.
But even if you extended the definition of existence so that all events with time "t" smaller than your time, according to your coordinate system, exist "now", there would still be no contradiction because you can't incoherently mix different reference systems when defining "now" or the "future".
Your zigzag way of getting from A to C just has no meaning. Of course that you can get any interval in spacetime - timelike or spacelike - as a sum of purely spacelike intervals; or as a sum of purely timelike intervals. And what? There's no importance about this point.
I think that you haven't even begun to start to understand the depth of my comment that "future doesn't exist now" which is based on the free-will theorem. This statement means that in the quantum world, one cannot consider the future to be a function in the past. The future events aren't decided by any hidden variables that could exist in the past light cone.
Cheers
LM
8. Of course it is experimentally important to try and answer how any universe came into being. Is time a emergent product then?
Cycle of Birth, Life, and Death-Origin, Indentity, and Destiny by Gabriele Veneziano
In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined with a grand set of concerns, one famously encapsulated in an 1897 painting by Paul Gauguin: D'ou venons-nous? Que sommes-nous? Ou allons-nous? "Where do we come from? What are we? Where are we going?"
How would information be transferred from the previous universe, and is this an important question in terms of the now, as too, any universe as containing the past and future??
"Where," would this be possible in our universe? String theorists have push back our perspective on time. How far can they go?
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2016-12-08 03:57:29
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https://learncheme.com/quiz-yourself/interactive-self-study-modules/diffusion-and-reaction-in-porous-catalysts/diffusion-and-reaction-in-porous-catalysts-summary/
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#### Diffusion and Reaction in Porous Catalysts: Summary
The answers to the ConcepTests are given below and will open in a separate window.
ConcepTest 1 Answer — for more details see this screencast
##### Key points from this module:
• The rate of reaction in a porous catalyst pellet is the rate that reactant diffuses into the pellet.
• When comparing several porous catalyst spheres that have the same rate constant (for a positive-order reaction) and the same diameter, the sphere with the highest reactant concentration in the sphere forms the most product.
• For a positive-order reaction, the effectiveness factor is highest for the catalyst with the highest concentration of reactant in the catalyst.
• At the center of a catalyst pellet or cylinder, $$dC_A/dr$$ = 0, where $$C_A$$ is the reactant concentration and $$r$$ is the radius.
• The concentration of reactant at the catalyst surface may be less than in the bulk because bulk diffusion may also limit reaction.
• As the Thiele modulus increases, the effectiveness factor decreases.
• For a given catalyst, smaller particles have higher effectiveness factors.
##### From studying this module, you should now be able to:
• Calculate the Thiele modulus and effectiveness factor for a catalyst pellet.
• Explain what a Thiele modulus represents and what an effectiveness factor represents.
• Explain what the concentration profile looks like in a catalyst pellet for fast and slow reactions (or for slow and fast diffusivities).
• Calculate the rate of reaction in the pellet, given a concentration profile in a catalyst pellet.
Prepared by John L. Falconer, Department of Chemical and Biological Engineering, University of Colorado Boulder
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2023-03-24 18:34:03
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https://brilliant.org/problems/magnetic-fields-due-to-currents-in-wires/
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# Field Around A Wire
An electrical current $$i$$ flows across an infinite rectilinear wire. If the intensity of $$i$$ is doubled, the magnetic field at a generic point $$\text{__________}.$$
×
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2017-05-28 09:02:12
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http://mathhelpforum.com/calculus/16188-how-do-u-take-second-derivative-wen-doesn-t-start-y.html
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# Math Help - how do u take the second derivative wen it doesn't start with a "y="
1. ## how do u take the second derivative wen it doesn't start with a "y="
how do u find the second derivative of this
3y^2 - 4x = 16
2. Originally Posted by calchelp
how do u find the second derivative of this
3y^2 - 4x = 16
we can solve for y first (which isn't hard) and then take the derivative twice, or we can take the derivative implicitly, which would you prefer? Have you learnt implicit differentiation?
3. can u briefly explain implicit diffrentiation cause thats only one from the many that i have...and the entire section is implicit diffrentiation
4. Originally Posted by calchelp
can u briefly explain implicit diffrentiation cause thats only one from the many that i have...and the entire section is implicit diffrentiation
In implicit differentiation, we take nothing for granted. we always identify what we are taking the derivative of, and with respect to what. That is, if we differentiate a y-term with respect to x, we attach the notation $\frac {dy}{dx}$ to it. This means we took the derivative of y with respect to x. We can simply call this y'. We don't attach anything if we differentiate a variable that is the same as the variable that we are differentiating with respect to. That is, if we differentiate x with respect to x, we don't attach anything. Why is that? Technically we do, if we differentiate an x-term with respect to x, we attach $\frac {dx}{dx}$, but since derivative notations can function as fractions, we simplify this to 1, so you don't see it. If we differentiate a term with both x's and y's in it, we use the product rule. and we attach the appropriate notation for each part. when we differentiate the x-term we attach nothing. when we differentiate the y-term, we attach $\frac {dy}{dx}$
Let's see how this works
Originally Posted by calchelp
how do u find the second derivative of this
3y^2 - 4x = 16
$3y^2 - 4x = 16$
We proceed by Implicit differentiation
$\Rightarrow 6y~y' - 4 = 0$ .......remember, the derivative of a constant is zero, so the 16 disappears. we attach y' to the derivative of the y-term, but nothing to the derivative of the x-term as explained above.
Now we simply solve for y'
$\Rightarrow y' = \frac {4}{6y}$
Now try the second derivative
5. ## tell me if this is the right approach
so the first derivative is
y'=4/6y
y''=[6y * 0] - [4 * 6y'] /(6y^2)
y"= -4 * 6 y' / (36y^2)
what do we do with the 6y' left in the equation?
6. Originally Posted by calchelp
so the first derivative is
y'=4/6y
y''=[6y * 0] - [4 * 6y'] /(6y^2)
y"= -4 * 6 y' / (36y^2)
what do we do with the 6y' left in the equation?
you can replace it with the original expression for y' if it bothers you, so you could replace it with 4/6y
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2014-12-18 06:17:38
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http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=C1301&l=en
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Magyar Information Contest Journal Articles
# Problem C. 1301. (September 2015)
C. 1301. Prove that if $\displaystyle x_1$ and $\displaystyle x_2$ are positive real numbers, then
$\displaystyle (x_1+x_2+1) \left(\frac{1}{x_1}+\frac{1}{x_2}+1\right)\ge 9.$
(5 pont)
Deadline expired on 12 October 2015.
### Statistics:
199 students sent a solution. 5 points: 168 students. 4 points: 11 students. 3 points: 6 students. 2 points: 2 students. 1 point: 5 students. 0 point: 5 students. Unfair, not evaluated: 2 solutions.
Our web pages are supported by: Morgan Stanley
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2017-12-11 03:54:30
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https://www.appropedia.org/ECM_-_Telecommuting
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Project data
Telecommuting is a work arrangement for which an employee is allowed flexibility in their working location and hours. Its main purpose and advantage is that it reduces the need to commute to a central place of work. Instead, the employee works at a remote location (such as their home) while in contact with the workplace through telecommunication links, such as video conferencing.
## Technology
By definition "telecommuting" means replacing an employee's regular daily commute to work, in a personal car or public transit, with virtual communication. This communication could take the form of e-mails or phone messages, although most businesses will generally link employees through a remote network access. This allows them access to data stored on a company network. In the interest of security, a Virtual Private Network (VPN) is usually used. A VPN allows employees to securely access the company's network through making use of an insecure network such as the Internet.
Long distance telework is further facilitated by the progressive decrease in cost of telecommunication and improvements in personal computers (such as Laptops and Wi-Fi adapters). With the increasing availability of tools such as groupware, conference calling, videoconferencing, and Voice Over IP (VOIP), the need to physically travel to a centralized place of work diminishes further.
• Reduces the need for office space, resulting in reduced company costs (less utilities consumed, less required parking space, less required work space, available office space can be shared by multiple employees by "office hoteling").[1] On average, in 1995, energy costs were $1.51 per square foot of office space per year (with larger commercial buildings at about$1.19 per square foot per year)[2]. AT&T reported that $550 million in cash flow had been made between 1991 and 1998 due to telecommuting employees.[3] • An agency may find that by offering the flexibility to work from home, they can hire back a retiree with the right specialized experience to do a job on a part-time, rather than full-time, basis.[4] • When properly managed, can increase employee efficiency.[5] • In the event of a disaster, where workers can no longer use or reach their office, telecommuters are able to continue business. • In the event of employee sickness or personal issues that don't allow them to travel, work can still be done. Office hoteling[1]can be taken advantage of by the employer in order to reduce office space requirements as each office can be used by multiple employees on separate days. #### To the employee • Travel time is reduced • Fuel consumption is reduced • Convenient • Reduced work-family conflict • When properly managed, increases job satisfaction and reduces stress • Increased mobility: more likely that one can move to another location without losing one's job • Reduced involvement in office politics that may affect job satisfaction or disrupt the work setting #### Other • Reduces traffic, which results in: better driving conditions, fewer accidents, reduced congestion, reduced road maintenance costs, faster commutes, and more efficient fuel consumption. • Reduces greenhouse gas emissions. • Preserves the environment by reducing the need for large offices and large highways. #### Balancing between employee and employer It is important for telecommuting that both the employer and employee agree upon what the employer will provide in terms of resources. For example, will the employer supply a computer, or will the employee? What amount of internet and phone bills will the employer pay? A list of common resources that need to be considered are listed below: • Computer and peripherals (fax machine, scanner, printer, etc.) • Internet connection and broadband allowance • Extra phone line(s) • Printing paper, ink, and other small office supplies (pens, rulers, etc.) • Office desks and chairs • Software licenses Another important question is whether the company will handle the installation and removal of such equipment or not. ## California Pilot Project The state of California ran a pilot project to determine the impacts of home-based telecommuting on travel behaviour and personal vehicle emissions. The authors compared participants' travel behaviour before and after telecommuting, and found a 27% reduction in the number of personal vehicle trips, a 77% decrease in vehicle-miles-traveled (VMT), and 39% (4%) decreases in the number of cold (hot) engine starts. The authors determined that these decreases translated into emissions reductions of: 48% for total organic gases (TOG), 64% for carbon monoxide (CO), 69% for nitrogen oxides (NOx) and 78% for particulate matter (PM).[6] The number of personal vehicle trips and VMT partitioned into commute-related and non-commute-related purposes revealed that non-commute personal vehicle trips increased by 0.5 trips per day on average, whereas the non-commute VMT decreased by 5.3 miles.[6]This finding supports the hypothesis that non-commute travel generation is a potential negative impact of telecommuting, though this small increase in non-commute trips has a negligible impact compared to the overall travel and emission savings. ## Cas well & Associates Cas well & Associates, in Bloomfield Hills, Mich. , was a$650,000 firm that decided to give up its 1,700-square-foot office space, and instead gave each employee their own home office.
Cas well reported that the cost was $200 to$500 a head for modems and extra phone lines; each new employee also required a computer and a fax machine, at a per-employee total cost between $2,000 and$3,000. Since the transition, Cas well's phone bills doubled, but the company claims that all the total costs didn't come near to their previous rent of over \$3,000 a month.[7]
## Limitations/Concerns
Limitations and concerns of telecommuting can include:
• Employees fear the isolation. From Kurland & Cooper, 2002: "Professionally, employees fear that when they're out of sight, they're out of mind for promotions and other organizational rewards. Socially, employees comment that they miss the informal interaction they garner by being around colleagues and friends".[8]
• Research has shown that managers fear they lose control over employees' behavior as employees gain autonomy by telecommuting.[9]
• Safety concerns over the equipment or data provided to the out-of-office employee
## Telework Associations
A number of associations have been established to help advance the growth and success of work independent of location through online resources.
## Literature Review
A full literature review was conducted prior to creating our ECM. It can be found here: Telecommuting Literature Review
## Energy Conservation Measures (ECM)
The following telecommuting ECM prepared for Mech425 GreenIT Project can be used to determine the monetary costs and savings, as well as the greenhouse gas emission savings, derived from implementing a telework system. A copy of the ECM can be found here: File:Mech425 greenITProject Telecommuting ECM.xls.
The attached is most up to date. Please be mindful in the environmental section, total savings are assumed same every year and are summed cumulatively in the green cells that follow.
## References
1. ["'Hoteling': Employees share desks as they check in to work". Central Penn Business Journal. FindArticles.com. 06 Feb, 2010. [qa5295/is 199804/ai n24334137/] Copyright Journal Publications Inc. Apr 17, 1998]
2. <"A Look at Office Buildings: How do they use energy and how much does it cost?" (2001). [howuseenergy.htm] U.S. Energy Information Administration Independant Statistics and Analysis.
3. [ Apgar, M. (1998). The alternative workplace: Changing where and how people work. Harvard Business Review, 76(3), 121-137.]
4. [Polcastro, Mike. "Wages, benefits and tighter belts: agencies must not overlook the impact of pay and perks on their bottom line." Best's Review 110.8 (2009): 64. Academic OneFile. Web. 6 Feb. 2010.]
5. [Shafizadeh (P.E.), Kevan R., et al. "Costs and Benefits of Home-Based Telecommuting: A Monte Carlo Simulation Model Incorporating Telecommuter, Employer and Public Sector Perspectives." Journal of Infrastructure Systems 13.1 (2007): 12-25. [[1]]]
6. [Koenig, Brett E., Dennis K. Henderson and Patricia L. Mokhtarian. "The Travel and Emissions Impacts of Telecommuting for the State of California Telecommuting Pilot Project." Transportation Research Part C: Emerging Technologies 4.1 (1996): 13-32. Available on-line at: [[2]]]
7. [Christopher Caggiano. "Five Ways to Save Money on Office Space" Mansueto Ventures LLC. July 1, 2000. [[3]]]
8. [Nancy B. Kurland, Cecily D. Cooper, "Manager control and employee isolation in telecommuting environments", The Journal of High Technology Management Research, Volume 13, Issue 1, 2002, Pages 107-126.[[4]].
9. [Tomaskovic-Devey, D. and Risman, B.J. "Telecommuting innovation and organization: a contingency theory of labor process change." Social Science Quarterly 74 2, 1993, Pages 367–385.]
Page data
Part of Mech425, Mech425 GreenIT ProjectMech425 GreenIT Project Project energy SDG07 Affordable and clean energy Stephen K. Vickers, Ken MacDougall 2010 CC-BY-SA-4.0 Queen's University 225 No main image Stephen K. Vickers, Ken MacDougall (2010). "ECM - Telecommuting". Appropedia. Retrieved August 8, 2022.
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2022-08-08 22:30:28
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https://wrfranklin.org/pmwiki/pmwiki.php/Research/NonGeometricDataStructuresAlgorithms
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(in WR FranklinResearch)
Here are some algorithms and data structures that are neither geometric nor cartographic.
1. bibtexsummary:[/wrf.bib,wrf-cacm-82]
2. bibtexsummary:[/wrf.bib,wrf-ipl-79]
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2023-02-03 03:08:30
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https://brilliant.org/problems/ratio-of-sides/
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# Ratio of Sides
Level pending
Triangle $$ABC$$ has side lengths $$a, b$$ and $$c$$ which satisfy $$\frac{a+b}{11}=\frac{b+c}{12}=\frac{c+a}{13}$$. If $$\sin A:\sin B:\sin C$$ can be expressed as an irreducible ratio $$p:q:r$$, where $$p$$, $$q$$ and $$r$$ are positive integers, what is the value of $$p+q+r?$$
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2017-01-24 01:19:31
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https://study.com/academy/answer/michelle-wie-a-teenage-golf-prodigy-who-earned-16-million-in-endorsements-and-4-million-in-prize-money-and-appearance-fees-in-2006-announced-that-she-would-enroll-as-a-student-at-stanford-university-in-the-fall-of-2007-what-was-her-opportunity-cost-o.html
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# Michelle Wie, a teenage golf prodigy who earned $16 million in endorsements and$4 million in...
## Question:
Michelle Wie, a teenage golf prodigy who earned {eq}\$16 {/eq} million in endorsements and {eq}\$4 {/eq} million in prize money and appearance fees in 2006, announced that she would enroll as a student at Stanford University in the fall of 2007. What was her opportunity cost of a year of college?
## Opportunity costs
Opportunity cost defined as the benefits lost when a person chooses one alternative over another alternative. In other words, it is the "cost" incurred by not choosing the benefits involved with the nest best alternative option.
