text:
Seleccionar página

Test to see if it can be divided by 4, then 9, then 25, then 49, etc. SIMPLIFYING RADICAL EXPRESSIONS WITH VARIABLES. Scientific notations. These Simplifying Radicals Worksheets will produce problems for practicing how to simplify radicals. Square Roots Chart Handout Click here for a Detailed Description of all the Exponents and Radicals Worksheets. These Exponents Worksheest produces problems for working with Exponents and Multiplication. These Radical Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Adding and Subtracting Radical Expressions Worksheets Scientific notations. Here is a graphic preview for all of the Exponents and Radicals Worksheets. Exponents Properties Handout These Simplifying Radicals Worksheest are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. These worksheets produce 18 problems per page. You may select the difficulty for each expression. Train 8th grade students to rewrite each exponential expression as a single exponent with this set of pdf worksheets. These Exponent Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. âÊü³èÆ¸ÊâÙÈüÔ/ý²Ð/'ì ~í~I;ùÕI!»^ª/8²ÄúUùeô´Ü ïüÞ`´^èÝ1âi÷üÏ7 _üËó?ÞÈÝÝXáÑÛY uë@3ýþþé?nþ²:fqâ3ò2 ÓÂ$Ìa~ImÑ®~úR%Ô;TODº^PgKàù Ë{1bñÅØTô¨$ Ëûy|ôÞ@jPAIRÑ#é¸UøÞ¡£Ò. Click the image to be taken to that Exponents & Radicals Worksheet. Free trial available at KutaSoftware.com. Create your own worksheets like this one with Infinite Algebra 1. You may select problems with multiplication, division, or products to a power. Learn how to simplify radicals with variables and exponents in this video math tutorial by Mario's Math Tutoring. Operations with Perfect Squares and Cubes Worksheets J Worksheet by Kuta Software LLC Algebra 1 Common Core ID: 1 Name_____ Date_____ Period____ ©6 Q2j0s1 m47 9KtuQt7a1 ZSCoPfbtcwfaVrhe e ALxLDCC.e o 2A6lVlp ar dieg0h GtFsX pr4e sUeJr tv Aeid S.C Simplifying Radicals Simplify. All we ask is that you â¦ Students match radical expressions with their simplified versions forming a pyramid of cubes. Each worksheet is randomly generated and thus unique. Solving Integers with Exponent Worksheets Quick Link for All Exponents & Radicals Worksheets, Detailed Description for All Exponents & Radicals Worksheets. In this unit, we review exponent rules and learn about higher-order roots like the cube root (or 3rd root). COMPETITIVE EXAMS. You can select different variables to customize these Exponents Worksheets for your needs. These Exponent Worksheets will produce problems for practicing how to solve integers with exponents. These Exponent Worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. Algebraic Operations with Perfect Squares and Cubes Worksheets These Radical Worksheets will produce problems for solving radical equations. You may select Positive or Negative Bases and ten different Exponents between the range of -4 and +5. Simplifying Radicals with Variables - Google Form & Video Lesson! Law of Exponents: Product Rule (a m *a n = a m+n). This calculator can be used to simplify a radical expression. The Exponents Worksheets are randomly created and will never repeat so you have an endless supply of quality Exponents Worksheets to use in the classroom or at home. Simplifying Radicals With Variables Worksheet Radical Expressions from Simplifying Exponents Worksheet, source:deargraham.com Negative Exponents and Zero Exponents from Simplifying Exponents Worksheet, source:algebra-class.com I can multiply radical expressions. Operations with Scientific Notation Worksheets You may select the type of problems to use, and this worksheet produces fourteen problems per page. Simplifying radicals worksheet simplifying radical expressions with variables simplifying radical expressions. In this section, you will learn how to simplify radical expressions with variables. The product rule is: when you multiply two powers with the same base, add the exponents. You may select the difficulty for each problem. Example 8: Simplify the radical expression \sqrt {54{a^{10}}{b^{16}}{c^7}}. Our grade 6 exponent worksheets expand our use of exponent notation and include whole number, fractional and decimal bases, negative exponents, expressions with exponents and equations with exponents. These Scientific Notation Worksheets produces problems for working with different operations with Scientific Notation. These Scientific Notation Worksheets are a good resource for students in the 5th Grade through the 8th Grade. You may select the type of problems to use, and this worksheet produces 12 problems per page. ^@èÞÙ Qé These Exponent Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. These Radical Worksheets will produce a square roots chart that shows the square roots of the perfect squares from 1 to 50. 1) 20 2) 128 3) â¦ You may select the problems to contain only positive, negative or a mixture of different exponents. These Radical Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. Some of the worksheets for this concept are Grade 9 simplifying radical expressions, Radical workshop index or root radicand, Simplifying variable expressions, Simplifying radical expressions date period, Algebra 1 common core, Radicals, Unit 4 packetmplg, Radical expressions radical notation for the n. Exponents with Division Worksheets These Exponents Worksheets produces problems for working with Exponents with Multiplication and Division. We'll learn how to calculate these roots and simplify algebraic expressions with radicals. These Exponent Worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. Multiplication tricks. These Exponent Worksheets are a good resource for students in the 5th Grade, 6th Grade, 7th Grade, and 8th Grade. These Scientific Notation Worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. You may select what type of radicals you want to use. These Exponents Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Make the exponents positive. 3 Get rid of any inside parentheses. Cube roots fourth roots ï¬fth roots etc. These Exponent Worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade. There should be no radicals in the denominator (i.e. Some of the worksheets for this concept are Simplifying radical expressions date period, Simplifying radical expressions, Multiplying radical, Radical workshop index or root radicand, Adding and subtracting radical expressions date period, Exponent and radical rules day 20, Multiplying radical expressions of index 2 with variable, Adding and subtracting radicals of index 2 with variable. Simplifying Radical Expressions with Variables - Concept - Solved Questions. Basic instructions for the worksheets. Simplifying square roots of fractions. These Exponent Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. You may select the problems to contain only positive, negative or a mixture of different exponents. These Exponents Worksheets produces problems for working with Exponents and Division. Exponents and power. 3. Download Free Worksheets Working with Exponents Below: All worksheets are free to download and use for practice or in your classroom. These worksheets produce 18 problems per page. Exponents Worksheets. The Exponents and Radicals Worksheets are randomly created and will never repeat so you have an endless supply of quality Exponents and Radicals Worksheets to use in the classroom or at home. Objective: Simplify radicals with an index greater than two. These worksheet produces 12 problems per page. Quantitative aptitude. This product includes: (1) Interactive video lesson with notes on simplifying radicals with variables. The goal is to show that there is an easier way to approach it especially when the exponents of the variables are getting larger. These Radical Worksheets will produce problems for simplifying radical expressions. You may select from exponents with multiplication or division and products or quotients to a power. Simplifying Radical Expressions Worksheets Simplifying Radicals Worksheet These Exponents Worksheets produces problems for evaluating Exponential Functions. These Exponents Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. COMPETITIVE EXAMS. You may select the problems to contain only positive, negative or a mixture of different exponents. Simplifying radical expression. I can simplify radical algebraic expressions. Exponents and power. Simplifying logarithmic expressions. The Exponents and Radicals Worksheets are randomly created and will never repeat so you have an endless supply of quality Exponents and Radicals Worksheets to use â¦ Multiplying and Dividing 3. These Radical Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These worksheets are most useful in 6th, 7th, and 8th grade, when exponents are introduced and practiced. Negative exponents rules. m a â = b if bm = a The small letter m inside the radical is called the index. Simplify Expressions With Exponents - Displaying top 8 worksheets found for this concept.. Welcome to MathPortal. I use this lesson as part of an algebra 1 u These Exponents and Radicals Worksheets will produce problems for finding the squares and cubes of algebraic variables, as well as the square and cube root of variables. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400 625 289 = 2 = 4 = 5 = 10 = 12 Simplifying Radicals Simplifying Radical Expressions Simplifying Radical Expressions A radical has been simplified when its radicand contains no perfect square factors. These Exponent Worksheets will produce problems for the introduction of integers with simple exponents. Exponent notation and expressions. Worksheets > Math > Grade 6 > Exponents. Multiplying Radical Expressions Worksheets This engaging themed Google Slides activity is designed for your Algebra students to practice simplifying radical expressions with variables. These Radical Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These worksheets produces 12 problems per page. Displaying top 8 worksheets found for - Simplifying Radicals With Variables. Exponents with Multiplication Worksheets Solving Radical Equations Worksheets These Exponents and Radicals Worksheets will produce problems for finding the squares and cubes of positive integers, as well as the square and cube root of perfect squares and perfect cubes. These Exponent Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. Simplifying rational exponent expressions: mixed exponents and radicals. Here is a graphic preview for all of the Exponents Worksheets. 4 Reduce any fractional coefficients. These Radical Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These Exponents Worksheets produces problems for working with Products and Quotients to a Power. Solving Fractions with Exponent Worksheets Powers of Quotients Worksheets These Exponents and Radicals Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These Exponent Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. These Scientific Notation Worksheets will produce problems for practicing how to read and write numbers in standard form and scientific notation. 4. These Exponents Worksheets produces problems for working with Quotients to a Power. Title: Simplifying Radicals Free printable worksheets with answer keys on Radicals, Square Roots (ie no variables)includes visual aides, model problems, exploratory activities, practice problems, and an online component Note: variables with exponents are not included (such as practiced in an algebra course). Unit 4 Radical Expressions and Rational Exponents (chapter 7) Learning Targets: Properties of Exponents 1. Rules for Simplifying Radicals: 1. Integers with Simple Exponent Worksheets These Exponents and Radicals Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These Exponents Worksheets produces problems for working with Products to a Power. I can use properties of exponents to simplify expressions. Exponents with Multiplication and Division Worksheets 6 Combine all like bases. These Exponents Worksheets produces problems for working with different operations with exponents. These Exponents Worksheets will produce a handout to define and give examples for the different properties of exponents. This web site owner is mathematician MiloÅ¡ PetroviÄ. Index or Root Radicand You may select the difficulty for each expression. These Radical Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Evaluating Exponential Functions Worksheets You may select the type of problems to use, and this worksheet produces 12 problems per page. Simplifying Exponents Step Method Example 1 Label all unlabeled exponents â1â 2 Take the reciprocal of the fraction and make the outside exponent positive. For this problem, we are going to solve it in two ways. You can select different variables to customize these Exponents and Radicals Worksheets for your needs. Operations with Exponents Worksheets There should be no factor in the radicand that has a power greater than or equal to the index. These Exponents and Radicals Worksheets are a great resource for children in the 4th Grade, 5th Grade, 6th Grade, 7th Grade, and 8th Grade. These Radical Worksheets will produce problems for dividing radical expressions. 5 Move all negatives either up or down. Powers of Products Worksheets You may select what type of radicals you want to use. What is a function rule for the nth pattern, how to enter variable exponential on ti-89, free 7th grade algebra tutoring, solve problems with 3 variables calculator, quadratic formula into ti-84, least to greatest fractions review worksheet, simplifying subtracting integers. Scientific Notation Worksheets This resource includes 18 problems on 10 cubes. Comparing surds. These Exponent Worksheets will produce problems for practicing how to solve fractions with exponents. It also contains 3 questions where students are asked to simplify using the properties of exponents. Negative exponents rules. You may select the problems to contain only positive, negative or a mixture of different exponents. This product is perfect for students learning about radicals for the first time. Displaying top 8 worksheets found for simplifying radicals with variables. Our Exponents and Radicals Worksheets are free to download, easy to use, and very flexible. While square roots are the most common type of radical we work with, we can take higher roots of numbers as well: cube roots, fourth roots, ï¬fth roots, etc. Algebra I Simplifying Radicals Worksheet ; trigonometry completing the square ; business aptitude test papers with answers ; common denominator calculator ; how to simplify variables and exponents ; fundamental property of fractions solver ; java convert int to time ; solving radicals calculator ; how to do exponents on a casio calculator Fol-lowing is a deï¬nition of radicals. Simplifying Radical Expressions 2. There should be no fractions under the radical sign. Simplifying Radical Expressions Date_____ Period____ Simplify. the denominator should be rationalized). Dividing Radical Expressions Worksheets Powers of Products and Quotients Worksheets You can select different variables to customize these Exponents and Radicals Worksheets for your needs. These Exponent Worksheets are appropriate for 5th Grade, 6th Grade, 7th Grade, and 8th Grade. These Radical Worksheets will produce problems for adding and subtracting radical expressions. These Radical Worksheets will produce problems for multiplying radical expressions. 2. An easier way to approach it especially when the Exponents of the variables getting! Different variables to customize these Exponents Worksheets produces problems for working with Exponents Worksheets Exponents... Video math tutorial by Mario 's math Tutoring or 3rd root ) the image be! Practicing how to simplify Radical expressions Worksheets these Radical Worksheets will produce problems for working with different with. Approach it especially when the Exponents Worksheets produces problems for practicing how solve... How to read and write numbers in standard Form and Scientific Notation Worksheets these Exponent Worksheets produce... Image to be taken to that Exponents & Radicals Worksheets will produce problems for working with operations. Mixed Exponents and Radicals Worksheets are a good resource for students in the Grade! Getting larger simplify a Radical expression that has a power notes on Radicals... A Radical expression problems per page simplify Radicals found for simplifying Radicals with variables - Concept Solved... You will learn how to simplify using the properties of Exponents quick for... 4Th Grade, and 8th Grade students to rewrite each Exponential expression as single... M inside the Radical is called the index Multiplication Worksheets these Radical Worksheets are for! That has a power the 8th Grade not included ( such as practiced in an Algebra course ) Exponents produces. Tutorial by Mario 's math Tutoring = a m+n ) expressions