In this case, If Michelle Wie choose to get enroll as a student at Stanford University, She has to sacrifice the income of $16 +$4 = $20 which she could have earned in 2007. Thus, her opportunity cost of a year of college is$20.
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2020-06-01 06:49:40
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https://www.semanticscholar.org/paper/Lorentz-Violating-Extension-of-the-Standard-Model-Colladay-Kosteleck%C3%BD/6acb9372eb21801234e5d8208b41cf791d3a0b4e
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# Lorentz-Violating Extension of the Standard Model
@article{Colladay1998LorentzViolatingEO,
title={Lorentz-Violating Extension of the Standard Model},
journal={Physical Review D},
year={1998},
volume={58},
pages={116002}
}
• Published 24 September 1998
• Physics
• Physical Review D
In the context of conventional quantum field theory, we present a general Lorentz-violating extension of the minimal $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ standard model including $\mathrm{CPT}$-even and $\mathrm{CPT}$-odd terms. It can be viewed as the low-energy limit of a physically relevant fundamental theory with Lorentz-covariant dynamics in which spontaneous Lorentz violation occurs. The extension has gauge…
175 Citations
### Dimensional reduction of a Lorentz- and CPT-violating Maxwell-Chern-Simons model
• Physics
• 2003
Taking as a starting point a Lorentz and CPT noninvariant Chern-Simons-like model defined in $1+3$ dimensions, we proceed to realize its dimensional reduction to $D=1+2.$ One then obtains a new
### Lorentz violating scalar Casimir effect for a D -dimensional sphere
• Mathematics, Physics
• 2020
We investigate the Casimir effect, due to the confinement of a scalar field in a $D$-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by an
### One-loop structure of the photon propagator in the standard model extension
• Physics
Physical Review D
• 2019
We study radiative corrections on the photon propagator from the electroweak sector of the minimal Lorentz- and $CPT$-violating Standard Model Extension. We derive the most general Lorentz-violating
### Maxwell electrodynamics modified by a CPT -odd dimension-five higher-derivative term
• Physics
Physical Review D
• 2019
In this paper, we consider an electrodynamics of higher derivatives coupled to a Lorentz-violating background tensor. Specifically, we are interested in a dimension-five term of the CPT-odd sector of
### Photon sector analysis of Super and Lorentz symmetry breaking: effective photon mass, bi-refringence and dissipation
• Physics
The European Physical Journal C
• 2018
Within the standard model extension (SME), we expand our previous findings on four classes of violations of Super-Symmetry (SuSy) and Lorentz Symmetry (LoSy), differing in the handedness of the
### Thermal aspects of interacting quantum gases in Lorentz-violating scenarios
• Physics
• 2021
In this work, we study the interaction of quantum gases in Lorentz-violating scenarios considering both boson and fermion sectors. In the latter case, we investigate the consequences of a system
### Leading-order classical Lagrangians for the nonminimal standard-model extension
• Physics
• 2018
In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal Standard-Model Extension (SME). Such a Lagrangian is considered to be the
### Noncommutative gauge theory without Lorentz violation
• Mathematics, Physics
• 2002
The most popular noncommutative field theories are characterized by a matrix parameter ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}$ that violates Lorentz invariance. We consider the
### Lorentz-violating supersymmetric quantum field theories
We study the possibility of constructing Lorentz-violating supersymmetric quantum field theories under the assumption that these theories have to be described by Lagrangians which are renormalizable
### Testing Lorentz and CPT invariance with ultracold neutrons
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Physical Review D
• 2018
In this paper we investigate, within the standard model extension framework, the influence of Lorentz- and CPT-violating terms on gravitational quantum states of ultracold neutrons. Using a
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New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been
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### This bound, obtained from observation of the Jovian magnetosphere during the Pioneer-10 mission, might eventually be improved through measurements on the solar magnetosphere
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• 1975
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2022-12-02 17:06:01
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http://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-9-inequalities-and-problem-solving-test-chapter-9-page-624/17
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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
$n=\{ -15,15 \}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $|n|=15 ,$ use the definition of absolute value equality. Then graph the solution set. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to \begin{array}{l}\require{cancel} n=15 \\\\\text{OR}\\\\ n=-15 .\end{array} Hence, $n=\{ -15,15 \} .$
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2018-04-22 18:39:24
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https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5444572&punumber=8919
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# IEEE Transactions on Circuits and Systems I: Regular Papers
## Filter Results
Displaying Results 1 - 24 of 24
Publication Year: 2010, Page(s):C1 - C4
| |PDF (47 KB)
• ### IEEE Transactions on Circuits and Systems—I: Regular Papers publication information
Publication Year: 2010, Page(s): C2
| |PDF (38 KB)
• ### Spectral Analysis of Phase Noise in Bipolar LC-Oscillators—Theory, Verification, and Design
Publication Year: 2010, Page(s):737 - 751
Cited by: Papers (10)
| |PDF (929 KB) | HTML
Interpretation of phase-noise generating mechanism in oscillators relies on approximate and numerical calculations for analysis, and simulation tools for synthesis. In this paper, a comprehensive, yet intuitive, phase-noise model is derived as a function of oscillator circuit parameters, suiting both analysis and synthesis of oscillators. Contributions of all noise sources to the phase noise of bi... View full abstract»
• ### Full 360$^{circ }$ Vector-Sum Phase-Shifter for Microwave System Applications
Publication Year: 2010, Page(s):752 - 758
Cited by: Papers (20) | Patents (3)
| |PDF (1029 KB) | HTML
An innovative vector-sum phase shifter with a full 360° variable phase-shift range is proposed and experimentally demonstrated in this paper. It employs an active balun and a very high-speed CMOS operational transconductance amplifier (OTA) integrator to generate the four quadrature basis vector signals. The fabricated chip operates in the 2-3 GHz, it exhibits an average insertion gain of 1.5... View full abstract»
• ### Theory and Bandwidth Enhancement of Cascaded Double-Stage Distributed Amplifiers
Publication Year: 2010, Page(s):759 - 772
Cited by: Papers (8)
| |PDF (2017 KB) | HTML
Theoretical analysis and bandwidth enhancement of the cascaded double-stage distributed amplifiers (CDSDA) are presented. The characteristics of the general cascaded multi-stage distributed amplifiers (CMSDA) with open idle drain terminations at intersections for a high gain are investigated with lossy artificial lumped line models. This reveals the inherent bandwidth limitation of the CMSDA due t... View full abstract»
• ### A Wideband Low Power Low-Noise Amplifier in CMOS Technology
Publication Year: 2010, Page(s):773 - 782
Cited by: Papers (28)
| |PDF (1012 KB) | HTML
A T-coil network can be implemented as a high order filter for bandwidth extension. This technique is incorporated into the design of the input matching and output peaking networks of a low-noise amplifier. The intrinsic capacitances within the transistors are exploited as a part of the wideband structure to extend the bandwidth. Using the proposed topology, a wideband low-noise amplifier with a b... View full abstract»
• ### Far-Field Acoustic Source Localization and Bearing Estimation Using $SigmaDelta$ Learners
Publication Year: 2010, Page(s):783 - 792
Cited by: Papers (8)
| |PDF (1743 KB) | HTML
Localization of acoustic sources using miniature microphone arrays poses a significant challenge due to fundamental limitations imposed by the physics of sound propagation. With sub-wavelength distances between the microphones, resolving acute localization cues become difficult due to precision artifacts. In this paper we propose a framework which overcomes this limitation by integrating signal-me... View full abstract»
• ### A Low-Power Quadrature VCO and Its Application to a 0.6-V 2.4-GHz PLL
Publication Year: 2010, Page(s):793 - 802
Cited by: Papers (38) | Patents (1)
| |PDF (883 KB) | HTML
A novel circuit topology of the quadrature voltage-controlled oscillator (QVCO) is presented in this paper for low-voltage and low-power applications. With the antiphase coupling provided by the MOSFETs in a passive mode, quadrature output phases can be generated at minimum power consumption while maintaining desirable circuit performance in terms of phase error and phase noise. Based on the propo... View full abstract»
• ### A Low-Cost VLSI Architecture for Fault-Tolerant Fusion Center in Wireless Sensor Networks
Publication Year: 2010, Page(s):803 - 813
Cited by: Papers (3)
| |PDF (1129 KB) | HTML
A fault-tolerant distributed decision fusion in the presence of sensor faults via collaborative sensor fault detection (CSFD) was proposed in our previous research . The scheme can identify the faulty nodes efficiently and improve the performance of the decision fusion significantly. It achieves very good performance at the expense of such extensive computations as exponent and multiplication/divi... View full abstract»
• ### Minimizing Soft Errors in TCAM Devices: A Probabilistic Approach to Determining Scrubbing Intervals
Publication Year: 2010, Page(s):814 - 822
Cited by: Papers (30)
| |PDF (507 KB) | HTML
Ternary content addressable memory (TCAM) is more susceptible to soft errors than static random access memory (SRAM). The large di/dt issue during comparison operation reduces operating voltage ranges, which in turn reduces soft error immunity. The tight structural coupling of TCAM comparison circuits and memory cells does not allow for an interleaving design scheme in mitigating soft errors. Regu... View full abstract»
• ### Efficient Reverse Converter Designs for the New 4-Moduli Sets ${2^{n} -1, 2^{n}, 2^{n} +1, 2^{2n + 1}-1}$ and ${2^{n} -1, 2^{n} +1, 2^{2n}, 2^{2n} +1}$ Based on New CRTs
Publication Year: 2010, Page(s):823 - 835
Cited by: Papers (60)
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In this paper, we introduce two new 4-moduli sets {2n-1, 2n, 2n+1, 22n+1-1} and {2n-1, 2n+1, 22n, 22n+1} for developing efficient large dynamic range (DR) residue number systems (RNS). These moduli sets consist of simple and well-formed moduli which can result in efficient implementation of the reverse converte... View full abstract»
• ### Jointly Designed Architecture-Aware LDPC Convolutional Codes and High-Throughput Parallel Encoders/Decoders
Publication Year: 2010, Page(s):836 - 849
Cited by: Papers (11) | Patents (1)
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A novel design approach is proposed for low-density parity-check convolutional codes (LDPC-CCs), that jointly optimizes the code, encoder and decoder to achieve high-throughput parallel encoding and decoding. A series of implementation-oriented constraints are applied to construct architecture-aware (AA) codes by introducing algebraic structures into the parity-check matrix. The resulting AA codes... View full abstract»
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Publication Year: 2010, Page(s):850 - 862
Cited by: Papers (57)
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The conventional digital hardware computational blocks with different structures are designed to compute the precise results of the assigned calculations. The main contribution of our proposed Bio-inspired Imprecise Computational blocks (BICs) is that they are designed to provide an applicable estimation of the result instead of its precise value at a lower cost. These novel structures are more ef... View full abstract»
• ### A Direct Digital Frequency Synthesizer Based on the Quasi-Linear Interpolation Method
Publication Year: 2010, Page(s):863 - 872
Cited by: Papers (21)
| |PDF (664 KB) | HTML
This paper introduces a novel direct digital frequency synthesizer (DDFS) with an architecture based on the quasi-linear interpolation method (QLIP). The QLIP method is a hybrid polynomial interpolation in which the first quarter of a cosine function is approximated by two sets of linear and parabolic polynomials. The section of the cosine function that is closer to its peak is interpolated by par... View full abstract»
• ### A Low-Complexity Viterbi Decoder for Space-Time Trellis Codes
Publication Year: 2010, Page(s):873 - 885
Cited by: Papers (6) | Patents (1)
| |PDF (1811 KB) | HTML
Space-time trellis code (STTC) has been widely applied to coded multiple-input multiple-output (MIMO) systems because of its gains in coding and diversity; however, its great decoding complexity makes it less promising in chip realization compared to the space-time block code (STBC). The complexity of STTC decoding lies in the branch metric calculation in the Viterbi algorithm and increases signif... View full abstract»
• ### Design of a Robust Multi-Channel Timing Recovery System With Imperfect Channel State Information for 10GBASE-T
Publication Year: 2010, Page(s):886 - 896
Cited by: Papers (2)
| |PDF (911 KB) | HTML
The interdependence among multiple channels and the interaction between timing and equalization loops bring new challenges to the design of a multi-channel symbol timing recovery (STR) system for 10GBASE-T. In addition, the nonlinear Tomlinson-Harashima precoding (THP) technique used in the 10GBASE-T system is vulnerable to the imperfect channel state information (CSI). In this paper, we address t... View full abstract»
• ### Hybrid Structures for Low-Complexity Variable Fractional-Delay FIR Filters
Publication Year: 2010, Page(s):897 - 910
Cited by: Papers (38)
| |PDF (911 KB) | HTML
This paper proposes a pair of new structures for implementing low-complexity odd-order and even-order variable fractional-delay (VFD) FIR filters using hybrid structures with both even-order and odd-order subfilters. For odd-order VFD filter design, the main idea is to replace the conventional even-symmetric odd-order (type-2) subfilters with the cascade of a type-2 half-delay filter and even-symm... View full abstract»
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Publication Year: 2010, Page(s):911 - 924
Cited by: Papers (8)
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This paper presents a fast split-radix- (2×2)/(8×8) algorithm for computing the 2-D discrete Hartley transform (DHT) of length N ??N with N = q ?? 2 m, where q is an odd integer. The proposed algorithm decomposes an N ?? N DHT into one N /2 ?? N /2 DHT and 48 N /8 ?? N /8 DHTs. It achieves an ef... View full abstract»
• ### A Robust Channel Estimator for High-Mobility STBC-OFDM Systems
Publication Year: 2010, Page(s):925 - 936
Cited by: Papers (8)
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In this paper, a robust channel estimator for high- mobility space-time block code-orthogonal frequency division multiplexing (STBC-OFDM) systems is proposed and applied in IEEE 802.16e systems. A high-performance two-stage channel estimation method is adopted. The proposed architecture reduces computational complexity effectively and improves 85.2% of the hardware implementation. The performances... View full abstract»
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Cited by: Papers (22)
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In this article bifurcation analysis of the 9 bus power system model corresponding to the Western Systems Coordinating Council is performed. In order to use standard continuation packages like MATCONT, a full ordinary differential equations model, including the corresponding dynamics of the control loops and the transmission lines, is derived. Different loading conditions are studied by using the ... View full abstract»
• ### 17th IEEE International Conference on Electronics Circuits and Systems(ICECS 2010)
Publication Year: 2010, Page(s): 950
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• ### ISCAS 2010
Publication Year: 2010, Page(s): 951
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• ### IEEE Transactions on Circuits and Systems—I: Regular Papers Information for authors
Publication Year: 2010, Page(s): 952
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• ### IEEE Circuits and Systems Society Information
Publication Year: 2010, Page(s): C3
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## Aims & Scope
The theory, analysis, design, and practical implementations of circuits, and the application of circuit techniques to systems and to signal processing.
Full Aims & Scope
## Meet Our Editors
Editor-in-Chief
Andreas Demosthenous
Dept. Electronic & Electrical Engineering
University College London
London WC1E 7JE, UK
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2018-02-23 23:05:25
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https://www.meritnation.com/cbse-class-8/math/rs-aggarwal-2017/three-dimensional-shapes/textbook-solutions/10_1_3134_5674_215_53202
|
Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 19 Three Dimensional Shapes are provided here with simple step-by-step explanations. These solutions for Three Dimensional Shapes are extremely popular among Class 8 students for Math Three Dimensional Shapes Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 8 Math Chapter 19 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.
Question 1:
Write down the number of faces of each of the following figures:
(i) Cuboid
(ii) Cube
(iii) Triangular prism
(iv) Square pyramid
(v) Tetrahedron
(i) A cuboid has 6 faces, namely ABCD, EFGH, HDAE, GCBF, HDCG and EABF.
(ii) A cube has 6 faces, namely IJKL, MNOP, PLIM, OKJN, LKOP and IJNM.
(iii) A triangular prism has 5 faces (3 rectangular faces and 2 triangular faces), namely QRUT, QTVS, RUVS, QRS and TUV.
(iv) A square pyramid has 5 faces (4 triangular faces and 1 square face), namely OWZ, OWX, OXY, OYZ and WXYZ.
(v) A tetrahedron has 4 triangular faces, namely KLM, KLN, LMN and KMN.
Question 2:
Write down the number of edges of each of the following figures:
(i) Tetrahedron
(ii) Rectangular pyramid
(iii) cube
(iv) Triangular prism
(i) A tetrahedron has 6 edges, namely KL, LM, LN, MN, KN and KM.
(ii) A rectangular pyramid has 8 edges, namely AB, AE, AD, AC, EB, ED, DC and CB.
(iii) A cube has 12 edges, namely PL, LK, KO, OP, MN, NJ, JI, IM, PM, LI, ON and KJ.
(iv) A triangular prism has 9 edges, namely QR, RS, QS, TU, TV, UV, QT, RU, and SV.
Question 3:
Write down the number of vertices of each of the following figures:
(i) Cuboid
(ii) Square pyramid
(iii) Tetrahedron
(iv) Triangular prism
(i) A cuboid has 8 vertices, namely A, B, C, D, E, F, G and H.
(ii) A square pyramid has 5 vertices, namely O, W, X, Y and Z.
(iii)A tertrahedron has 4 vertices, namely K, L, M and N.
(iv) A triangular prism has 6 vertices, namely Q, R, S, T, U and V.
Question 4:
Fill in the blanks:
(i) A cube has ....... vertices, ....... edges and ....... faces.
(ii) The point at which three faces of a figure meet is known as its .......
(iii) A cuboid is also known as a rectangular .......
(iv) A triangular pyramid is called a .......
(i) A cube has 8 vertices, 12 edges and 6 faces.
Vertices: I, J, K, L, M, N, O and P
Edges : IJ, JN, NM, MI, PL, LK, KO, OP, PM, LI, KJ, and ON
Faces : MNJI, POKL, PLIM, OKJN, PONM and LKJI
(ii) The point at which the three faces of a figure meet is known as its vertex.
(iii) A cuboid is also known as a rectangular cube.
(iv) A triangular pyramid is called a tetrahedraon.
Question 1:
Define Euler's relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures.
The Euler's relation for a three dimensional figure can be expressed in the following manner:
Question 2:
How many edges are there in a
(i) cuboid
(ii) tetrahedron
(iii) triangular prism
(iv) square pyramid?
(i) A cuboid has 12 edges, namely AD, DC, CB, BA, EA, FB, HD, DC, CG, GH, HE, and GF.
(ii) A tetrahedron has 6 edges, namely KL, LM, MN, NL , KM and KN.
(iii) A triangular prism has 9 edges, namely QR, RS, SQ, TU, UV, VT, RU, SV and QT.
(iv) A square pyramid has 8 edges, namely OW, OX, OY , OZ , WX, XY, YZ and ZW.
Question 3:
How many faces are there in a
(i) cube
(ii) pentagonal
(iii) tetrahedron
(iv) pentagonal pyramid?
(i) A cube has 6 faces, namely IJKL, MNOP, PLIM , OKJN, POKL and MNJI.
(ii) A pentagonal prism has 7 faces, i.e. 2 pentagons and 5 rectangles, namely ABCDE, FGHIJ, ABGF, AEJF , EDIJ, DCHI and CBGH.
(iii) A tetrahedron has 4 faces, namely KLM, KLN, LMN and KMN.
(iv) A pentagonal pyramid has 6 faces, i.e. 1 pentagon and 5 triangles, namely NOPQM, SNM, SOP, SNO, SMQ and SQP.
Question 4:
How many vertices are there in a
(i) cuboid
(ii) tetrahedron
(iii) pentagonal prism
(iv) square pyramid?
(i) A cuboid has 8 vertices, namely A, B, C, D, E, F, G and H.
(ii) A tetrahedron has 4 vertices, namely K, L, M and N.
(iii) A pentagonal prism has 10 vertices, namely A, B, C, D, E, F, G, H, I and J.
(iv) A square pyramid has 5 vertices, namely O, W, X, Y and Z.
Question 5:
Verify Euler's relation for each of the following:
(i) A square
(ii) A tetrahedron
(iii) A triangular prism
(iv) A square pyramid
Euler's relation is:
(i) A square prism
(There is an error in this question. It should have been a square prism rather than square.)
(ii) A tetrahedron
(iii) A triangular prism
(iv) A square pyramid
View NCERT Solutions for all chapters of Class 8
|
2022-09-25 11:28:25
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http://www.mathnet.ru/php/archive.phtml?jrnid=im&wshow=issue&year=1998&volume=62&volume_alt=&issue=2&issue_alt=&option_lang=eng
|
RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PERSONAL OFFICE
General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS
Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find
On discriminants of multilinear formsV. V. Dolotin 3 Fourier coefficients of piecewise-monotone functions of several variablesM. I. Dyachenko 35 Typical integrable Hamiltonian systems on a four-dimensional symplectic manifoldV. V. Kalashnikov 49 Analytic continuation of functions from invariant subspaces in convex domains of the complex spaceA. S. Krivosheev 75 The Lipschitz constants of the metric $\varepsilon$-projection operator in spaces with given modules of convexity and smoothnessA. V. Marinov 103 Invariant subspaces in some function spaces on symmetric spaces. IIS. S. Platonov 131 Analogues of the Markov and Bernstein inequalities on convex bodies in Banach spacesV. I. Skalyga 169 A boundary-value problem for hyperbolic equationsS. D. Troitskaya 193
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2019-03-26 21:52:36
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http://mathematica.stackexchange.com/questions/39786/how-does-locationtest-choose-its-automatictest
|
# How does LocationTest choose its “AutomaticTest”?
Is there a way of determining how LocationTest chooses its "AutomaticTest"?
Sometimes it's clear from the VerifyTestAssumptions option
sample = BlockRandom[SeedRandom[7];RandomVariate[SkewNormalDistribution@2, 10]];
{LocationTest[sample, Automatic, "AutomaticTest", VerifyTestAssumptions ->{"Normality"}],
LocationTest[sample, Automatic, "AutomaticTest", VerifyTestAssumptions -> "Normality" -> True]}
{SignedRank, T}
other times less so
{LocationTest[sample, Automatic, "AutomaticTest", SignificanceLevel -> 0.05],
LocationTest[sample, Automatic, "AutomaticTest", SignificanceLevel -> 0.0005]}
{SignedRank, T}
( i.e. how can the level of the apriori-decided "burden of proof" affect the resulting sampling distribution? )
Update 1:
Following on from the comments - Perhaps the setting for the significance level is somehow being inherited in checks for normality i.e.
{DistributionFitTest[sample, NormalDistribution[],"ShortTestConclusion", SignificanceLevel -> 0.05],
DistributionFitTest[sample, NormalDistribution[],"ShortTestConclusion", SignificanceLevel -> 0.0005],
DistributionFitTest[sample, NormalDistribution[], "PValue"]}
{Reject,Do not reject,0.00836514}
The critical point is not around the previous p-value instead appearing just after 0.03
Plot[If[LocationTest[sample, Automatic, "AutomaticTest", SignificanceLevel -> x] === "T", 1, 0], {x, 0.01, 0.05}]
If so, perhaps some sort of Bonferroni correction is taking place?
Update 2:
From the answer from Andy Ross, the relevant test is not
DistributionFitTest[sample, NormalDistribution[]]
(*0.00836514*)
but rather
DistributionFitTest[sample]
(*0.0307822*)
indicating that indeed this significance level is being filtered down. This doesn't however, provide a systematic answer to determining how this choice is made in general. In this case, the logic used by LocationTest can be deduced because it is a standard example but applying NHST can be a bit of an art that depends heavily on circumstance for its ultimate interpretation. Hence, having a black box for this logic seems limiting in perhaps a far more consequential way than say for other "more deterministic" and clear-cut algorithms.
Also, what is the rationale behind this inheritance? - in NHST machinery, the significance level has a specific meaning in relation to Type 1/Type 2 errors, power, experimental context etc with the theory being predicated on a test's conditions being apriori satisfied without concession to their own uncertainty (e.g. despite a p-value being returned, is an error message for a failed test of normality in say TTest invocations counted as a false negative/positive in defining a Type 1/Type2 error?).
sample2 = {6.1, -8.4, 1, 2, 0.75, 2.9, 3.5, 5.1, 1.8, 3.6, 7., 3, 9.4,
7.5, -6};
TTest@sample2
(* TTest::nortst: At least one of the p-values in {0.0903246}, resulting from a test for
normality, is below 0.05. The tests in {T} require that the data is normally distributed. >> *)
(* 0.0498525 *)
The warning above doesn't seem to fit since 0.0903246 is not below 0.05 but explicitly set the significance level to the default 5% however, and the warning message disappears?
TTest[sample2, SignificanceLevel -> 0.05]
(* 0.0498525 *)
At any rate, in general it is quite conceivable that a different significance level for the overarching test might be needed in comparison with the significant level required for an apriori test checking the data's normality, symmetry, heterogeneity etc (n.b. also how are all these combined from the initial setting?)
Update 3: To be a little more systematic: Define a function ShowSignificanceLevelThresholds to show those significant levels at which LocationTest changes its choice of "AutomaticTest" (the "HighlightAutomaticTest" option highlights this choice - both are defined at the post's end).
LocationTest[sample2, Automatic, {"TestDataTable", All},"HighlightAutomaticTest" -> True]
// ShowSignificanceLevelThresholds
As deduced, the first transition appears due to the Koglomorov-Smirnof test of normality and its p-value of 0.09.
DistributionFitTest[sample2, Automatic, {"TestDataTable", All},
"HighlightAutomaticTest" -> True]
The second transition at a significance level 0.604 would appear to involve the violation of a symmetry assumption (observable by manual setting the "Symmetry" and "Normality" options to in the "VerifyTestAssumption" option) so that a related question becomes what Test is used by default to test for symmetry?
While a high significance level of 0.604 is unlikely to have much practical significance in this particular case, this may not apply more generally. Again, the unknown effects of passing a significance level down to diagnostic tests is not straightforward and suggests caution in applying LocationTest and its ilk together with scope for further improvements (discussed in more detail here).
(*Needs to be evaluated twice*)
ALocationTest[sample_, x_, {tableType_, All}, y___ : OptionsPattern] /;
TrueQ@("HighlightAutomaticTest" /. {y}) :=
With[{\[ScriptCapitalH]2 =
LocationTest[sample, x, "HypothesisTestData",
FilterRules[{y}, Except["HighlightAutomaticTest"]]]},
Module[{AT = \[ScriptCapitalH]2["AutomaticTest"],
AllTests = \[ScriptCapitalH]2["AllTests"],
TableDataType = StringDrop[tableType, -5],(*Dropping "Table"*)
TableData = \[ScriptCapitalH]2[{TableDataType, All}];
pos = 1 + Position[AllTests, AT][[1, 1]];
Switch[TableDataType, "TestData", {" ", "Statistic", "P-Value"},
"TestStatistic", {" ", "Statistic"},
"PValue", {" ", "P-Value"}];
Sequence @@
Flatten[Join[{#1}, {#2}]] &, {AllTests, TableData}]},
Alignment -> Left,
Background -> {Automatic, pos -> GrayLevel@0.9},
Dividers -> {2 -> True, 2 -> True},
FrameStyle -> Directive[GrayLevel@.7]] // Text]];
Unprotect@LocationTest;
PrependTo[DownValues@LocationTest,
DownValues[ALocationTest] /. ALocationTest -> LocationTest];
Protect@LocationTest;
AVarianceTest[sample_, x_, {tableType_, All}, y___ : OptionsPattern] /;
TrueQ@("HighlightAutomaticTest" /. {y}) :=
With[{\[ScriptCapitalH]2 =
VarianceTest[sample, x, "HypothesisTestData",
FilterRules[{y}, Except["HighlightAutomaticTest"]]]},
Module[{AT = \[ScriptCapitalH]2["AutomaticTest"],
AllTests = \[ScriptCapitalH]2["AllTests"],
TableDataType = StringDrop[tableType, -5],(*Dropping "Table"*)
TableData = \[ScriptCapitalH]2[{TableDataType, All}];
pos = 1 + Position[AllTests, AT][[1, 1]];
Switch[TableDataType, "TestData", {" ", "Statistic", "P-Value"},
"TestStatistic", {" ", "Statistic"},
"PValue", {" ", "P-Value"}];
Sequence @@
Flatten[Join[{#1}, {#2}]] &, {AllTests, TableData}]},
Alignment -> Left,
Background -> {Automatic, pos -> GrayLevel@0.9},
Dividers -> {2 -> True, 2 -> True},
FrameStyle -> Directive[GrayLevel@.7]] // Text]];
Unprotect@VarianceTest;
PrependTo[DownValues@VarianceTest,
DownValues[AVarianceTest] /. AVarianceTest -> VarianceTest];
Protect@VarianceTest;
y___ : OptionsPattern] /;
TrueQ@("HighlightAutomaticTest" /. {y}) :=
With[{\[ScriptCapitalH]2 =
DistributionFitTest[sample, x, "HypothesisTestData",
FilterRules[{y}, Except["HighlightAutomaticTest"]]]},
Module[
{AT = \[ScriptCapitalH]2["AutomaticTest"],
AllTests = \[ScriptCapitalH]2["AllTests"],
TableDataType = StringDrop[tableType, -5],
(* Dropping "Table" *)
},
TableData = \[ScriptCapitalH]2[{TableDataType, All}];
pos = 1 + Position[AllTests, AT][[1, 1]];
"TestData", {" ", "Statistic", "P-Value"},
"TestStatistic", {" ", "Statistic"},
"PValue", {" ", "P-Value"}
];
Grid[{
Sequence @@
}, Alignment -> Left,
Background -> {Automatic, pos -> GrayLevel@0.9},
Dividers -> {2 -> True, 2 -> True},
FrameStyle -> Directive[GrayLevel@.7]] // Text
]];
Unprotect@DistributionFitTest;
PrependTo[DownValues@DistributionFitTest,
Protect@DistributionFitTest;
SetAttributes[SignificanceLevelThresholds, HoldFirst];
SetAttributes[ShowSignificanceLevelThresholds, HoldFirst];
SignificanceLevelThresholds[test_[A__]] :=
With[{firstTest = test[A, SignificanceLevel -> 0.0001]},
Last /@
Split[Table[{i, test[A, SignificanceLevel -> i]}, {i, 0.001, .999,
0.001}], Last@#1 === Last@#2 &]];
ShowSignificanceLevelThresholds[test_[A__]] :=
Module[{NForm},
NForm[n_] := If[MemberQ[{0, 1}, n], n, NumberForm[n, {4, 3}]];
With[{SLT = SignificanceLevelThresholds[test[A]]},
With[{intervals =
StringForm[
"1 < \[FilledSquare] < 2", #[[1]] // NForm, #[[2]] //
NForm] & /@
Partition[Prepend[SLT[[All, 1]] /. .999 -> 1, 0], 2, 1],
TestOutputs = SLT[[All, 2]]},
Grid[{{HoldForm@
test[A, SignificanceLevel -> \[SelectionPlaceholder]] //
Style[#, Bold] &,
Sequence @@ ConstantArray[SpanFromLeft, Length@SLT - 1]},
intervals, TestOutputs},
Spacings -> {2, {1 -> 2, 2 -> 2, 3 -> 1, 4 -> 1}},
Background -> {None, 2 -> LightBlue},
ItemStyle -> {None, 2 -> Directive[15]},
Dividers -> {{True, True, 3, 4}, {True, True, False, True}},
ItemSize -> 16, Frame -> True]]]]
-
Wrt to your last example: This is at least partly documented in the last example of the Possible Issues section of the LocationTest doc page. The significance level has an impact on internal diagnosis tests (in this case a test on equal variance) which changes the degrees of freedom. – Sjoerd C. de Vries Jan 4 '14 at 9:20
Yes, and curiously LocationTest[sample, Automatic, "AutomaticTest", SignificanceLevel -> 0.05, VerifyTestAssumptions -> #] & /@ {"Normality", "EqualVariance", "EqualVariance" -> True, "EqualVariance" -> False} gives {"SignedRank", "T", "T", "T"} but in this example there is only one sample so I'm not sure what variances are being checked for equality? – Ronald Monson Jan 4 '14 at 11:00
In the first case you are saying "check for normality" in the remaining examples you are saying "ignore normality and just check for equal variances". Since there is only one sample the equal variances test has no impact on the test that is chosen. – Andy Ross Jan 4 '14 at 17:37
With that in mind, there should probably be a message saying the equal variance test is being ignored... – Andy Ross Jan 4 '14 at 17:41
Yes but one might have expected that there is an outcome of the variance check that results in "SignedRank" still being chosen. I.e. otherwise we are moving into Heisenberg territory in which the mere process of "checking" equal variances becomes pivotal (given NHST's dichotomous tradition of being either true or false). At any rate, I agree this is a red herring since there is only one sample. Perhaps what is going on ... see addition to question – Ronald Monson Jan 5 '14 at 0:21
With a single sample the test for normality is the deciding factor in what test to choose.