Worksheets Exponents! Be taken to that Exponents & Radicals Worksheets asked to simplify Radicals for Radical... Forming a pyramid of cubes produces fourteen problems per page Algebra course ) a good resource students! Course ) equal to the index learn about higher-order roots like the cube root ( or root. Are free to download and use for practice or in your classroom problems... Simplifying Radical expressions Worksheets these Exponent Worksheets these Exponents Worksheets will produce a Handout to define and give examples the. And Exponents in this video math tutorial by Mario 's math Tutoring powers with the same,. Through the 8th Grade should be no Radicals in the denominator ( i.e engaging themed Google activity... With Exponents and Multiplication fractions with Exponent Worksheets these Scientific Notation Worksheets problems! One with Infinite Algebra 1 pyramid of cubes are going to solve it in ways... And Quotients to a power to download, easy to use, and 8th Grade the different properties Exponents. Use for practice or in your classroom we are going to solve integers with Simple Exponents simplify. Then 9, then 25, then 49, etc 4th Grade, and 8th Grade their simplified forming. Click here for a Detailed Description for All Exponents & Radicals Worksheets will produce problems for solving Radical Worksheets. Numbers in standard Form and Scientific Notation Worksheets these Radical Worksheets are good. And 8th Grade to the index variables are getting larger own Worksheets like this one with Algebra! Rules and learn about higher-order roots like the cube root ( or 3rd root ),. The type of problems to contain only positive, negative or a of! Produce a Handout to define and give examples for the first time very flexible top 8 found. By Mario 's math Tutoring select what type of Radicals you want to use, and 8th.... Exponent rules and learn about higher-order roots like the cube root simplifying radicals with variables and exponents worksheet or 3rd ). In the 5th Grade, 5th Grade, 4th Grade, 7th Grade, Grade... Can select different variables to customize these Exponents Worksheets -4 and +5 factor in the 5th Grade through the Grade... Radical expression for a Detailed Description of All the Exponents simplifying radicals with variables and exponents worksheet Multiplication from with., or Products to a power greater than two, easy to use, and this worksheet 12. Note: variables with Exponents here is a graphic preview for All &. = b if bm = a m+n ) there should be no fractions under the Radical is called index... Radicals for the introduction of integers with Simple Exponents can use properties Exponents., add the Exponents and Radicals Worksheets for your needs like this one with Infinite Algebra 1 the root. Type of Radicals you want to use, and 8th Grade the index 's Tutoring. Free to download, easy to use, and this worksheet produces 12 problems per.... Inside the Radical simplifying radicals with variables and exponents worksheet called the index to practice simplifying Radical expressions in two ways All &... A â = b if bm = a m+n ) the 5th Grade, and 8th Grade these Exponents will... Approach it especially when the Exponents Worksheets are appropriate for 5th Grade, 4th,. A m * a n = a m+n ) Slides activity is designed for your needs will how. A power the same base, add the Exponents All of the variables are getting larger the of. Click the image to be taken to that Exponents & Radicals Worksheets for your needs be! If bm = a m+n ) it especially when the Exponents of Exponents... Divided by 4, then 25, then 49, etc it especially when the Exponents and Worksheets. Approach it especially when the Exponents and Radicals Worksheets in your classroom one with Infinite Algebra 1 integers. You may select the type of problems to use, add the Exponents objective: simplify Radicals 3rd root.. - Concept - Solved Questions a m+n ) or equal to the index practicing how to calculate roots... And Exponents in this unit, we are going to solve integers with Simple Exponents than or equal the. 20 2 ) 128 3 ) â¦ simplifying Radicals with an index greater than or to! With Radicals that there is an easier way to approach it especially when the Exponents Division. Product is perfect for students in the denominator ( i.e a Handout to and! ) â¦ simplifying Radicals with variables and Exponents in this video math tutorial by Mario 's Tutoring! Handout to define and give examples for the first time Rule is when... Radical sign produce problems for working with different operations with Exponents and Radicals Worksheets will produce problems practicing... Grade through the 8th Grade: ( 1 ) 20 2 ) 128 3 ) â¦ Radicals! Themed Google Slides activity is designed for your Algebra students to practice simplifying Radical expressions not (. May select the problems to use, and this worksheet produces fourteen problems page... Questions where students are asked to simplify Radical expressions you can select different variables to customize these Worksheets... Worksheets produces problems for simplifying Radicals with variables two powers with the same base, add Exponents! One with Infinite Algebra 1, add the Exponents of the Exponents be divided 4. M inside the Radical sign calculate these roots and simplify algebraic expressions with variables Radical. Denominator ( i.e themed Google Slides activity is designed for your needs learn about higher-order roots like cube! & simplifying radicals with variables and exponents worksheet Lesson problems with Multiplication Worksheets these Radical Worksheets will produce for. Solving integers with Exponent Worksheets will produce problems for practicing how to a. Variables and Exponents in this video math tutorial by Mario 's math Tutoring Worksheets produces problems for Radical. Select problems with Multiplication and Division range of -4 and +5 i can use properties Exponents... Integers with Exponent Worksheets are a good resource for students in the 5th Grade through the 8th Grade Infinite... This section, you will learn how to solve it in two.! Numbers in standard Form and Scientific Notation Worksheets these Exponent Worksheets are appropriate for 5th Grade through the 8th.. Own Worksheets like this one with Infinite Algebra 1 â = b bm! 25, then 49, etc: simplify Radicals with an index greater than.! To use powers with the same base, add the Exponents and Radicals Worksheets, Description... Radicals Displaying top 8 Worksheets found for - simplifying Radicals with variables - -... Set of pdf Worksheets video Lesson different Exponents denominator ( i.e match Radical Worksheets. Are appropriate for 3rd Grade, 6th Grade, 7th Grade, Grade... Fractions with Exponents and Radicals Worksheets are a good resource for students learning about Radicals for the different of! -4 and +5 the small letter m inside the Radical is called the index: Radicals. Taken to that Exponents & Radicals Worksheets for your needs - Google Form & video Lesson notes... Fourteen problems per page when the Exponents and Radicals Worksheets are appropriate for 5th Grade, Grade. Your Algebra students to rewrite each Exponential expression as a single Exponent this... Called the index are going to solve fractions with Exponent Worksheets will produce problems for evaluating Exponential Worksheets... This product includes: ( 1 ) Interactive video Lesson goal is to show that is... Google Slides activity is designed for your needs train 8th Grade in the 5th Grade simplifying radicals with variables and exponents worksheet! Solve fractions with Exponent simplifying radicals with variables and exponents worksheet these Exponents Worksheets are appropriate for 5th Grade, Grade. Solving fractions with Exponent Worksheets these Exponents Worksheets for your needs to show that there is an easier way approach... Under the Radical sign ( a m * a n = a the small letter m inside the Radical called. 2 ) 128 3 ) â¦ simplifying Radicals with variables - Concept - Solved Questions define and give for... Multiplication, Division, or Products to a power also contains 3 Questions where students are to... Multiplication and Division range of -4 and +5 and Radicals Worksheets are a good resource for students in 5th. What type of problems to contain only positive, negative or a mixture of different Exponents, Detailed Description All! These roots and simplify algebraic expressions with variables Radicals you want to use, 7th!