The key here is that DistributionFitTest is not testing against NormalDistribution[0,1] by default. It is testing against the family of normal distributions.
DistributionFitTest[sample]
(*0.0307822*)
DistributionFitTest[sample, NormalDistribution[]]
(*0.00836514*)
`
The T test is chosen until the significance level is greater than the p-value for the test for normality.
-
Yes I similarly overlooked this point and it does seem to confirm that this significance level is being inherited from the original invocation. – Ronald Monson Jan 22 '14 at 15:04
|
2015-03-29 23:56:30
|
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|
https://gt.rstudio.com/reference/fmt_time.html
|
Format input values to time values using one of five presets. Input can be in the form of POSIXt (i.e., date-times), character (must be in the ISO 8601 forms of HH:MM:SS or YYYY-MM-DD HH:MM:SS), or Date (which always results in the formatting of 00:00:00).
Once the appropriate data cells are targeted with columns (and, optionally, rows), we can simply apply a preset time style to format the times. The following time styles are available for use (all using the input time of 14:35:00 in the example output times):
1. "hms": 14:35:00
2. "hm": 14:35
3. "hms_p": 2:35:00 PM
4. "hm_p": 2:35 PM
5. "h_p": 2 PM
We can use the info_time_style() function for a useful reference on all of the possible inputs to time_style.
## Usage
fmt_time(data, columns, rows = everything(), time_style = 2, pattern = "{x}")
## Arguments
data
A table object that is created using the gt() function.
columns
The columns to format. Can either be a series of column names provided in c(), a vector of column indices, or a helper function focused on selections. The select helper functions are: starts_with(), ends_with(), contains(), matches(), one_of(), num_range(), and everything().
rows
Optional rows to format. Providing everything() (the default) results in all rows in columns being formatted. Alternatively, we can supply a vector of row captions within c(), a vector of row indices, or a helper function focused on selections. The select helper functions are: starts_with(), ends_with(), contains(), matches(), one_of(), num_range(), and everything(). We can also use expressions to filter down to the rows we need (e.g., [colname_1] > 100 & [colname_2] < 50).
time_style
The time style to use. Supply a number (from 1 to 5) that corresponds to the preferred time style, or, provide a named time style ("hms", "hms_p", "h_p", etc.). Use info_time_style() to see the different numbered and named time presets.
pattern
A formatting pattern that allows for decoration of the formatted value. The value itself is represented by {x} and all other characters are taken to be string literals.
## Value
An object of class gt_tbl.
## Details
Targeting of values is done through columns and additionally by rows (if nothing is provided for rows then entire columns are selected). Conditional formatting is possible by providing a conditional expression to the rows argument. See the Arguments section for more information on this.
## Examples
Use exibble to create a gt table. Keep only the date and time columns. Format the time column to have times formatted as hms_p (time style 3).
exibble %>%
dplyr::select(date, time) %>%
gt() %>%
fmt_time(
columns = time,
time_style = 3
)
Use exibble to create a gt table. Keep only the date and time columns. Format the time column to have mixed time formats (times after 16:00 will be different than the others because of the expressions used in the rows argument).
exibble %>%
dplyr::select(date, time) %>%
gt() %>%
fmt_time(
columns = time,
rows = time > "16:00",
time_style = 3
) %>%
fmt_time(
columns = time,
rows = time <= "16:00",
time_style = 4
)
## Function ID
3-11
Other Format Data: data_color(), fmt_bytes(), fmt_currency(), fmt_datetime(), fmt_date(), fmt_engineering(), fmt_fraction(), fmt_integer(), fmt_markdown(), fmt_number(), fmt_partsper(), fmt_passthrough(), fmt_percent(), fmt_scientific(), fmt(), sub_large_vals(), sub_missing(), sub_small_vals(), sub_zero(), text_transform()
|
2022-05-23 19:55:43
|
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|
https://webwork.maa.org/moodle/mod/forum/discuss.php?d=3803
|
## WeBWorK Problems
### Problems with NAMED_ANS_RADIO in PGbasicmacros.pl
by Andrew Parker -
Number of replies: 1
I found an error in generating TeX code when using parserRadioButtons.pl
The problem arises when attempting to use answers that containing "$" - both from using contextCurrency.pl or by including$DOLLAR in the multiple choice responses. (The latter is not recommended, as the correct answer will still return incorrect to the student - which is a separate problematic issue, though fixed by using "Currency".)
When WeBWorK attempts to generate the TeX file for an assignment containing such a problem, the code for the multiple choice responses gets converted to a double-escaped "\\$" instead of "\$" as one would expect. I'm not sure where the extra escape character is coming from either.
I hacked the problem by inserting "$tag =~ s/\\\$/\$/; into the code for NAMED_ANS_RADIO and NAMED_ANS_RADIO_EXTENSION in PGbasicmacros.pl, which had the result of producing a properly functioning TeX file. I would have used s/\\\\\$/\\\$/; but this had no effect - suggesting that the additional escape character is being added further down the line somewhere? So, I suspect that this is an inappropriate place for this hack and perhaps some code elsewhere should be checking whether or not this "$" is already escaped...
|
2022-05-23 01:52:08
|
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|
http://mathoverflow.net/feeds/question/85031
|
A positive semidefinite programming problem - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T14:22:53Z http://mathoverflow.net/feeds/question/85031 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85031/a-positive-semidefinite-programming-problem A positive semidefinite programming problem KOMA 2012-01-06T05:49:52Z 2012-01-07T05:07:20Z <p>Dear all,</p> <p>I've got a SDP problem as follows:</p> <p>$\min_{{\bf H}\succeq0}\quad trace({\bf H}) - {\bf a}^{\top}{\bf H}{\bf b}$,</p> <p>where ${\bf a}$ and ${\bf b}$ are two constant vectors. May somebody tell me how to solve this SDP problem? Thank you very much in advance.</p> <p>[Added] Thanks for Suvrit to point out some issues. I add one more parameter $\lambda$ (to be pre-defined) and assume ${\bf b}={\bf a}$ for the second term in the above problem as:</p> <p>$\min_{{\bf H}\succeq0}\quad trace({\bf H}) - \lambda{\bf a}^{\top}{\bf H}{\bf a}$.</p> http://mathoverflow.net/questions/85031/a-positive-semidefinite-programming-problem/85043#85043 Answer by S. Sra for A positive semidefinite programming problem S. Sra 2012-01-06T11:06:57Z 2012-01-06T11:06:57Z <p>Your problem has no solution. Here is why.</p> <p>Let $H$ be $2 \times 2$. Let $a=(2, 0)$ and $b=(1, 0)$. Then, since $a^THb=\mbox{tr}(Hab^T)$, the objective function of your problem can be rewritten as $\mbox{tr}(H-Hab^T) = \mbox{tr}(HC)$, where $$C = I-ab^T = \begin{bmatrix} -1 & 0\\ 0 & 1\end{bmatrix}.$$ Now you can see that if we set \begin{equation*} H=\begin{bmatrix} \alpha & 0\\ 0 & 0 \end{bmatrix}, \end{equation*} then as $\alpha\to\infty$, your objective function goes to $-\infty$. Thus, in general, there is no solution. </p> <p>Even if you let $a=b$, the same example above shows that there is no solution. You need to restrict $H$ to lie in a compact set.</p>
|
2013-05-23 14:22:58
|
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|
http://math.stackexchange.com/questions/203328/is-there-an-analytical-solution-to-the-following-integral/203332
|
# Is there an analytical solution to the following integral:
Is there a nice solution to this integral: $$\int\frac{-a^2 da} {C^2 \sqrt{1-\frac{a^2}{C^2}}}$$
-
You can use the trigonometric substitution $a = C \sin{\theta}$, $da = C \cos{\theta} \, d\theta$. However, you need to have limits of integration because your integrand is not defined for all values of $a$. – Christopher A. Wong Sep 27 '12 at 7:34
Yes. For integrals you can always go to wolfram|alpha and they'll tell you what to do. The solution is
$$\frac{1}{2} \left(-a \sqrt{1-\frac{a^2}{c^2}}+c \text{ArcSin}\left[\frac{a}{c}\right]\right)$$
-
Take $a=C\sin(\theta)$ so your integral became: $$\frac{-1}{C}\int \sin^2(\theta)d\theta$$ which is elementary.
-
Yes. You should try some trigonometric substitution (or install sympy, then can you answer by yourself. A related (simplified= integral:
In [3]: integrate( x**2/sqrt(1-x**2), x)
Out[3]:
⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
╱ 2
x⋅╲╱ - x + 1 asin(x)
- ─────────────── + ───────
2 2
In [4]:
-
Yes. To solve it you need to do a trig substitution.
-
# Hint
Try substitution $a=C\sin{t}$
-
|
2015-12-02 03:33:24
|
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|
http://aas.org/archives/BAAS/v25n2/aas182/abshtml/S211.html
|
CRAB WISP SPECTRA
Session 2 -- Planetary Nebula and Supernova Remnants
Display presentation, Monday, 9:20-6:30, Pauley Room
## [2.11] CRAB WISP SPECTRA
R.W.Romani, B.HP.Gilroy (Stanford), J.M.Cordes (Cornell)
The bulk of the energy lost by spinning, magnetized neutron stars is believed to carried off in a relativistic wind of particles and fields. The particle content of this wind is, however, very poorly known. Instances in which the pulsar wind interacts with surrounding material offer perhaps the best opportunities to unravel the wind physics and probe the underlying pulsar accelerator. We report here on analyses of optical/near-IR spectra of the the Crab pulsar's wind as it passes through the `wisps' and merges with the surrounding nebula. These wisps have been inferred to be the location of the termination shock of the freely expanding flow from the nebula. They represent a possible site for conversion of the high $\gamma$ output of the pulsar magnetosphere to the $\sigma \sim 0.003$, power-law energy distribution magnetized pair plasma believed to support the bulk of the Crab's continuum output. Spectral variation in the continuum synchrotron radiation through the wisps constrain the acceleration of the pairs which dominate the downstream plasma and can be used to probe for a possible baryonic component in the pulsar's accelerated particle beam.
|
2015-10-13 07:40:18
|
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|
https://codegolf.stackexchange.com/questions/140794/im-thinking-of-a-number-robbers-thread/141028#141028
|
# I'm thinking of a number (Robber's thread)
In this challenge cops will think of a positive integer. They will then write a program or function that outputs one value when provided the number as input and another value for all other positive integer inputs. Cops will then reveal the program in an answer keeping the number a secret. Robbers can crack an answer by finding the number.
Your job as robbers is to find that number. Once found you can make an answer here detailing the number and how you found it. You should link the original answer being cracked in your answer.
Your score will be the number of cracks with more being better.
• Are "hunches" good enough to post here, instead of definite proof? Aug 28, 2017 at 23:29
• @OlivierGrégoire You should know that your answer works for sure. Aug 28, 2017 at 23:31
• But I must know it, I don't have to prove it with the program given in the cops thread? Can I prove it otherwise, using math for instance? Aug 28, 2017 at 23:35
• @OlivierGrégoire Sure that's fine. As long as you know your answer is correct. You need not actually run the program if it takes too long. Aug 28, 2017 at 23:35
# Perl 6, by Ramillies
11
The function series($x) is simply the first 108 terms of the Taylor series for e^x evaluated at i*(x % 8*π). Since e^2πi = 1, this reduces to simply e^ix: the % 8*π serves only to bound the error of the truncated series. The ∫ function integrates the provided Callable in the interval [0,2π] using the trapezoid method. The integrand in question is (e^ix)^11/(e^inx), or simply e^(11-n)ix. This integrates to 0 in that interval for all n != 11. At n = 11, the integrand reduces to simply 1. Hence the answer is 11, and the desired output is 6.28. While 11 is the only answer in theory, the sampling in the integral is imperfect. Consequently, any integer of the form 87931k+11 should work. • Very nicely done! You surprised me with the last paragraph however. I'll put it to some thought. Aug 29, 2017 at 9:35 • Ah, I now see the problem. I'm afraid I can't remove it however (even if I use intervals of different widths, you would use the product of the widths as a coefficient for your k)... Thanks for pointing it out. Aug 29, 2017 at 9:49 # Java, by okx Note: the original challenge to which this post answers has been deleted, it's however still accessible with the link to anyone having the privilege to see deleted answers. The explanations below include what the challenge was about. Number: 18 The code is effectively looking for primes with the form 112n-2. By this Wikipedia list, we know that the 20th largest known prime number has 2,900,832 digits. No prime with the form 112n-2 are in that list, so that digit number will be our limit. All numbers of the form 112n-2 that have at most that many digits have this constraint: n < 22. Factordb tells us that 11222-2 has 4,367,918 digits. This is proof enough. The code by okx limits us to n above 6. So, let's do the list: 112n-2 is factorizable for n = 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20 and 21 (factors proofs are on factordb.com and wolfram alpha; factordb has some proofs that wolfram alpha hasn't and vice-versa). The only value n for which we can't prove the factorization is 18 (factordb, WolframAlpha). So (a) if there is a prime number of the form 112n-2 with n > 6, then (b) 6 < n < 22, and (c) I proved each number with such n is composite except for 18, so (d) the prime we're looking for has n = 18. Note that I don't exclude that 11218-2 is composite. I haven't proved that that number is a prime: I only proved that if the OP thought about that number, it can only be 18. If that number is indeed a prime, congrats to okx for finding it :-) ### However There are no proof that 11218-2 is the only number, though. It's the only number in the range of numbers for which we can currently prove the primality. So I don't exclude the fact that one day someone might prove that 11251-2 or 112124-2 is prime. I therefore believe that the original entry by okx is invalid because there are no such proof that for n between 19 and the (231-1)231-1 (the theoretical limit of Java's BigInteger), there are no other primes. • 11^(2^51) - 2 is divisible by 7. Or any odd n. Aug 29, 2017 at 9:35 • Sorry guys, I bruteforced my way here. I haven't analyzed in details ;) Aug 29, 2017 at 10:43 • @JollyJoker that's just from the binomial theorem: (10+1)^n = sum (nCr) 10^r Aug 29, 2017 at 11:34 • Damn, the original challenge got deleted. Am I required to delete this answer as well? Aug 29, 2017 at 14:23 • @OlivierGrégoire I think you should be okay. The solution took the same amount of effort, regardless of the original post. Aug 29, 2017 at 19:11 # Python 3, Erik Brody Dreyer ### Number: 105263157894736842 Try it online! ### How? Everyone's favorite tool: OEIS! 1. Go to oeis.org 2. Search "last digit first doubles number" 3. Find Entry A087502 entitled Smallest positive integer which when written in base n is doubled when the last digit is put first. 