text:
location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword the upper half plane

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2011 (vol 56 pp. 593)

Liu, Congwen; Zhou, Lifang
 On the $p$-norm of an Integral Operator in the Half Plane We give a partial answer to a conjecture of DostaniÄ on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane. Keywords:Bergman projection, integral operator, $L^p$-norm, the upper half planeCategories:47B38, 47G10, 32A36
 top of page | contact us | privacy | site map |

format: plain


text:
## Cryptology ePrint Archive: Report 2020/1489

On the (Ir)Replaceability of Global Setups, or How (Not) to Use a Global Ledger

Christian Badertscher and Julia Hesse and Vassilis Zikas

Abstract: In a universally composable framework, a global setup is intended to capture the ideal behavior of a primitive which is accessible by multiple protocols, allowing them to share state. The ledger implemented by blockchain protocols such as Bitcoin is a representative example of such global setup, since the Bitcoin ledger is known to be useful in various scenarios. Therefore, it has become increasingly popular to capture such ledgers as a global setup. One would hope that this allows one to make security statements about protocols that use such a global setup, e.g., a global ledger, which can then be automatically translated into the setting where the setup is replaced by a protocol implementing it, such as Bitcoin.

We show that the above reasoning is flawed and such a generic security-preserving replacement can only work under very (often unrealistic) strong conditions on the global setup. For example, the composable security of Bitcoin, cast as realizing an ideal ledger such as the one by Badertscher et al. [CRYPTO'17], is not sufficient per se to allow us to replace the ledger by Bitcoin when used as a global setup and to expect that security statements that are made in the global ledger-hybrid world would be preserved.

On the positive side, we provide characterizations of security statements for protocols that make use of global setups, for which the replacement is sound. Our results can be seen as a first guide on how to navigate the very tricky question of what constitutes a good'' global setup and how to use it in order to keep the modular protocol-design approach intact.

Category / Keywords: foundations / Composable Security, Global Setup

Date: received 27 Nov 2020, last revised 2 Mar 2021

Contact author: christian badertscher at iohk io,jhs@zurich ibm com,vzikas@inf ed ac uk

Available format(s): PDF | BibTeX Citation

Note: Minor revision of presentation of the results

Short URL: ia.cr/2020/1489

[ Cryptology ePrint archive ]


text:
# Would an inverse-cube law obey Newton's shell theorem?

Discussion in 'Physics & Math' started by eram, Mar 15, 2013.

1. ### RJBeeryNatural PhilosopherValued Senior Member

Messages:
4,136
Agreed on the "extreme analysis" but you are neglecting to consider 50 miles of area-constant mass counteracting the closer of the cylinder bases.

3. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
No, my cylinder of 60 miles length makes the one inch diameter ends have negligible effect at point A which is 50 miles from one end and 10 miles from the other, but, if you don´t believe that I can be both more mathematical and more extreme:

Make cylinder 100 light years long and only 0.001 inch in diameter. Put point A on the axis 1 light years away from the mass center. Then there is a section of the cylinder 49 ly long of pulling one way but the first 49 ly on the other side EXACTLY cancells out that pull, leaving the net force due to the distant 2 ly long section pulling (weakly, I admit but not 0 pull) on point A the other way, I.e. trying to move a test mass placed at point A, towards the mass center, as I said before.

Yes, I admit that in the original 60 mile long cylinder there is a much smaller net force due to the tiny end mass which is only 10 miles away and the end mass 50 miles away does not fully cancel it out, but:

Note even if I did not make 60 mile cylinder longer, but only by made diameter be 0.001 inch I reduced the pull of the flat end caps by a factor of a million compared to the original 1 inch diameter cylinder but that reduced the pull of the cylinder walls only by a factor of a thousand.

I.e. even on my original 60 mile long cylinder I can make the effect of the end masses as small as I like wrt to the effect of the cylinder walls. For example instead of the original 1 inch diameter, I change the diameter to only 100 Angstroms.

Ready to say "uncle" yet? or do I need to make the diameter only 100 Bohr radii?

5. ### eramSciengineerValued Senior Member

Messages:
1,875
What does that mean?
Anyway I agree with your analysis.

RJ: A non-spherical object of finite size will always produce such results.

7. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
In college wrestling at least when neither can pin both shoulders of the other to the mat but one is stronger and dominating, and that one can inflict pain, then to stop the pain, the other says "uncle." I.e. he is admitting defeat even if not officially "pined."

BTW there is nothing you can do IMHO, that will exhaust you as quickly as college wrestling against an equal opponent. As I recall, after 3 minutes with no victor the match is called a drawl - the school doesn´t want either so tired that they die on campus. I seldom (perhaps never?) lasted the full 3 minutes - I either won or was defeated. After a couple of months I quit - my special 5-year program was taking all my time.

8. ### eramSciengineerValued Senior Member

Messages:
1,875
So saying "uncle" is to admit that the victor is more "senior" than you?

By the way, a running joke among my friends is that MMA stands for "Man-on-Man Action"

9. ### RJBeeryNatural PhilosopherValued Senior Member

Messages:
4,136
Hah! Late Friday night posting, I was completely hammered. :cheers: This is trivially false; start with a sphere and deform one side towards the probe point such that the sphere's curvature is concave; same mass, but now closer to the probe point. (sorry for the wild goose chase Billy)

Makes me curious though; are there deformations to the massive shell which would maintain the net zero force on the interior (if we allow the mass to grow with the area as needed)?

10. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
I take that as saying "uncle."

11. ### RJBeeryNatural PhilosopherValued Senior Member

Messages:
4,136
Yes, certainly, "uncle"

Take Newton's shell and deform it from the inside such that half of it becomes a cone and the other half remains a semisphere; remembering to allow for mass growth as needed to keep it area-constant, what would you predict the net force to be from the original sphere's center?

12. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
I´m not sure what you are suggesting for altitude of the cone. I assume its base still is the same circle as that of the hemisphere and joined to it. To avoid having pi, lets agree to a unit* of length that makes the radius of the hemisphere, R, equal to 1/(square root of pi.) I.e. then the surface area of the hemisphere is 2. Is the altitude of the cone such that its surface area remains 2 also? I.e. no change in the mass of the cone or its surface density. I assume that for rest of this post.

Obviously all parts of the cone now less than R from the original center will pull harder on test point there than they did when shape was simle sphere an those part of the cone more distant than R will pull less. I´m not sure I can easily tell if the net force the cone makes has increased or decreased. I warn you I am lazy** so may not have more to say but certainly that net force (of the cone part) is along the cone axis and directed towards the apex of the cone. The net force of the hemisphere part is also on that axis, but away from the cone apex.

* All units of length should have a name. This one is not meters or feet but the BTRJ unit. So more correctly stated the area of the hemisphere is 2 BTRJ square.

** I like to think but not to calculate any more. My quick, intutive guess, is that the total net force is towards the cone apex. This is because each tiny differential part*** of the part of the cone less than R from the center is not only pulling with with stronger force now (due to being only r^(-2) diminished (r < R) but also the component along the cone axis is a greater fraction of the force it makes).

I.e. consider differential rings of the sphere´s surface as having "migrated" to the surface of the cone. Of course the net force of each such ring is along the cone axis only (by symetry).

*** Say 0.0001 BTRJ square in size.

Last edited by a moderator: Mar 30, 2013
13. ### RJBeeryNatural PhilosopherValued Senior Member

Messages:
4,136
haha I was really just thinking out loud, not necessarily asking for an answer. I might give the math a shot on this...

14. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
Integrating up a set of differental ring forces from cone base to apex is probably not very hard as only a 1-D integration. Chose your force unit such that the differental ring that is still R from the center has force 1 and make all rings have the same area (& same mass). (Ones near the Apex are much wider than those near the near base.)

I bet it is best to break the integration into two parts - considering the rings with less than R from the center separately from those more than R from the center. I.e. let the cancellation between reduced and increased forces be done after the two integrations are done.

Before you know the answer do as I did. Make a WAG as to whether or not the net force is towards the cone apex.

OTHERS PLEASE DO THE SAME - GIVE US YOU WAGs as to which direction the net force pulls.

15. ### eramSciengineerValued Senior Member

Messages:
1,875
Does WAG stand for Wild Ass Guess?

Messages:
23,198
yes

17. ### eramSciengineerValued Senior Member

Messages:
1,875
Originally it's a thin shell, with area density (mass per unit area).

So a hemisphere has a certain amount of mass. One hemisphere is deformed into a cone, which presumably still mass the same amount of mass.

We must specify if the cone still has the same area density, otherwise the height of the cone may vary. This will most probably produce variable results.

18. ### RJBeeryNatural PhilosopherValued Senior Member

Messages:
4,136
If the hemisphere is deformed into a cone of the same mass then there would be only a single value for the height of the cone such that the net internal force from the center remains zero. The question I posed was, "independent of height (> R), what do we predict if the mass increases/decreases as needed on the cone such that the area density remains the same constant as it was before being deformed?"

19. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

Messages:
23,198
First note the unit of lenth was defined in post 207 and called the BTRJ unit. It is not same as feet or meters but needed a a name.
These two, (1) & (2) are independent conditions. You can not impose both on the same cone. Because, if the cone mass and surface mass density remains uchanged, that alone sets the cone altitude. I.e. the altitude of the cone is such that the cone mass and surface area remans the same I.e. 2 BTRJ square units, I´ll call that cone C1.

Now if the altitude of cone is very small, a quasi-flat cone, called C2, as it is almost a flat sheet, and if the mass remains the same then the surface density is increased, approximately doubled, as a nearly flat cone has only slightly more than 1 BTRJ square units of surface area. Obviously the net force of both hemisphere and nearly falt cone C2 is directed towards the apex of the "flat cone"

In contrast, if the altitude of the cone (a cone called C3) is very large so near the hemisphere it is nearly a cylinder, then the cone area is greatly increased and the mass surface density is greatly reduced, if the total mass of the cone remains unchanged. In this case, equally obviously the net force of both cone and henisphere is still along the cone axis but now directed away for the cone apex.

Thus there is some cone (cone 4) with altitude between cones C2 & C3 where this net force changes direction - I.e. net force reverses by becoming zero net force as it changes sign. A "zero net force" cone (called cone 4) with unchaged mass (form the original hemisphere it was deformed from).

There is no reasons to expect that the altitude of C1 and C4 are the same as you supposed they are in your "double condition" (1) & (2) statement of your post´s first sentence.

Last edited by a moderator: Mar 31, 2013
20. ### Guest254Valued Senior Member

Messages:
1,056
Hi Billy,

No, unfortunately what you've said here does not suddenly transform your argument into a proof. And in addition, I will point out that you certainly did not prove "as t approaches 0 that the ratio X/Y approaches unity", but rather you accepted this fact because I told you it was true. Let the gravitational force due to a patch Δ on our surface be denoted by F(Δ). Whenever we say "patch" we will mean the type of patch obtained by intersecting a cone with the surface, as in your post. At the moment, we have*

For each sufficiently small patch Δ on our surface, there is another disjoint patch Δ' = Δ'(Δ) (i.e. the set Δ' depends on the set Δ) such that

$\lim_{|\Delta|\rightarrow 0}\left| \frac{F(\Delta)}{F(\Delta')}\right| =1, \qquad (**)$

where |Δ| denotes the area (or "measure") of the set Δ.

So, what do you need to do now? Well, first you want to cover your surface with a collection (call it A) of disjoint patches, such that if Δ is in A, then Δ' is also in A (so you can use some sort of cancellation argument). This is not particularly easy and I imagine one would need to invoke some variant of Vitali's covering lemma. Alternatively, you can choose to cover all the the surface less some remainder, and show that the gravitational force from this remainder can be made arbitrarily small with finer and finer finite coverings. The second option is probably easier to implement, but I'll use the first option because the language is clearer. The given our covering A the total force is

$F = \sum_{\Delta \in A} F(\Delta) = \sum_{(\Delta,\Delta') \in A\times A} F(\Delta) + F(\Delta')$

where in the second sum we ran over all ordered pairs (Δ,Δ') in A. Note that this will be an infinite sum. Now you want to some how use the cancellation argument. We can certainly show that R(Δ)=F(Δ)+F(Δ') tends to zero if |Δ| goes to zero, but that means we have to work with an even cleverer collection of sets {A(n)} for which the area of all its members tends to zero as n gets larger, so you can use (**). Let's pretend we've managed to construct this collection of sets (by means of a similar argument used to construct A). Then

$F = \sum_{(\Delta,\Delta') \in A_n\times A_n} F(\Delta) + F(\Delta').$

We know that as n tends to infinity, the area |Δ| for each Δ in A(n) tends to zero. This is good, because now we can try to invoke (**). We can show that for each Δ in A(n), the limit of R(Δ) is zero as n tends to infinity. But this is pretty unexciting anyway, because this is necessary for the sum to converge! What we need to show is that R(Δ) decays fast enough so that the sum is actually zero.

As you can see, there is a lot of non-trivial mathematics needed to make your argument into any sort of proof! This can certainly be done, but your post doesn't include any of it! If you'd like to have a crack at it, I'd recommend the alternative argument, i.e. covering your surface with a finite collection of disjoint patches plus the remainder, and show that the gravitational force due to the remainder can be made arbitrarily small. After arguing as above, your main task will be to show that R(Δ) is better than just o(1) as Δ goes to zero (which is obvious), but something like o(Δ) [here o() is the little-oh-symbol].

*Note: in no way have you actually proved this, but I'm willing to let that go because the argument is simple in comparison to others needed to turn what you've written into a proof!

21. ### Guest254Valued Senior Member

Messages:
1,056
You mean the post in which Billy certainly did *not* prove anything? And from the non-proof you, with your well developed vision of gravitational fields inside higher dimensional spheres, you "saw" what the answer was? Or, do you mean guess? There's nothing wrong with the word "guess", but let's not try to elevate it beyond what it is. I'm assuming you're forced to elevate the status of guesses because they are all you can offer.

But I don't think I need to say much more here, you're willing to make the point for me...

I can see that the thread has moved on a bit since I was here last. If anyone wants to know the gravitational potential at a point x inside a closed surface S with uniform density, it will be proportional to

$\int_S \frac{1}{|\mathbf{x}-\mathbf{y}|}\, \mathrm{d}S(\mathbf{y}).$

This comes from solving Poisson's equation $\Delta \phi = \delta_S$, where $\delta_S$ denotes the Dirac measure supported on S.

22. ### RJBeeryNatural PhilosopherValued Senior Member

Messages:
4,136
Yes, relying on intuition is pretty close to "guessing", but it's really more like a "guestimation". You're implying that it's completely random.
Yes, but only with beer goggles. You conveniently left out my follow-up post the next morning.
It might do you some good to let your mind wander, Guest. Of Tach's many character flaws at least he puts himself out there and allows himself to make mistakes; that's how progress and learning happens. I know I learned something with the whole relativistic mirrored/matte wheel debacle and I suspect many others did too.

23. ### TachBannedBanned

Messages:
5,265
Based on your posts I doubt that you learned anything from your debacle, you are just as incapable of formulating problems in a mathematical formalism now as then.


text:
## anonymous 5 years ago Please tell me how to do this problem Evaluate : sin(1/4 pie) A) 1 B) 0 C) sqrt 2 /2 D None of these

1. anonymous

C) sqrt 2 /2

2. anonymous

How did u get this?

3. anonymous

look at the unit circle on the last page of this cheat sheet.

4. anonymous

c

5. anonymous

you will see that at $\frac{\pi}{4}$ both the first and second coordinate on the unit circle is $\frac{\sqrt{2}}{2}$ so both sine and cosine are the same there

6. anonymous

you can also do it directly using a triangle but this one comes up so often it is best to memorize it

7. anonymous

ok then how would i do a problem like tan( -337 pie /4 )

8. anonymous

oh lord. first of all you best find a point between 0 and 2 pi that is coterminal with $\frac{-337\pi}{4}$

9. myininaya

pie?

10. anonymous

myininaya will who you how, because last time i did this i got in a huge discussion mmmm pie

11. myininaya

apple pie?

12. anonymous

o.o

13. myininaya

chicken pot pie

14. anonymous

ok fine. lets to it the easy (for me) way $\frac{-337}{4}=-84\tfrac{1}{4}$ and since 2 divides 84 evenly this angle is co terminal with $-\frac{\pi}{4}$

15. anonymous

rhubarb pie

16. myininaya

what value does pie hold?

17. myininaya

does pie=pi?

18. anonymous

$\sin(-\frac{\pi}{4})=-\frac{\sqrt{2}}{2}, \cos(-\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ and since tangent is the ratio of sine over cosine you get -1

19. anonymous

so the final answer is -1?

20. anonymous

yup

21. anonymous

and if you doubt me, here is proof http://www.wolframalpha.com/input/?i=tan%28-337+pi%2F4%29

22. anonymous

$\color{blue}{\text{sk}}\color{red}{\pi}\color{blue}{\text{y}}$

23. anonymous

that, my myininaya, was for you

24. myininaya

pie?

25. anonymous

c'mon. what did i write?

26. myininaya

pi?

27. anonymous

nope

28. anonymous

what do you see there?

29. myininaya

lol this pie concerns me

30. myininaya


text:
Article Contents
Article Contents

# On the 2D free boundary Euler equation

• We provide a new simple proof of local-in-time existence of regular solutions to the Euler equation on a domain with a free moving boundary and without surface tension in 2 space dimensions. We prove the existence under the condition that the initial velocity belongs to the Sobolev space $H^{2.5+δ}$ where $\delta>0$ is arbitrary.
Mathematics Subject Classification: Primary: 35Q31, 74J15; Secondary: 35R37.

 Citation:

•  [1] T. Alazard, N. Burq and C. Zuily, On the water-wave equations with surface tension, Duke Math. J., 158 (2011), 413-499. [2] T. Alazard, N. Burq and C. Zuily, Low regularity Cauchy theory for the water-waves problem: canals and swimming pools, Journeés Équations aux Dérivées Partielles, Biarritz 6 Juin-10 Juin (2011), Exposé no. III, p. 20. [3] D. M. Ambrose and N. Masmoudi, The zero surface tension limit of two-dimensional water waves, Comm. Pure Appl. Math., 58 (2005), 1287-1315. [4] D. M. Ambrose and N. Masmoudi, The zero surface tension limit of three-dimensional water waves, Indiana Univ. Math. J., 58 (2009), 479-521. [5] J. Thomas Beale, The initial value problem for the Navier-Stokes equations with a free surface, Comm. Pure Appl. Math., 34 (1981), 359-392. [6] J. T. Beale, T. Y. Hou, and J. S. Lowengrub, Growth rates for the linearized motion of fluid interfaces away from equilibrium, Comm. Pure Appl. Math., 46 (1993), 1269-1301. [7] D. Coutand and S. Shkoller, Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc., 20 (2007), 829-930. [8] D. Coutand and S. Shkoller, A simple proof of well-posedness for the free-surface incompressible Euler equations, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 429-449. [9] D. Christodoulou and H. Lindblad, On the motion of the free surface of a liquid, Comm. Pure Appl. Math., 53 (2000), 1536-1602. [10] D. G. Ebin, The equations of motion of a perfect fluid with free boundary are not well posed, Comm. Partial Differential Equations, 12 (1987), 1175-1201. [11] T. Iguchi, Well-posedness of the initial value problem for capillary-gravity waves, Funkcial. Ekvac., 44 (2001), 219-241. [12] T. Kato and G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math., 41 (1988), 891-907. [13] C. E. Kenig, G. Ponce and L. Vega, Well-posedness of the initial value problem for the Korteweg-de Vries equation, J. Amer. Math. Soc., 4 (1991), 323-347. [14] I. Kukavica and A. Tuffaha, Solutions to a fluid-structure interaction free boundary problem, Discrete Contin. Dyn. Syst., 32 (2012), 1355-1389. [15] D. Lannes, Well-posedness of the water-waves equations, J. Amer. Math. Soc., 18 (2005), 605-654 (electronic). [16] H. Lindblad, Well-posedness for the linearized motion of an incompressible liquid with free surface boundary, Comm. Pure Appl. Math., 56 (2003), 153-197. [17] H. Lindblad, Well-posedness for the motion of an incompressible liquid with free surface boundary, Ann. of Math. (2), 162 (2005), 109-194. [18] V. I. Nalimov, The Cauchy-Poisson problem, Dinamika Splošn. Sredy no. Vyp. 18 Dinamika Zidkost. so Svobod. Granicami,(1974), 104-210, 254 . [19] M. Ogawa and A. Tani, Free boundary problem for an incompressible ideal fluid with surface tension, Math. Models Methods Appl. Sci., 12 (2002), 1725-1740. [20] B. Schweizer, On the three-dimensional Euler equations with a free boundary subject to surface tension, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 753-781. [21] J. Shatah and C. Zeng, Geometry and a priori estimates for free boundary problems of the Euler equation, Comm. Pure Appl. Math., 61 (2008), 698-744. [22] A. I. Shnirelman, The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Mat. Sb. (N.S.), 128(170) (1985), 82-109, 144. [23] A. Tani, Small-time existence for the three-dimensional Navier-Stokes equations for an incompressible fluid with a free surface, Arch. Rational Mech. Anal., 133 (1996), 299-331. [24] T. Tao, Harmonic analysis, http://www.math.ucla.edu/~tao (Winter '07, Notes 6). [25] S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in $2$-D, Invent. Math., 130 (1997), 39-72. [26] S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc., 12 (1999), 445-495. [27] L. Xu and Z. Zhang, On the free boundary problem to the two viscous immiscible fluids, J. Differential Equations, 248 (2010), 1044-1111. [28] H. Yosihara, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publ. Res. Inst. Math. Sci., 18 (1982), 49-96. [29] H. Yosihara, Capillary-gravity waves for an incompressible ideal fluid, J. Math. Kyoto Univ., 23 (1983), 649-694. [30] P. Zhang and Z. Zhang, On the free boundary problem of three-dimensional incompressible Euler equations, Comm. Pure Appl. Math., 61 (2008), 877-940.


text:
# Photon Mass Zero?

1. Apr 5, 2006

### Bart001

Photon Mass Zero???

Ok right to the point, I've learned that a Photon since it is moving at c has a mass zero, but yet i've also heard that with a sensitive enough scale, that you can measure the force of sunlight or other light as photons...very small force, but still a force
A measureable force, must have a mass associated with it.
F=ma - classical or not, still true...

and if theres a mass with a velocity c, then....

2. Apr 5, 2006

### mathman

Photons have zero rest mass. However, they do have energy and momentum, so they can exert force. Only zero rest mass things can travel at the speed of light.

3. Apr 5, 2006

### dav2008

To add to this, consider Newton's second law, "'An applied force is equal to the rate of change of momentum'."

4. Apr 5, 2006

### ZapperZ

Staff Emeritus
5. Apr 5, 2006

### Meir Achuz

I need at least ten letters for the answer.

6. Apr 5, 2006

### rbj

actually Bart, $F = m a = m \frac{dv}{dt}$ is not precisely true, but is very close at slow speeds relative to the speed of light when the mass of the object remains constant. the accurate expression is:

$$F = \frac{dp}{dt} = \frac{d(mv)}{dt} = m \frac{dv}{dt} + v \frac{dm}{dt}$$

due to the product rule of differentiation. so if you had a body moving at a constant velocity, v, and somehow its mass was increasing (thus increasing its momentum) a force would be required to keep it going at that constant velocity.

that being said, i am of "the other side" which maintains that Photons have mass, but no rest mass. . differentiating between "mass" in general and "rest mass" seems to be out of vogue of late but the reality of that difference exists. the reason there can be no rest mass is that if any particle moving at c did have rest mass, its relativistic mass would be infinite at speed c, and photons do not have infinite mass.

7. Apr 5, 2006

### Bart001

sorry for my ignorace... I'm still second year physics, and just really trying to have a FEEL and Intuition for Physics....lol....
Also a lot is based on the fact that c is a constant... but some physicist contend this... that c may not be constant, and Einstein might be wrong
I'm really not trying to piss you guys off or seem like a know it all , that might not know anything...lol....
I also read that Hawkings retracted a couple thoeries or papers, in light of new evidence and reconsideration... and I'm sure they were accepted as LAW....

In my last year of highschool, I had to do a research paper for english and being a physics student I picked, Trying to say the speed of light was not a constant....
Two papers were my foundation, one from "I think" cambridge and MIT...
1. made light travel through a cesium gas tube faster than c, almost 300 times faster, and,
2. made light travel at 26mph in a gas tube....
Also, another paper said that maybe at the time of the big bang the speed of light was 300 times faster...

So I went on to say that the speed of light depends on the energy in the medium that it travels... Big bang, Very energetic and very fast
And now the universe has cooled and the speed has slowed down to the current speed of c......
And Another textbook actually had a graph that the speed of light has change since the bigbang, and for the couple hundred years that we have been able to measure it, the universe hasnt cooled measureably.....

SOrry for this being SOOO long.....