4. Find the base 10 entry (105263157894736842) 5. Confirm it works • Can't comment on Erik's post due to lack of rep. Welp, can only hope he sees this :) Aug 29, 2017 at 0:47 • Not sure if I would have thought of OEIS in this case, but just a few days ago I saw this Aug 29, 2017 at 14:14 # Tampio, fergusq Number: 27 The program prints nolla for 27 and "1" negatiivisena for all other inputs. It times out on TIO, unfortunately, but works offline. Whew, this was a fun one to work through. Wiktionary and this Finnish dictionary I found online actually helped a surprising amount, as a lot of Tampio syntax relies on inflection. I first tried translating the program into Haskell-like pseudocode, but the "case system" of Tempio and how function calls worked kept tripping me up. Eventually, I ended up running all of the code from the definition of sata downward, which gave me surprisingly easily that sata == 55, and funktio wasn't difficult to reverse engineer from there as it was simple arithmetic that could be deduced from trial and error. • Can someone help me comment this on the original post, by the way? My rep is way too low for that - thanks! Aug 29, 2017 at 16:35 • I've left a comment on the original. Aug 29, 2017 at 16:37 • @WheatWizard thanks! Aug 29, 2017 at 16:39 # JavaScript, by Eli R The number is 7464822360768511 I first disabled the anti-debugging function (by overwriting Function.prototype.constructor to a function with evals any code except debugger) then debugged the guess function by stepping into it. From what I understood the guess function initializes a random number generator on a fixed seed then generate a random number and compare it to the input. As the input isn't used in the random number generation it can be ignored allowing to skip directly to the result. • Amazing job. That's exactly how it works. Aug 29, 2017 at 15:03 # Jelly, Erik the Outgolfer's answer Number: 134 The following program: 5ȷ2_c⁼“ḍtṚøWoḂRf¦ẓ)ṿẒƓSÑÞ=v7&ðþạẆ®GȯżʠṬƑḋɓḋ⁼Ụ9ḌṢE¹’ can be cracked using the number 134. This outputs 0 for all numbers except for 134, which gives 1. Try it online! # How did I find it? TBH, I have no idea how it works. I have added Ç€G at the end and mapped over [1...1000] to see where the 1 is. Then, I ran script to count the number of zeros before the 1. • This just checks that (500-x) choose (x) is equal to 11087887200298332182662619677215658902328839774316188391031942332464244226619146288405430113510542767630, which it is for x=134 (as you found). Aug 29, 2017 at 3:01 # Ly, LyricLy Answer: 239 I already wrote two Ly programs, so this wasn't too difficult. I think I would have somehow used the result from the loop in case someone tries to remove it. BTW, the fragment nI means that it doesn't always terminate successfully. # Python 2, Sisyphus print~~[all([c[1](c[0](l))==h and c[0](l)[p]==c[0](p^q) for c in [(str,len)] for o in [2] for h in [(o*o*o+o/o)**o] for p,q in [(60,59),(40,44),(19,20),(63,58),(61,53),(12,10),(43,42),(1,3),(35,33),(37,45),(17,18),(32,35),(20,16),(22,30),(45,43),(48,53),(58,59),(79,75),(68,77)]] + [{i+1 for i in f(r[5])}=={j(i) for j in [q[3]] for i in l} for q in [(range,zip,str,int)] for r in [[3,1,4,1,5,9]] for g in [q[1]] for s in [[p(l)[i:i+r[5]] for p in [q[2]] for i in [r[5]*u for f in [q[0]] for u in f(r[5])]]] for l in s + g(*s) + [[z for y in [s[aprint~~[all([c[1](c[0](l))==h and c[0](l)[p]==c[0](p^q) for c in [(str,len)] for o in [2] for h in [(o*o*o+o/o)**o] for p,q in [(60,59),(40,44),(19,20),(63,58),(61,53),(12,10),(43,42),(1,3),(35,33),(37,45),(17,18),(32,35),(20,16),(22,30),(45,43),(48,53),(58,59),(79,75),(68,77)]] + [{i+1 for i in f(r[5])}=={j(i) for j in [q[3]] for i in l} for q in [(range,zip,str,int)] for r in [[3,1,4,1,5,9]] for g in [q[1]] for s in [[p(l)[i:i+r[5]] for p in [q[2]] for i in [r[5]*u for f in [q[0]] for u in f(r[5])]]] for l in s + g(*s) + [[z for y in [s[i+a][j:j+r[0]] for g in [q[0]] for a in g(r[0])] for z in y] for k in [[w*r[0] for i in [q[0]] for w in i(r[0])]] for i in k for j in k] for f in [q[0]]]) for l in [int(raw_input())]][0] Try it online! Answer: 126437958895621473374985126457193862983246517612578394269314785548769231731852649 ## Explanation Slightly less convoluted: print~~[all( [len(str(l))==81 and str(l)[p]==str(p^q) for p,q in [(60,59),(40,44),(19,20),(63,58),(61,53),(12,10),(43,42),(1,3),(35,33),(37,45),(17,18),(32,35),(20,16),(22,30),(45,43),(48,53),(58,59),(79,75),(68,77)] ] + [{i+1 for i in range(9)}=={int(i) for i in l} for s in [[str(l)[9*u:9*u+9] for u in range(9)]] for l in s + zip(*s) + [[z for y in [s[i+a][j:j+3] for a in range(3)] for z in y] for k in [[w*3 for w in range(3)]] for i in k for j in k]]) for l in [int(raw_input())]][0] Try it online! Firstly, this part: [len(str(l))==81 and str(l)[p]==str(p^q) for p,q in [(60,59),(40,44),(19,20),(63,58),(61,53),(12,10),(43,42),(1,3),(35,33),(37,45),(17,18),(32,35),(20,16),(22,30),(45,43),(48,53),(58,59),(79,75),(68,77)] ] checks if the sudoku is in the following form: .2.|...|... ...|6..|..3 .74|.8.|... ----------- ...|..3|..2 .8.|.4.|.1. 6..|5..|... ----------- ...|.1.|78. 5..|..9|... ...|...|.4. Then this part checks for validity: [{i+1 for i in range(9)}=={int(i) for i in l} for s in [[str(l)[9*u:9*u+9] for u in range(9)]] for l in s + zip(*s) + [[z for y in [s[a][j:j+3] for a in range(3)] for z in y] for k in [[w*3 for w in range(3)]] for i in k for j in k]] # Pyth, Mr. Xcoder hqQl+r@G7hZ@c." y|çEC#nZÙ¦Y;åê½9{ü/ãѪ#¤ ØìjX\"¦Hó¤Ê#§T£®úåâ«B'3£zÞz~Уë"\,a67Cr@G7hZ Try it here. Number: 9 • Well done! It lived long Aug 28, 2017 at 18:00 • @Mr.Xcoder I just removed the hqQ part :p Aug 28, 2017 at 18:06 • That's weird. I tried 9 but it didn't work. That was before it was temporarily deleted, though, so it may not originally have been 9. Aug 28, 2017 at 19:00 • @Shaggy Me too, but after it was undeleted. Aug 28, 2017 at 19:03 # Swift 3, TheIOSCoder Number: 387849. This returns 222 for the number above, and 212 for others. Test Here. # How? The relation is quite obvious: .pi*123456.0 multiplies 3.1415... by 123456.0 and converts it to an Integer. This means it is equal to 387848. Then, it checks if the parameter equals the number above incremented by 1 (n==1+...). The value is 387848 + 1, which is 387849... # Java, Sleafar 23 The program traces n iterations of a fractal, and checks whether a specific point is removed in the nth iteration. In each iteration, each segment is replaced by eight smaller segments in the following pattern: + | +-+ | +-+-+ | +-+ | + Since no points are ever added to the line y=.5 after the first iteration, I only had to handle the set of points included along this line. This set is similar to the construction of the Cantor set, but with the middle half removed instead of the middle third. The program I used to crack it: import java.math.BigDecimal; public class Main { public static int f(BigDecimal x) { BigDecimal[] result = x.divideAndRemainder(BigDecimal.ONE); if (result[0].compareTo(BigDecimal.ZERO) == 0 || result[0].compareTo(BigDecimal.valueOf(3)) == 0) { return 1+f(result[1].multiply(BigDecimal.valueOf(4))); } return 0; } public static void main(String[] args) { BigDecimal x = new BigDecimal(args[0]); System.out.println(f(x)); } } Try it online! • This is correct, congratulations! Aug 30, 2017 at 6:17 # Haskell, flawr I think the number is 12018. I found it by defining in PARI/GP f(x,k)=1/x^2-1/x^(2-1/k) and g(k)=sumpos(x=1,f(x,k))-sumpos(x=12345679,f(x,k)) and some binary searching. I don't like that one could trivially transform the program into one that returns the number and uses the same time and memory as the original program needs for any input. # Brain-Flak, Nitrodon The number is: 1574 Try it online! Here's the program I use to crack it n!(0:_)=n n!a=(n+1)!zipWith(+)a(tail a++[0]) main=print$0![45646,253224,392678,8676,-24]
Try it online!
# Java, user902383
The secret number is 3141592
Explanation:
After expanding all the \u00xx escapes, you get:
public class Mango {
static void convert(String s){for(char c : s.toCharArray()){ System.out.print("\\u00"+Integer.toHexString(c));}}
public static void main(String[] args) {int x = Integer.parseInt(args[0]);
double a= x/8.-392699;double b = Math.log10((int) (x/Math.PI+1))-6;
System.out.println((a/b==a/b?"Fail":"OK" ));
}}
(the convert method isn't used).
This computes some floating point math on the result, and then requires that a/b isn't equal to itself. The number for which that is true is nan, which is produced by 0/0. It turns out that if a is 0, then b is log10(0/pi + 1) which is also 0, so a has to be 0 and x has to be 392699*8.
# Python 3, user71546
def check(x):
if x < 0 or x >= 5754820589765829850934909 or pow(x, 18446744073709551616, 5754820589765829850934909) != 2093489574700401569580277 or x % 4 != 1:
return "No way ;-("
return "Cool B-)"
print(check(141421356237))
Try it online!
The number is 141421356237.
The other three numbers which satisfy the first two conditions are 1459265341309891512760823, 5754820589765688429578672, and 4295555248455938338174086.
### How I solved it
The gist of this challenge is to find the number that meets the following, given the prime p = 5754820589765829850934909 and a value a = 2093489574700401569580277:
• 0 <= x < p
• x ** (2 ** 64) % p == a
• x % 4 == 1
The second one can be rephrased to "find the modular square root of modular square root of ... (64 times) of a modulo p."
Since the given prime is 5 modulo 8, we can use the following formula from the above link (though I couldn't find the reference that supports it):
$v = (2a)^{(p-5)/8} \mod p$
$i = 2av^2 \mod p$
$r = av(i-1) \mod p$
$r' = p - r$
Then we have two output values r and r' for an input value a. But not every number has such a square root, so we have to check if r*r % p == a is actually met.
So I wrote a quick J script to find the 64th modular square roots.
p =: 5754820589765829850934909x
a =: 2093489574700401569580277x
powmod =: p&|@^
for. i.64 do.
v =: p | (2*a) powmod (p-5)%8
i =: p | 2*a*v*v
x =: p | a*v*i-1 NB. Apply the above formula
a =: (a=p|x*x) # x NB. Filter by actually being the modular square root
a =: a, p-a NB. Concat r with r'
a
end.
)
res =: f ''
Try it online!
res has the four values shown above; the last filtering by modulo 4 gives the answer.
• Link to "module square root" is dead. Sep 20, 2019 at 23:43
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2023-03-27 17:04:39
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http://wiki.lazarus.freepascal.org/Site_Feedback
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# Site Feedback
English (en) español (es) français (fr) magyar (hu) Bahasa Indonesia (id) português (pt) Türkçe (tr)
## Older requests
• Add some kind of chapters/tree/index on the main page, searching for various documents is harder without it.
• You could add a few links on the main Lazarus website to various sections in the Lazarus-CCR(Component and Code Repository) like Components, Examples, Online Docs, Tutorials.
• The Components section should contain various components that are not used for "normal" programming or have similar behaviour to existing IDE components, maybe also platform specific components that can not be implemented in a CrossPlaform fashion.
• The Examples section should contain as many useful examples as possible, many people report that examples made them appreciate the "power" of other RAD tools like Delphi/Kylix, C++Builder, JBuilder and even Visual Basic, so i think examples will also help the Lazarus project too in becomeing the most widely used tool by OpenSource and Commercial software developers.
• The Online Docs section should contain FCL, LCL, IDE, Compiler, Classes organisation and description, various popular API calls, even some OS specific calls.
• The Tutorials section is one of the most important parts for productivity, it should cover various aspects of programming ranging from Console, GUI, Database, Component Design, IDE/Compiler Enhancing to Hardware I/O and even Multimedia, 3D Graphics, Audio, Game Design.
• The IDE could also have some links in the Help menu.
• The documentation of RTL, FCL and LCL could contain hints on dependencies of functions which will only work after other specific functions have been called (for example: "InitKeyboard" has to be called before "PollKeyEvent" can work as suggested). Otherwise it could be difficult to track errors down using the documentation provided.
The lazarus documentation is located on the lazarus subversion on the directory lazarus/docs. The RTL and FCL documentation is located at http://svn.freepascal.org/svn/fpcdocs/trunk/. It is composed of XML files. Please send a patch improving the documentation in the way you suggested and it will be applied.
## IRC ?
Nowhere on the main site is something written about contact via IRC or something.
It is a bit hidden, but is there: http://www.lazarus.freepascal.org/modules.php?op=modload&name=News&file=article&sid=47
## Running logo
• You can get rid of the animated gif logo by logging in and choosing a different skin under My Pages | Preferences | Appearance. I use the Cologne Blue skin and it looks and works fine.
• You can also flag it with AdBlock - this seems to get rid of it from any site that uses it.
• easiest: use wiki.lazarus.freepascal.org instead of wiki.freepascal.org : http://wiki.lazarus.freepascal.org/Site_Feedback - Arent (talk) 13:00, 22 September 2016 (CEST)
## Editor
Is this still alive? Any changes to get update for the mediawiki engine, the editor is so much developed [1] since the version in use in this wiki. Also something like [2] might be handy for indexing ie. FPC category with lots of cluttered subcategories. --LV 15:51, 28 January 2016 (CET)
## Layout
Please set default skin to vector instead of monobook in LocalSettings.php so that not-logged-in users (most?) do not see the archaic interface anymore. Arent (talk) 11:13, 21 September 2016 (CEST)
\$wgDefaultSkin = "vector";
## Help
mediawiki:helppage should point to Help:Contents instead of default https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents - Arent (talk) 12:25, 23 September 2016 (CEST)
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2018-09-21 09:37:22
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http://math.virginia.edu/seminars/colloq/2007-08/
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# Colloquium 2007-08
September 6 Skip Garibaldi (Emory University) Host: Andrei Rapinchuk Title: Cohomological Invariants A popular strategy for proving that two things are not isomorphic is to show that an invariant takes different values on the two objects. But sometimes all the invariants in one's toolkit agree on the two objects, which leads to the problem of classifying all of the possible invariants. In algebra, recent results of Serre and Rost -- exploiting the fact that many algebraic objects can be viewed as torsors under an algebraic group -- have made this problem tractable in some cases. Current work focuses on the invariants of G-torsors, for various connected simple groups G. September 14* Mathematics Symposium for Loren Pitt Milne Anderson (University College, London) Title: The Logarithmic Derivative of a Polynomial Daniel Stroock (MIT) Title: Some Queer Diffusions Several years ago, David Williams and I studied a simple looking diffusion equation on the right half line. What made the problem challenging was our imposition of a boundary condition which invalidated the minimum principle. As a consequence, non-negative initial data does not necessarily stay non-negative under the evolution. Our search for the necessary and sufficient condition on the initial data which guarantees that the solution stays non-negative involved an interesting and novel connection between classical analysis and probability theory. After explaining the simplest case, I will report on some more recent progress on this type of problem. September 20 Brian Sutton (Randolph-Macon College) Host: Don Ramirez Title: Computing the complete CS decomposition The CS decomposition (CSD) is a matrix decomposition reminiscent of the eigenvalue and singular value decompositions. The existence of the CSD for any partitioned unitary matrix was proved by Stewart in 1977, but since then, no algorithm for computing the decomposition has been available. (Existing CSD algorithms only solve a reduced version of the problem.) We present a solution to the problem of computing the complete CS decomposition. September 27 Francis Su (Harvey Mudd College) Host: IMS Title: Combinatorial Fixed Point Theorems and Fairness The Brouwer fixed point theorem is a well-known classical theorem in topology with important applications. Less well-known is an equivalent combinatorial formulation known as Sperner's lemma. We survey some recent applications of variants and relatives of Sperner's lemma, including an extension to polytopes and combinatorial equivalents of other topological theorems. These have some striking applications in "fair division" problems in mathematical economics: cake-cutting, rent-splitting among housemates, and resource allocation. Proofs exhibit interesting connections between combinatorics, topology and the social sciences. Research with undergraduates has played a big role. October 4 David Sherman (UVa) Title: Symmetries of noncommutative Banach spaces Many Banach spaces are described most naturally as spaces of functions. Motivated partially by quantum mechanics, their noncommutative versions are built out of operators. Examples are C*-algebras, von Neumann algebras, and noncommutative Lp spaces. I'll begin this talk by showing how the symmetry group of a square underlies Banach's classical results on isometries of C(K) and Lp spaces. Then I will explain how these results have gradually evolved into fully noncommutative theorems. Although new phenomena have appeared and the proofs have gotten more complicated, there is a surprising unity (and simplicity) in the results: all of these isometries should be viewed as "noncommutative weighted composition operators." October 11 Michael Desai (Princeton) Host: IMS Title: How Large Asexual Populations Adapt We often think of beneficial mutations as being rare, and of adaptation as a sequence of selected substitutions: a beneficial mutation occurs, spreads through a population in a selective sweep, then later another beneficial mutation occurs, and so on. This simple picture is the basis for much of our intuition about adaptive evolution, and underlies a number of practical techniques for analyzing sequence data. Yet many large and mostly asexual populations -- including a wide variety of unicellular organisms and viruses -- live in a very different world. In these populations, beneficial mutations are common, and frequently interfere or cooperate with one another as they all attempt to sweep simultaneously. This radically changes the way these populations adapt: rather than an orderly sequence of selective sweeps, evolution is a constant swarm of competing and interfering mutations. I will describe some aspects of these dynamics, including why large asexual populations cannot evolve very quickly and the character of the diversity they maintain. I will explain how this changes our expectations of sequence data, how sex can help a population adapt, and the potential role of "mutator" phenotypes with abnormally high mutation rates. I will also describe ways to study these dynamics directly using experimental yeast populations. October 18 Benjamin Wells (UVa) Title: Fourier Transforms Vanishing at Infinity The talk will survey some old and some more recent results on the behavior of the Fourier transform of functions and measures defined on the circle and on the real line as values of their arguments become large. In the case of the circle one can ask whether a transform vanishing at infinity on a subset of integers E must necessarily vanish on the complement of E. My interest in the subject arises from an old question concerning subsets E of integers having the property that the only measures whose transforms vanish on E are absolutely continuous with respect to Lebesgue measure. October 25 Jason Papin (UVa) Host: IMS Title: Interrogating emergent properties of biochemical networks The reconstruction and mathematical analysis of genome-scale biochemical networks is a pressing challenge for making the connection between genotype and phenotype of biological systems. Three topics will be discussed: (1) the development of novel computational approaches for interrogating properties of mathematical representations of these networks; (2) the discovery of fundamental biology with these systems-level models; and (3) the application of such network analysis tools to address clinical problems. These network reconstructions and analyses facilitate the integration of high-throughput datasets to characterize properties that arise from the biochemical networks and are thus beginning to drive fundamental discoveries in biology. November 1 Yiftach Barnea (University of London) Host: Mikhail Ershov Title: Pro-p groups with few normal subgroups During the 80's Charles Leedham-Green and Mike Newman came with five striking conjectures on the structure of finite p-groups. Some of these conjectures were formulated as a structure theory on the class of pro-p groups of finite coclass. In combined efforts of many mathematicians including Donkin, Leedham-Green, Shalev, and Zelmanov the conjectures were proved. The main tool was the theory of p-adic analytic pro-p groups developed by Lubotzky and Mann based on Lazard's solution of Hilbert's fifth problem over the p-adics. I will discuss various generalizations of the notion of coclass in pro-p groups and relations between them. I will then show that all the known examples of pro-p groups with few normal subgroups, not only have few normal subgroups, but strikingly have periodicity in the lattice of normal subgroups. Following these examples I will pose several problems. This talk is self contained, there is no need to know what a pro-p group is, and I will give all the necessary background. This is joint work with N. Gavioli, A. Jaikin-Zapirain, V. Monti, and C. Scoppola. November 8 Larry Smith (University of Göttingen) Host: Bob Stong Retirement Conference Title: On a Theorem of Chevalley about Algebras of Coinvariants Let rho: G --> GL(n, F) be a faithful representation of a finite group G over the field F. By means of rho the group G acts on the algebra F[V] of polynomial functions on the representation space V = F^n, fixing the subalgebra F[V]^G (the invariant algebra) and hence also on the algebra F[V]_G = F tensor_{F[V]^G} F[V] of coinvariants. Chevalley's Theorem states that, in the case that F=R and G is a real reflection group, the coinvariant algebra as a G-representation is isomorphic to the regular representation of G. In this talk I will describe joint work with Abraham Broer of the Universite de Montreal, Victor Reiner and Peter Webb of the University of Minnesota, in which we generalize Chevalley's Theorem in three ways. (1) we need no assumption on the ground field F, in particular it can be of any characteristic, even one dividing the order of G, (2) we need no assumption on the representation rho, so in particular G need not be a reflection group, nor must F[V]^G be a polynomial algebra, and finally (3) we can deal with a relative situation of H < G being a subgroup of G and dealing with the algebra F \tensor_{F[V]^G} F[V]^H as a representation of the group W_G(H) = N_G (H) /H where N_G (H) is the normalizer of G in H. Our methods are a mixture of homological algebra, representation theory, and invariant theory. November 15 Ronald Fintushel (Michigan State University) Host: Tom Mark Title: The countdown to CP2 One of the key problems in 4-manifold topology is to understand whether "standard manifolds" admit exotic smooth structures, i.e. given a smooth 4-manifold, if there are manifolds homeomorphic but not diffeomorphic to it. In the last several years dramatic progress has been made in understanding this problem for the manifolds obtained by blowing up CP2 at a small number of points. I will describe the problems in this area, the techniques that have been used to study them, and the results that have been obtained, starting with work of Donaldson from the 1980's and leading to some outstanding results of young mathematicians in this last year. November 29 David Blecher (University of Houston) Host: David Sherman Title: Operator spaces and algebras, and their duality We describe some beautiful and accessible ideas from the new theory of linear spaces or algebras of continuous linear operators between Hilbert spaces. We will also describe some of our results on the duality of such spaces, and on the relations between the metric structure' and the underlying algebraic structure. --Cancelled-- December 6 Gianluca Guadagni (UVa) Title: Exact Renormalization Group on the lattice I will give a description of the RG transformation for functional integrals of weakly perturbed Gaussian measures. The method is based on polymer expansions and it will be applied to a simplified model on a lattice. December 13 Paul Kirk (Indiana University) Host: Tom Mark Title: Constructing symplectic 4-manifolds with prescribed fundamental groups
January 17 (Postponed due to weather)
January 18* Philip Gressman (Yale University) Special Colloquium
Title: Lebesgue and Sobolev estimates for geometric averaging operators A geometric averaging operator is any mapping which sends a function on a manifold to its integral over some family of submanifolds, the canonical examples being the X-ray and Radon transforms. For general families of submanifolds, little is known about the boundedness properties of these operators. This talk will discuss the motivations for studying such objects and recent sharp results (in terms of $L^p$-improving and Sobolev smoothing estimates) for "generic" degenerate averaging operators.
January 21* Alexey Cheskidov (University of Chicago) Special Colloquium
Title: On the regularity of weak solutions to the 3D Navier-Stokes equations in critical Besov spaces In this talk, I will make a brief introduction to the regularity problem for the 3D Navier-Stokes equations. Even thought it is far from been solved, numerous regularity criteria have been proved in critical spaces since the work of Leray. However, the regularity problem remains completely open in supercritical spaces. We will discuss a new regularity criterion in the largest critical space.
January 22* Michael Goldberg (Johns Hopkins University) Special Colloquium
Title: Strichartz Estimates for a Wealth of Schrödinger Operators The Strichartz estimates are a fundamental family of Lp inequalities governing solutions to the free Schrödinger equation. They decribe the dispersive nature of the evolution -- local concentrations of mass can only exist for a specified finite period of time. The associated function spaces can be used to assess well-posedness and scattering properties of perturbed or nonlinear Schrödinger equations.
I will review the efforts to identify other Schrödinger operators on Rn that satisfy the same range of Strichartz estimates as the Laplacian. On the technical side, recent progress is driven by improvements in the underlying harmonic and functional analysis. On the motivational side, specific applications often give rise to operators that fall outside (or at the edge) of our current understanding. I will present the orbital stability of solitons in NLS as one such application.
January 28* Marcin Bownik (University of Oregon) Special Colloquium
Title: How to construct multidimensional wavelets with good time-frequency localization? In this talk I will discuss the problem of constructing orthogonal wavelets in higher dimensions. In general this is a difficult problem if we require some special properties on wavelets, such as regularity or fast decay. I will present some positive results on the existence of regular wavelets. I will also describe certain inherent limitations on the existence of wavelets with good time-frequency localization.
January 31
February 7
February 14 Olivier Pfister (UVa) Host: IMS
Title: Towards quantum computing with graphs and light Quantum computing and quantum information have attracted much attention over the past decade because they predict spectacular enhancements of computational performance for historically (if not provably) hard problems such as factoring. Quantum computing has fundamental overlaps with group representation theory, topology, and graph theory, and the physical implementation of nontrivial quantum computing is an exciting, if daunting, challenge to physicists devoted to the experimental study of quantum systems. In this talk, I will introduce an interesting flavor of quantum computing, called one-way quantum computing, which interfaces with mathematical graph theory. I will then outline how the power and elegance of graph quantum states translate into "physical reality" in our experimental setup, next door.
February 21 Jaydeep Chipalkatti (University of Manitoba) Host: Malek Abdesselam
Title: Polar polyhedra, and the polynomial Waring's problem The polynomial version of Waring's problem (which originated in the 19th century) asks under what conditions a homogeneous form may be expressed as a sum of powers of linear forms. There are geometrically peculiar cases where such a representation is impossible even though a priori one has enough parameters available. I will explain the solution to the general problem by Alexander and Hirschowitz, and a little of what remains to be done. The talk should be generally accessible, and no special knowledge of algebraic geometry will be assumed.
February 28 Dave Witte Morris (University of Lethbridge) Host: Andrei Rapinchuk
Title: Some arithmetic groups that cannot act on the line It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no (orientation-preserving) actions on the real line. This naturally led to the conjecture that most other arithmetic groups (of higher real rank) also cannot act on the line. This problem remains open, but joint work with Lucy Lifschitz verifies the conjecture for many examples. This includes all finite-index subgroups of SL(2,Z[alpha]), where alpha is any irrational, real algebraic integer. The proof is based on the fact, proved by D.Carter, G.Keller, and E.Paige, that every element of these groups is a product of a bounded number of elementary matrices. No familiarity with arithmetic groups will be assumed.
March 6 Spring break
March 13 Andrei Jaikin-Zapirain (Universidad Autonoma de Madrid) Host: Mikhail Ershov
Title: On the p-gradient of finitely presented groups Let Γ be a finitely presented group and Γ = Γ0 > Γ1 > … a nested sequence of normal subgroups of Γ of finite index. W. Lueck proved that if {Γi} has trivial intersection, then
limi→∞ dimC H1 (Γi, C) |Γ : Γi|
2-Betti number of Γ. In particular, this limit does not depend on the sequence Γ = Γ0 > Γ1 > …. The L2-Betti numbers were introduced first by M. Atiyah for compact Riemann manifolds and later extended by J. Dodziuk to general CW-complexes of finite type. In my talk I consider an analogous problem in which instead of dimC H1i,C) we take dimFp H1i,Fp):
Conjecture 1: Let Γ be a finitely presented group and Γ = Γ0 > Γ1 > … a nested sequence of normal subgroups of Γ of finite index with trivial intersection. Then
limi→∞ dimFp H1 (Γi, Fp) |Γ : Γi|
0 > Γ1 > ….
In a particular case when the profinite completion of Γ with respect to {Γi} is a p-adic analytic group, Conjecture 1 is reformulated as a problem about embeddings of the group ring Fp[Γ] into division rings. Among the examples we consider are lattices in SL2C. We will establish a relation between Conjecture 1 and the structure of the congruence kernel of arithmetic lattices in SL2C.
March 20 Charles Akemann (UC Santa Barbara) Host: David Sherman
Title: The continuum hypothesis as a tool for constructing examples in functional analysis It is well-known that the Axiom of Choice is widely used in functional analysis for the construction of examples that would not otherwise exist. Examples include subsets of the real line that are not Lebesgue measurable, discontinuous linear functionals on Banach spaces and the like. If these were the only kind of examples, then the Axiom of Choice might have been left in the trash can. After all, who really needs things like these? On the other hand, non-principal ultrafilters on the integers, the Hahn-Banach Theorem, various fixed point theorems, and Tychonoff's Theorem (the product of compact spaces is compact) and the like would also be unavailable. The loss of these items would reduce the beauty of the subject substantially. Consequently, analysis without the Axiom of Choice is almost reduced to numerical analysis. At first glance the Continuum Hypothesis seems like the opposite of the Axiom of Choice. The latter is an existence axiom, while the former is a non-existence axiom. Functional analysts have adopted a "take it or leave it" attitude toward the Continuum Hypothesis. There never seemed to be a use for mysterious uncountable cardinals smaller than the continuum. Perhaps unexpectedly, the Continuum Hypothesis has allowed the construction of analysis examples, rather than showing the non-existence of interesting examples. In several cases the question of the need for that axiom is still open, thus leaving open questions for set theorists to answer. This talk will focus on the value of the Continuum Hypothesis in constructions. The key point is that many, many analysis objects have cardinality c (the continuum). Despite this, countability and sequences play a key role. It turns out to be very convenient to maintain countability for as long as possible in a transfinite construction. With the Continuum Hypothesis assumed, some constructions that require countability can go forward at every ordinal less that c. While some of these constructions are old, this method recently led Nik Weaver and me to the solutions of two problems from the 1950s.
March 27 Gerda de Vries (University of Alberta) Host: IMS
Title: Understanding Bursting Oscillations through Bifurcation Analysis Bursting oscillations are commonly seen to be the primary mode of electrical behavior in a variety of nerve and endocrine cells, and have also been observed in some biochemical and chemical systems. Bursting oscillations are characterized by an alternation of silent and active phases. An observable of a system (for example, the electrical potential across the membrane of a cell) remains relatively constant during the silent phase, while it undergoes rapid oscillations during the active phase. In this talk, I will begin by reviewing a well-studied bursting system, namely the electrical behavior of pancreatic beta cells. A minimal model of bursting oscillations in beta cells consists of three ordinary differential equations, with variables operating on different time scales. A decomposition of the system into a fast and a slow component facilitates a bifurcation analysis that reveals the mechanism underlying bursting. The main focus during the remainder of my talk will be to review efforts to understand the role of electrical coupling between individual cells in the modification of the bursting phenomenon and, possibly, the genesis of the bursting phenomenon in a network of cells.
April 3 Alexander Volberg (Michigan State University) Host: Don Ramirez
Title: Buffon Needle Probability and Analytic Capacity In 1733 count de Buffon asked the question: what is the probability for a needle of length L<1 to intersect a grid of parallel lines on the plane having distance 1 between each other? In 1898 Paul Painlevé asked another question: how to describe geometrically the compact sets on the plane such that the only functions analytic and bounded in the complement of these sets are constants. At the end of 20th century it became clear that these two questions are closely related. Moreover, they are closely related to a wide variety of problems: from percolation on graphs to electrostatics. In our talk we will explain some of these relationships.
April 10 Igor Kukavica (University of Southern California) Host: Zoran Grujic
Title: Partial regularity for the Navier-Stokes equations In this talk we will review the conditional and partial regularity of the Navier-Stokes equations in dimension three. A classical result of Caffarelli, Kohn, and Nirenberg states that the one dimensional Hausdorff measure of singularities of a suitable weak solution of the Navier-Stokes system is zero. We will review known results and different proofs of the partial regularity results including a recent short proof which reduces the assumption on the force term.
April 17 Alireza Salehi Golsefidy (IAS and Princeton) Host: Mikhail Ershov
Title: Lattices with small covolume Abstract: In this talk, I will discuss lattices with small" covolume in almost simple algebraic groups over non-Archimedean local fields. In the positive characteristic case, I will quickly recall my result, saying that up to isomorphism G(F_q[1/t]) is the only lattice of minimum covolume in G(F_q((t))), where G is a Chevalley group of classical type or of type E_6. Then I will give a partial answer to Lubotzky's question by showing that in `most" of the cases in characteristic p, a lattice of minimum covolume is non-uniform. I will also give a very short proof of Siegel-Klingen theorem on rationality of values of certain L-functions and zeta functions, using covolume of lattices. In the characteristic zero case, in a joint work with A. Mohammadi, we study discrete transitive actions on the Bruhat-Tits building, and prove that there is no lattice in PGL(n,K) which acts transitively on the vertices of the Bruhat-Tits building if n>8, in contrast to the positive characteristic where Cartwright and Steger constructed such an action for any dimension. For 9>n>4, we give a list of 14 lattices which are the only potential such examples, and show that at least one of them in dimension 5 actually acts transitively.
April 24 Xuhua He (Stony Brook) Host: Weiqiang Wang
Title: Introduction to G-stable pieces The notion of G-stable pieces was introduced by Lusztig in the study of parabolic character sheaves. It has a rich structure, combining combinatorics, group theory, geometric representation theory and other fields. In this talk, we will discuss the G-stable pieces from the point of view of combinatorics of Weyl groups. We will also talk about some connection with algebraic geometry and Poisson geometry.
May 1 Weimin Chen (University of Massachusetts, Amherst) Host: Thomas Mark
Title: Symmetries of 4-manifolds Consider the following question: is every smooth Z/pZ-action on the 4-dimensional sphere conjugate to an orthogonal action? In this talk we will discuss the current state of affairs of this problem and some of the ideas and techniques used to attack it. (The talk is intended for a general audience.)
May 8 Kevin Wortman (University of Utah) Host: Kai-Uwe Bux
Title: Finiteness properties of S-arithmetic groups over function fields Finiteness properties for groups can be thought of as generalizations of properties such as finite generation and finite presentability, and S-arithmetic groups over function fields can be thought of as generalizations of the groups SL(n,F[t]) where F is a finite field. In this talk I'll describe how the geometry of Euclidean buildings has been used to analyze the topic from the title. I'll talk about the progress that has been made, and discuss some work that remains to be done.
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2017-11-24 03:28:33
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https://fluidpower.pro/hydraulic-cooler-selection/
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# How to select a hydraulic cooler
• determine the value of the heat needs to be rejected from the system;
• calculate and select the right cooler size.
…and will provide an example of cooler calculation and selection.
#### What is a cooler and what is a heat exchanger?
The hydraulic cooler is one of the heat exchangers type. But, what is a heat exchanger? The best definition of the heat exchanger is:
Heat exchanger is a device that transfers heat between two fluids.
The simple sentence but a very good description, because fluids can be either oil, air, water, etc., and because transferred heat can be for either cooling or heating target.
There are two most popular types of heat exchangers in hydraulic systems:
#### Plate heat exchangers
Plate heat exchanger
This type has the best value of efficiency/reliability and designed for both cooling and heating applications and a very good for low-viscosity fluids. Pairs of plates can be removed individually for maintenance, cleaning, or replacement. Another advantage of the plate is exchangers is their low initial cost, as well as easy and inexpensive operation.
This type is the only option where water is unavailable or expensive for a delivery. From benefits: low maintenance and operating costs and the only option for oil cooling in mobile applications.
## Theory of cooler selection
#### Heat balance
Heat exchanger selection starts from the calculation of heat, generated by a hydraulic system, that needs to be rejected by the cooler. The right estimation of this value can keep balance of heat in a hydraulic system and prevent from both overcooling and overheating of a hydraulic system. It lets hydraulic components work in ideal temperature/viscosity conditions with maximum performance what makes hydraulic system reliable and efficient.
So, the question #1: where the heat comes from in the hydraulic system?
The short response is pressure losses:
• Friction between fluid and conduit’s wall transfers part of energy into the heat and this is why making pressure drop on the conduit.
• Cavitation in all hydraulic components (pumps, valves, fittings, etc.) due kinetic energy transformation generates major heat in the hydraulic system. Consider all components in the hydraulic systems as orifices, with pressure drop across equal to generated heat.
Elbow at the cylinder generates heat
Here is a good example: Take a look at the infrared picture at the right – the simple elbow at the cylinder generates heat due cavitation caused rapidly changed flow direction.
The next question is how to evaluate the required heat needs to be rejected?
This is a really good question because there no specific formula to calculate the exact value. As you understand, heat is generated by absolutely all components in the system, and even if you try to calculate the major parts it can take a while… Therefore, we usually take the next values just from historical experience:
20-25% of input power for close loop systems.
25-30% of input power for open loop systems.
For example, we have a hydraulic system with both open loop and close loop circuits. The power, needs to be provided to open loop is 90 HP and power, needs to be provided to open loop is 80 HP. In this case, we can assume generated and required to be rejected heat around 45..47 HP:
$p_{heat}=P_{op}\times\frac{30}{100}+P_{cl}\times\frac{25}{100}=90\times\frac{30}{100}+80\times\frac{25}{100}=47\;HP$
Another method to get generated by the system heat value is more precised and perfect for complex systems where open and close loops are mixed but requires more inputs. The idea is in a calculation of a difference between input and output power. All wasted power is transferred into heat, the value that we exactly looking for. Couple words about this method.
Any hydraulic system calculation starts from a technical design task where shown required functions performances: speed/force for cylinder or rpm/torque for motors. This data is a good start point to estimate the required system output power for the worst-case scenario: when max functions work at the same time.
The next steps are calculations of the input power needs to be provided from the electrical motor or diesel engine to the pumps using overall efficiency of all components in loops such as pumps, motors, and using pressure drop on valves or pressure losses at hoses, and etc. Detailed hydraulic system calculation I will provide in future articles.
For my projects, I usually do calculations by both these methods and take the highest value of the required rejection heat for cooler selection.
These are the simplest way to calculate rejected heat to keep heat balance in the system. In reality there many other factors like environment temperature and heat transfer via components surfaces (for example hydraulic tank) that affect heat balance. But for the regular hydraulic system, it is not required to dig so deep in calculations.
#### Estimation of flow through the cooler
The next step is a selection of place in the system where the cooler has to be installed and estimation a flow at this place.
There are three most popular places where heat exchanger can be installed:
• in the return line, between return manifold collector and a tank. This palce most popular for open loop system. To estimate flow trough the cooler, first, you need to figure-out flow for all functions that can work at the same time and, next, subtract drain flow, calculated from components via their volumetric efficiency.
• in the drain line, between case drain manifold collector and tank. Most popular for close loop system.To estimate flow through cooler, you need to figure-out drain flow, calculated from all components via their volumetric efficiency.
• as a separate loop with additional downstream filtration. Can be used for both open loop and close loop systems. To estimate flow trough cooler, first, you need to get the value of the rejected heat. Next, using vendors diagrams select flow from the cooler. And finally, select cooler loop pump size to provide required flow trough the cooler.
#### Adjusting the rejected heat to use vendor’s curves
Each application has specific conditions and cooler manufacturers can not provide performances for all of them. Therefore, in the cooler manufacture catalogs, you can find diagrams/curves for each cooler at specific conditions it was tested. For example, AKG coolers tested and published curves based on:
• Oil viscosity: 50 SUS
• Entering Temperature Difference (ETD): 100°F
Another example, Emmegi coolers tested and published curves based on:
• Oil viscosity: 16 cSt SUS
• Entering Temperature Difference (ETD): 50°F
Here the Entering Temperature Difference (ETD) is a difference between Entering oIl Temperature and Entering aIr Temperature to the cooler. Of course, your conditions will be different and to use vendor’s chart you need to calculate “Desired” ETD for your system. Your “Desired” ETD is the difference between Max ambient temperature (in the worst case) your system will be work and the highest desired entering oil temperature.
For example, for Texas I usually use 115°F, for Alaska – 70°F for Max ambient temperature (if the customer does not provide preffered value).
You need to estimate by yourself the expected highest desired entering oil temperature. For the drain line it can rise to 176°F, for return lines – around 160°F, but, again, it varies from the application.
As soon you know your “Desired” ETD you can make an adjustment for rejected power and use this value in manufacturer’s curves. You can find the formula in each vendor’s catalog for adjusted rejected power:
$p_{adj}=P_{heat}\times\frac{100^{\circ}F}{ETD_{des},^{\circ}F}$
#### Preliminary select the cooler.
As soon you get two values: flow trough cooler and adjusted heat you can use vendor’s curves to cooler preliminary selection. Try to find the cooler model close to the middle of the curve.
#### Checking pressure drop across cooler
This is a very important step and this is why the previous step was called “preliminary”.
It is important to check pressure drop across the cooler because in some cases you can damage hydraulic components if pressure is too high. For example, if cooler in the case drain line and pressure drop across it more than 50 psi you can destroy bearings in some pumps or motors (you need to check max available case pressure for them in the catalogue). Another issue is a back pressure that cooler can create if placed in the return line. In both these cases, the bypass valve integrated into a cooler will not save the system from overpressure because it passes through only a small part of the flow. Do not forget, the cracking pressure is a value when the valve just starts to open with a very small cross-section for flow. I had a case in my practice when cooler with a bypass valve craking pressure 20 psi rises back pressure up to 90 psi at cold start and up to 45 psi at normal work temperature and it isn’t applicable.
I do not know why, but for some reasons, some manufacturers published cooler performance diagrams at very low viscosity, not realistic for real operation. This is why the pressure drop at the curve looks so nice.
AKG cooler correction factor curve
Also, by some strange reasons, at the latest AKG catalogs there no info about pressure drop across cooler depends on the flow. So, I use older catalogs for the same cooler model (what is not right, because cooler modified and newest may not have the same performances). Emmegi continues to provide this useful info in their catalogs.
So, to get an actual pressure drop across the cooler you need to use the correction factor, depends on oil viscosity in your application. (You can use online converter if viscosity or temperature is different from units in vendors catalog).
It was the last step and if you satisfied by pressure drop across the cooler you selected, you can proceed with it, if not – try to check different model or brand of the cooler.
Actually, AKG TS provides with cooler selection online tool, that you can find by the link:
http://78.94.222.53:18000/cl1/
## Example of cooler selection
The example below is the real calculation for the real unit (Blender Trailer) that is working now somewhere in the north of Texas.
• Mobile unit is designed to work in a place where the max average ambient temperature is: 45°C = 113°F
• The oil going to be used: ISO VG46
• System input power: 120 HP
• The hydraulic system contains close loops only
• Cooler is in a drain line where estimated flow is approx. 42 GPM
• The highest expected entering oil temperature in drain line: 80°C = 176°F
• The cooler has to be electrically driven, 24VDC
#### Step 1. Calculation of the heat needs to be rejected
First, I assume in the worst case the heat can be generated is 25% of input power (as for close loop systems):
$p_{heat}=120\times\frac{25}{100}=30\;HP$
#### Step 2. Determine Desired ETD
$ETD_{des}=T_{oil}-T_{amb}=176-113=63\;^{\circ}F$
#### Step 3. Calculation of the adjusted rejected heat
Adjusted HP for cooler selection at 100°F ETD (for AKG coolers):
$p_{adj}=P_{heat}\times\frac{100^{\circ}F}{ETD_{des}, ^{\circ}F}=30\times\frac{100^{\circ}F}{63^{\circ}F}=50\;HP$
$50\;HP=127000\;BTU/h$
Adjusted HP for cooler selection at 50°F ETD (for Emmegi coolers):
$p_{adj}=P_{heat}\times\frac{50^{\circ}F}{ETD_{des}, ^{\circ}F}=30\times\frac{50^{\circ}F}{63^{\circ}F}=25\;HP$
$25\;HP=63600\;BTU/h$
#### Step 4. Preliminary cooler selection
Let’s select DCS series cooler from AKG. As you can see at the performance curves below, the best choice is model DCS-60:
AKG DCS Cooler curves
Checking coolerweight (111 lb), max work pressure (250 psi), electrical motor current (2x10A=20A), dimensions, cost, etc.
Let’s select DC series cooler from Emmegi. As you can see at the performance curves below, the good choices are models HPV-36 and SBV-6:
Emmegi DC Cooler curves
For this calculation, I selected model SBV-6 because both coolers AKG DCS-60 and Emmegi SBV-6 look similar, have the same dimensions and almost the same price. So it is a good choice for future comparison.
Checking cooler weight (82 lb), max work pressure (280 psi), electrical motor current (2×10.4A=20.8A), dimensions, cost, etc.
#### Step 5. Checking pressure drop across both coolers
From the DCS-60 series cooler curve above, for 42 GPM flow, I get approx. 22 psi pressure drop. But this is a pressure drop is test results for oil with viscosity 50 SUS. For our ISO VG46 oil at work temperature 40°C estimated viscosity is 212 SUS. Lets figure-out correction factor for our conditions from the curve in AKG catalog:
AKG cooler correction factor curve
So, the correction factor is equal to 3, therefore the real pressure drop across the cooler to be 22 PSI × 3 = 66 PSI.
Let’s check Emmegi SBV-6. From the curve above I get pressure drop around 7 psi for oil with viscosity 16 cSt at 42 GPM flow. Now, we need to get a correction factor, which is not published in the Emmegi catalog. But you are lucky, I was made a request to Emmegi and their technical specialist provided me with an approx curve that we can use for calculation:
Emmegi cooler correction factor curve
So, the correction factor is equal to 2.3, therefore the real pressure drop across the cooler to be 7 PSI × 2.3 = 16 PSI
As a result, my final selection is Emmegi SBV-6, because:
• Emmegi cooler provides much less pressure drop at the estimated flow (what is good for a drain line)
• Emmegi cooler weight is 25% lighter than AKG analog (what is critical for the mobile application)
• Other criteria (el. motor current, dimensions, cost, etc) are similar.
Easy? Oh yes, but some nuances exist…
## 1 Comment
1. YANG
This article has explained it very clearly, I feel I have gained a lot
! Thank you very much to the author of this article! I am so lucky!
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2021-10-16 11:29:18
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https://projecteuclid.org/euclid.jmsj/1257520503
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## Journal of the Mathematical Society of Japan
### Irreducible plane sextics with large fundamental groups
Alex DEGTYAREV
#### Abstract
We compute the fundamental group of the complement of each irreducible sextic of weight eight or nine (in a sense, the largest groups for irreducible sextics), as well as of 169 of their derivatives (both of and not of torus type). We also give a detailed geometric description of sextics of weight eight and nine and of their moduli spaces and compute their Alexander modules; the latter are shown to be free over an appropriate ring.
#### Article information
Source
J. Math. Soc. Japan, Volume 61, Number 4 (2009), 1131-1169.
Dates
First available in Project Euclid: 6 November 2009
https://projecteuclid.org/euclid.jmsj/1257520503
Digital Object Identifier
doi:10.2969/jmsj/06141131
Mathematical Reviews number (MathSciNet)
MR2588507
Zentralblatt MATH identifier
1183.14040
Subjects
Secondary: 14H45: Special curves and curves of low genus
#### Citation
DEGTYAREV, Alex. Irreducible plane sextics with large fundamental groups. J. Math. Soc. Japan 61 (2009), no. 4, 1131--1169. doi:10.2969/jmsj/06141131. https://projecteuclid.org/euclid.jmsj/1257520503
#### References
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• J. I. Cogolludo, Fundamental group for some cuspidal curves, Bull. London Math. Soc., 31 (1999), 136–142.
• A. Degtyarev, Isotopy classification of complex plane projective curves of degree 5, Algebra i Analis, 1 (1989), 78–101 (Russian); English translation in Leningrad Math. J., 1 (1990), 881–904.
• A. Degtyarev, Alexander polynomial of a curve of degree six, J. Knot Theory Ramifications, 3 (1994), 439–454.
• A. Degtyarev, Quintics in $\mbi{C}\mathrm{p}^{2}$ with nonabelian fundamental group, Algebra i Analis, 11 (1999), 130–151; (Russian); English translation in Leningrad Math. J., 11 (2000), 809–826.
• A. Degtyarev, On deformations of singular plane sextics, J. Algebraic Geom., 17 (2008), 101–135.
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2019-05-22 14:39:21
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https://zbmath.org/?q=an:1354.45010
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# zbMATH — the first resource for mathematics
Some coincidence point results in ordered $$b$$-metric spaces and applications in a system of integral equations. (English) Zbl 1354.45010
Summary: The aim of this paper is to present some coincidence point results for four mappings satisfying generalized $$(\psi,\phi)$$-weakly contractive condition in the framework of ordered $$b$$-metric spaces. An example and an application are also provided to support our results.
##### MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
Full Text:
##### References:
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R., Common fixed point results for four mappings satisfying almost generalized$$(S, T)$$-contractive condition in partially ordered metric spaces, Appl. Math. Comput., 218, 5665-5670, (2012) · Zbl 1245.54035 [7] Akkouchi, M., Common fixed point theorems for two selfmappings of a $$b$$-metric space under an implicit relation, Hacettepe J. Math. Stat., 40, 6, 805-810, (2011) · Zbl 1276.47071 [8] Alber, Ya. 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S.; Swaleh, M.; Sessa, S., Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30, 1-9, (1984) · Zbl 0553.54023 [24] Moradi, S.; Fathi, Z.; Analouee, E., Common fixed point of single valued generalized $$\varphi_f$$-weak contractive mappings, Appl. Math. Lett., 24, 5, 771-776, (2011) · Zbl 1296.54076 [25] Jungck, G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, 4, 771-779, (1986) · Zbl 0613.54029 [26] Khamsi, M. A.; Hussain, N., KKM mappings in metric type spaces, Nonlinear Anal., 73, 9, 3123-3129, (2010) · Zbl 1321.54085 [27] Khamsi, M. A., Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., (2010), Article ID 315398, 7 pages · Zbl 1194.54065 [28] Nashine, H. K.; Samet, B., Fixed point results for mappings satisfying $$(\psi, \varphi)$$-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74, 2201-2209, (2011) · Zbl 1208.41014 [29] Nieto, J. J.; López, R. R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013 [30] Nieto, J. J.; Pouso, R. L.; Rodríguez-López, R., Fixed point theorems in ordered abstract sets, Proc. Amer. Math. Soc., 135, 2505-2517, (2007) · Zbl 1126.47045 [31] Nieto, J. J.; Rodríguez-López, R., Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23, 2205-2212, (2007) · Zbl 1140.47045 [32] Olatinwo, M. O., Some results on multi-valued weakly Jungck mappings in $$b$$-metric space, Cent. Eur. J. Math, 6, 4, 610-621, (2008) · Zbl 1175.47055 [33] Pacurar, M., Sequences of almost contractions and fixed points in $$b$$-metric spaces, Analele Universitatii de Vest din Timisoara Seria Matematica-Informatica, XLVIII, 3, 125-137, (2010) · Zbl 1249.54086 [34] Radenović, S.; Kadelburg, Z., Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl, 60, 1776-1783, (2010) · Zbl 1202.54039 [35] Ran, A. C.M.; Reurings, M. C.B., A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132, 1435-1443, (2004) · Zbl 1060.47056 [36] Razani, A.; Parvaneh, V.; Abbas, M., A common fixed point for generalized $$(\psi, \varphi)_{f, g}$$-weak contractions, Ukrainian Math. J., 63, 11, (2012) · Zbl 1255.54025 [37] Rhoades, B. E., Some theorems on weakly contractive maps, Nonlinear Anal., 47, 2683-2693, (2001) · Zbl 1042.47521 [38] W; Shatanawi; Samet, B., On $$(\psi, \phi)$$-weakly contractive condition in partially ordered metric spaces, Comput. Math. Appl., 62, 3204-3214, (2011) · Zbl 1232.54041 [39] Singh, S. L.; Prasad, B., Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., 55, 2512-2520, (2008) · Zbl 1142.65360 [40] Zhang, Q.; Song, Y., Fixed point theory for generalized $$\varphi$$-weak contractions, Appl. Math. Lett., 22, 75-78, (2009) · Zbl 1163.47304
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-01-23 05:48:16
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https://www.iacr.org/cryptodb/data/author.php?authorkey=9470
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## CryptoDB
### Greg Zaverucha
#### Publications
Year
Venue
Title
2020
EUROCRYPT
Deterministic generation of per-signature randomness has been a widely accepted solution to mitigate the catastrophic risk of randomness failure in Fiat--Shamir type signature schemes. However, recent studies have practically demonstrated that such de-randomized schemes, including EdDSA, are vulnerable to differential fault attacks, which enable adversaries to recover the entire secret signing key, by artificially provoking randomness reuse or corrupting computation in other ways. In order to balance concerns of both randomness failures and the threat of fault injection, some signature designs are advocating a hedged'' derivation of the per-signature randomness, by hashing the secret key, message, and a nonce. Despite the growing popularity of the hedged paradigm in practical signature schemes, to the best of our knowledge, there has been no attempt to formally analyze the fault resilience of hedged signatures. We perform a formal security analysis of the fault resilience of signature schemes constructed via the Fiat--Shamir transform. We propose a model to characterize bit-tampering fault attacks, and investigate their impact across different steps of the signing operation. We prove that, for some types of faults, attacks are mitigated by the hedged paradigm, while attacks remain possible for others. As concrete case studies, we then apply our results to XEdDSA, a hedged version of EdDSA used in the Signal messaging protocol, and to Picnic2, a hedged Fiat--Shamir signature scheme in Round 2 of the NIST Post-Quantum standardization process.
2020
TCHES
Picnic is a digital signature algorithm designed to provide security against attacks by quantum computers. The design uses only symmetric-key primitives, and is an efficient instantiation of the MPC-in-the-head paradigm. In this work, we explore the Picnic design in great detail. We investigate and benchmark different parameter choices and show that there exist better parameter choices than those in the current specification. We also present improvements to the MPC protocol that shorten signatures and reduce signing time. The proposed MPC changes tailor the protocol to the circuit of interest in Picnic, but may also be of independent interest. Taken together, these changes give a new instantiation of Picnic that signs messages 7.9 to 13.9 times faster, and verifies signatures 4.5 to 5.5 times faster than the existing “Picnic2” design, while having nearly the same signature sizes.
2015
EPRINT
#### Coauthors
Diego F. Aranha (1)
Benjamin Dowling (1)
Daniel Kales (1)
Claudio Orlandi (1)
Douglas Stebila (1)
Akira Takahashi (1)
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2020-09-29 10:53:29
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https://www.sparrho.com/item/growth-and-characterization-of-homoepitaxial-dollarbetadollar-gadollar_2dollarodollar_3dollar-layers/27015ff/
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# Growth and Characterization of Homoepitaxial $\beta$-Ga$_2$O$_3$ Layers
Research paper by M. Brooks Tellekamp, Karen N. Heinselman, Steve Harvey, Imran Khan, Andriy Zakutayev
Indexed on: 21 Apr '20Published on: 17 Apr '20Published in: arXiv - Physics - Materials Science
#### Abstract
$\beta$-Ga$_2$O$_3$ is a next-generation ultra wide bandgap semiconductor (E$_g$ = 4.8 eV to 4.9 eV) that can be homoepitaxially grown on commercial substrates, enabling next-generation power electronic devices among other important applications. Analyzing the quality of deposited homoepitaxial layers used in such devices is challenging, in part due to the large probing depth in traditional x-ray diffraction (XRD) and also due to the surface-sensitive nature of atomic force microscopy (AFM). Here, a combination of evanescent grazing-incidence skew asymmetric XRD and AFM are investigated as an approach to effectively characterize the quality of homoepitaxial $\beta$-Ga$_2$O$_3$ layers grown by molecular beam epitaxy at a variety of Ga/O flux ratios. Accounting for both structure and morphology, optimal films are achieved at a Ga/O ratio of $\sim$1.15, a conclusion that would not be possible to achieve by either XRD or AFM methods alone. Finally, fabricated Schottky barrier diodes with thicker homoepitaxial layers are characterized by $J-V$ and $C-V$ measurements, revealing an unintentional doping density of 4.3 $\times$ 10$^{16}$ cm$^{-3}$ - 2 $\times$ 10$^{17}$ cm$^{-3}$ in the epilayer. These results demonstrate the importance of complementary measurement methods for improving the quality of the $\beta$-Ga$_2$O$_3$ homoepitaxial layers used in power electronic and other devices.
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2021-06-19 19:03:43
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http://mathoverflow.net/questions/118117/can-every-curve-be-written-as-fx-gy?sort=votes
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# Can every curve be written as $f(x)=g(y)$?
Does every irreducible curve admit an equation of the form $f(x)=g(y)$, where $f$ and $g$ are polynomials? What if we allow $f$ and $g$ to be rational functions?
Actually, I'd like to understand this in the presence of an additional constraint: if we're given a finite cover of curves $\pi\colon C\to\mathbb{P}^1$, do we expect there to be a cover $\phi\colon C\to\mathbb{P}^1$ and rational functions $f(x)$ and $g(x)$ such that $C$ is isomorphic to $f(x)=g(y)$ and also $f\circ\phi=g\circ\pi$? In other words, not only is $C$ isomorphic to $f(x)=g(y)$, but this isomorphism can be chosen so that $\pi$ is the projection onto the $y$ coordinate.
This is reminiscent of Chad Schoen's paper "Varieties dominated by product varieties", but I don't see a precise connection between the two.
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what do you mean by "curve"? since you mention a cover $C \to \mathbb{P}^1$, then it is probably a projective curve, but the nature of equation als suggests that you are talking about a plane affine curve. – Dima Sustretov Jan 5 '13 at 12:52
I mean a smooth projective curve. When I refer to "$f(x)=g(y)$", I mean the normalization of its projective closure. – Michael Zieve Jan 5 '13 at 14:00
Is $C$ meant to be geometrically irreducible? Is the ground field algebraically closed? Of characteristic 0? – user30180 Jan 5 '13 at 14:30
Yes, my question is for curves over the complex numbers. – Michael Zieve Jan 5 '13 at 14:32
Welcome, Mike!! – Lubin Jan 5 '13 at 14:35
This would contradict the Harris-Mumford(-Eisenbud) theorem that $M_g$ is non-uniruled for $g$ at least $23$. Let $C$ be a general curve of genus $g$. If $C$ is in "Zieve form", then it is the normalization of the (almost certainly) singular curve in $\mathbb{CP}^1 \times \mathbb{CP}^1$, $$D = \{ ([x_0,x_1],[y_0,y_1]) \in \mathbb{CP}^1\times \mathbb{CP}^1 \vert y_0^e f(x_0,x_1) - x_0^dg(y_0,y_1) \},$$ where $f(x_0,x_1)$, respectively $g(y_0,y_1)$, is a homogeneous polynomial of degree $d$, resp. $e$, such that $f(0,1)$ and $g(0,1)$ are nonzero (or else the defining polynomial factors to a simpler form). By direct computation, the singular points occur where $[x_0,x_1]$ is a multiple root of $f(x_0,x_1)$ and $[y_0,y_1]$ is a multiple root of $g(y_0,y_1)$ or the point is $([0,1],[0,1])$. Moreover, at each point, the local analytic type of the singularity is the same as the plane curve with equation $y^n-x^m$, where $m$, resp. $n$, is the vanishing order of $f(x_0,x_1)$, resp. $g(y_0,y_1)$ at that point. In particular, the "delta invariant" depends only on $(m,n)$. Thus, if you "deform" $f(x_0,x_1)$ and $g(y_0,y_1)$ so that the number and type of multiple roots remains constant, then the normalizations of the corresponding curves in $\mathbb{CP}^1\times \mathbb{CP}^1$ remain of genus $g$. However, the family of such deformations of $(f,g)$ is a rational variety. Precisely, if you write $$f(x_0,x_1) = (x_1-a_1x_0)^{m_1}(x_1-a_2x_0)^{m_2}\cdots (x_1-a_rx_0)^{m_r},$$ with $(a_1,\dots,a_r)$ pairwise distinct, then the deformation space for $f$ is just a Zariski open subset of the affine space with coordinates $(a_1,\dots,a_r)$, and similarly for $g(x_0,x_1)$. Since $M_g$ is non-uniruled, this is a contradiction: there is only the constant morphism from a rational variety to $M_g$ whose image contains the general point parameterizing $C$.
Edit. Mike also asks whether this could be true if $f$ and $g$ are rational functions rather than polynomial functions. This is equivalent to replacing the defining equation above in $\mathbb{CP}^1 \times \mathbb{CP}^1$ by the more general equation $$g_0(y_0,y_1)f_1(x_0,x_1) - f_0(x_0,x_1)g_1(y_0,y_1),$$ where $f_0$, $f_1$ are homogeneous of degree $d$ with no common factor, and where $g_0$, $g_1$ are homogeneous of degree $d$ with no common factor. The same observations apply: the number and types of singularities depend only on the number and multiplicities of the roots of $f_0$, $f_1$, $g_0$ and $g_1$. By varying those (distinct, likely repeated) roots as in the previous paragraph, one gets a morphism from a rational, quasi-projective variety to $M_g$. By Harris-Mumford(-Eisenbud), the only such morphism is constant if the image contains a general point of $M_g$.
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Thanks Jason! That's a very nice argument. – Michael Zieve Jan 5 '13 at 21:18
I'm totally going to start saying "Harris and Mumford proved that the generic genus g curve is not Zieve." – JSE Jan 5 '13 at 23:06
There is a geometric question (I believe inspired by arithmetic questions of Nick Katz): what is the maximal-dimensional uniruled or rationally connected subvariety of $M_g$. So far the biggest subvarieties are moduli spaces of trigonal curves. Perhaps moduli of Zieve curves are a contender(?). – Jason Starr Jan 6 '13 at 1:09
Suppose you restrict attention to curves defined over Q? Is the result still true, and can you exhibit an example? What about the Klein quartic for example? I believe its Jacobian is a factor of the Jacobian of the Fermat curve of degree 7, but it's not clear to me whether it is a model of some f(x)=g(y). – paul Monsky Jan 6 '13 at 16:38
@paul: I just remembered the Lang and Vojta conjectures about rational curves and rational points on varieties of general type. According to the conjectures, there is a proper, closed subvariety of $M_g$ that contains <B>all</B> rational curves in $M_g$. This strongly suggests that there are only finitely many sequences of multiplicities $(m_i)$ that give Zieve curves of genus $g$. I bet we could bound these sequences, and then use that to find a curve of genus $g$ defined over some number field that is not a Zieve curve. – Jason Starr Jan 7 '13 at 17:25
I think that the answer is no.
Here is a somewhat related problem. Every curve curve $C$ of genus >0, has meromorphic functions $x,y$ on it which are not related by any equation of the form $f(x)=g(y)$. I denote by $(x)=(x)^+-(x)^-$ the principal divisor of an element $x$, zeros minus poles. If $x$ and $y$ are two elemets of the field of meromorphic functions on $C$, related by $f(x)=g(y)$, where $f,g$ are ratonal functions, then the divisors of poles of $x$ and $y$ are related as follows: $$m(x)^-\sim n(y)^-,$$ where $\sim$ means the usual equivalence of divisors. (Two dividors $d$ and $e$ are equivalent if $d=e+(z)$). And $m,n$ are degrees of $f,g$.
Now the factor of the set of all divisors over this equivalent equation is a torus of dimension $g$ ($g$ is the genus of $C$). We only need the fact that it is uncountable for $g>0$. So we can always find incommensurable divisors of the form $(x)^-$ and $(y)^-$. These $x$ and $y$ are related by some polynomial relation $F(x,y)=0$, but cannot be related by an equation of the form $f(x)=g(y)$.
This solution was explained me by Drinfeld in 1980 when I asked him more general question: Can every algebraic relation $F(x,y)=0$ be obtained from a chain $x=x_1,x_2,x_3,\ldots,x_n=y$ where $x_i$ and $x_{i+1}$ are related by $f_i(x_i)=f_{i+1}(x_{i+1})$, with some rational functions $f_i$, by elimination of $x_2,...x_{n-1}$? The answer is no, for the same reason).
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How about over countable ground fields like $\overline{\mathbf{Q}}$? – user30379 Jan 5 '13 at 16:23
Hi Alex, you seem to be showing that if $g>0$, $x,y$ can be chosen so that $f(x)=g(y)$ cannot hold. But the question is whether $x,y$ can be chosen so that such a relation does hold. It is certainly possible sometimes, e.g. when $C$ is hyperelliptic. I suspect it is false for generic $C$, however. – Donu Arapura Jan 5 '13 at 16:32
Thanks Alex. But I agree with Donu: you showed that for most choices of $\pi\colon C\to\mathbb{P}^1$ and $\phi\colon C\to\mathbb{P}^1$, there do not exist nonconstant polynomials $f$ and $g$ such that $f\circ\phi=g\circ\pi$. Whereas my question is whether this can happen for every choice of $\phi$ and $\pi$, subject to the additional constraint that $f(x)=g(y)$ is irreducible. – Michael Zieve Jan 5 '13 at 16:51
Perhaps this is the same objection raised by Donu and Mike, but there are several problems with this answer. First of all, a generic curve depends on 3g-3 parameters, not g parameters. More importantly, although the arithmetic genus of the image curve in $\mathbb{P}^2_{\mathbb{C}}$ is quadratic in $d$, the image may be very singular. Thus the geometric genus of the normalization may be much smaller than $d$. So I do not see any very easy "parameter count" that rules this out. Probably a better approach is to argue that such curves have non-simple Jacobians. – Jason Starr Jan 5 '13 at 19:28
@pranavk: if $A$ is a (non-zero) Abelian variety over $k=\bar{\mathbf Q}$, the rank of $A(k)$ is infinite. Consequently, if $C$ is a curve over $k$, one may find effective divisors of arbitrary degree $D,E$ such that $D-E$ has degree zero, but is not torsion. If $\deg(D)>2g$, Riemann-Roch implies that $D$ is the divisor of zeroes of some function $x$, and same for $E={\rm div}^-(y)$. Then $x$ and $y$ are not related by an equation of the form $f(x)=g(y)$. – ACL Jan 5 '13 at 19:58
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2014-08-29 22:08:21
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