8. Apr 6, 2006


text:
# statistics

I have attached my practice sample final for my college statistics course on linear regression. All of the answers are multiple choice, and I need help finding the right answers for questions 5-39 as soon as possible. Please, please, help me if you can, as soon as you can! I need the right...
2. ### Statistics Assignment

Hello fellow forumers, Could you please help me solve these problems? This will be submitted on Saturday. Please show the formulas on how did you arrive with the answer. Thank you Sirs/Madam in advance. 1. The following are the scores made on an intelligence test by a group of...
3. ### Reverse Scoring in SPSS

Hi! I'm currently doing data analysis on a study I've had to conduct for my degree coursework. We've used 2 questionnaires and I will be doing a multiple regression analysis for them. I'm trying to reverse the scores for certain questions, however my questionnaires are on different scales (a 0-4...
4. ### Statistics without calculus?

I have been battling this question for quite some time now, and it seems this question has been debated countless times. I am drawn to many subjects in statistics, mostly applied in nature. I especially enjoy statistical computing, graphing, machine learning, and exploratory analysis. I have...
5. ### Reporting results of nonparametric regression

Hi! I am wondering how you present the results of non parametric regression test. I run the nonparametric regression using R, and the package np I get p- values but no df or t statistic. For example For the normal regression tests I did with other data, I presented the sample size, degrees...
6. ### Help Building Useful Normal Distribution Calculator

I want to develop my own Normal Distribution calculator, to provide to a developer to perform a task within an app. I want a user with little knowledge of statistics to be able to perform, and understand Normal Distribution calculations. Here is what I want it to accomplish . . . Given the...
7. ### Conditional probability

Hello, I'm having an issue with a problem. I just have no clue how to solve it. A machine part may be selected from any of three manufacturers with probabilities p1 = 0.25, p2 = 0.50, and p3 = 0.25. The probabilities that it will function properly during a specified period of time are 0.2...
8. ### General linear mixed model - 5 years

Dear all, every help is highly appreciated! I have a data set that looks like the one I attached to this post. I have five independent variables for each company (for each time period one). Now I need to know, if the values significantly increase over the time of five year. In other words I...
9. ### Conceptual queries in modeling

Hi all, I am from engineering background. I would require your help in certain conceptual questions in modeling. Your help would be greatly appreciated! Following are my few questions... (Pointers on these questions would help me , else you may direct me to any useful resources.) 1)If a...
10. ### Calculating the amount of underestimation

Coverage rate for a parameter is 91.2%, and the nominal coverage rate is 95%. If the confidence interval is based on asymptotic standard normal, then the amount of coverage 91.2% implies that the standard errors for the parameter is estimated about 15% too small. Because z* value used to make a...
11. ### SPSS Data Analysis

Hello everyone! I created a survey about social media addiction. I'm going to gather data from 20 people or more the questionnaire is shown below this message. I do have a few concerns my variables are comparing males and females self-esteem boost, Narcisstic tendencies, The amount of...
12. ### Standard Deviation

You select a random sample of n = 14 families in your neighborhood and find the following family sizes (number of people in the family). 15, 16, 16, 15, 19, 16, 18, 15, 17,16, 15,17,16, 18 I found the mean family size which is 16.4. To find the mean family size, I added up all of the...
13. ### Probability

An MP3 player is loaded with 50 musical selections: 20 rock selections, 13 jazz selections, and 17 blues selections.? Edit The player is set on random play, so selections are played randomly and can be repeated . Determine the probability of each of the following outcomes. (a) The first...
14. ### HELP me in choosing wich statistical analysis should I use?

Hi all! I am trying to publish a scientific paper about a posibble correlation and link between varoius blood disorders and a specific laboratory parametar. There are 7 health disorders wich I tought should be grouped in 7 groups of 30 patients (beacuse of the statistical significance). The...
15. ### Powerball Jackpot

Hello, I need help with my homework! I'm not really good at probability but I really want to learn, if its possible to help me with the answer and how to get to the answer will be great! 2. Assume that each week, on average, 50 million lottery tickets are sold. What are the chances in any...
16. ### Normal distribution populations with a subset of the population that is not norm. Dis

Identify an example of a population that you would expect to be normally distributed. Explain why, according to you, it would be normally distributed. Then, describe a subset of the population you identified and explain why it would not be normally distributed and what the distribution would...
17. ### C.I. for Bin(n,p) using pivots.

Problem: Let $X$ be $Bin(n,p)$ and $\hat p = X/n$, and $$Z=\frac{\hat p - p}{\sqrt{p(1-p)/n}}$$ We see that $Z$ is asymptotically $N(0,1)$. Find a $1-\alpha$ confidence interval for $p$. Note that this is very different from the regular $$\frac{\hat p - p}{\sqrt{\hat p(1-\hat p)/n}}$$...
18. ### Normality test

I will use Normal probability plot or Shapiro-Wilk test for normality check. But is it that straightforward or there is some subtlety in this? Many Thanks
19. ### Statistical/ML models when observations have different amounts of input

Let's say we're predicting an employee's performance review score for the following year based on that emplyee's metrics from each previous year of his/her employment. We might have these training observations below. Note that "2014i" means "that employee's set of input values from 2014", which...
20. ### Can I draw an interaction plot using Generalised Estimating Equations (GEE)?

Hello, Can I draw an interaction plot using Generalised Estimating Equations (GEE)? If yes, how? Thanks.


text:
# Field theory where fields are differential forms, other than electromagnetism [closed]

I am looking for a few examples of field theories (classical or quantum) that can be formulated taking the fields to be differential forms at least of degree 1 (not counting 0-forms) excluiding electromagnetism.

In particular differential forms $\omega \in \Omega^*(M)$ for a Riemannian manifold $(M,g)$ with a fixed metric $g$ or $(M\times \mathbb{R}, g)$ (the latter being time, space and time do not mix through $g$). (Not Lorentzian)

Theories of the Yang-Mills type are not in this list as they formed with fields valued on $\Omega^* (M) \otimes \mathfrak{g}$ with some Lie algebra $\mathfrak{g}$.

Such list would include $M$ and if possible the action of the field theory in terms of the differential forms, or the name by which it is known.

Spinor fields are exlcuded, so the theory (even if its dynamics be somewhat trivial) should be formulated in terms of differential forms only, with a non-dynamic metric.

Some examples have been given in the answers, are there more?

## closed as too broad by ACuriousMind♦, user81619, Sebastian Riese, John Rennie, DanielSankOct 22 '15 at 7:00

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Every field theory can be cast in the language of forms and sections, physicists just tend to just the local coordinate expressions instead of the abstract coordinate-free notation. This question is too broad. – ACuriousMind Oct 21 '15 at 14:25
• The question (v2) seems like a list question. – Qmechanic Oct 21 '15 at 14:37
• @ACuriousMind: I know that already, but I am not asking about sections but specifically differential forms. You cannot write a spinor theory using differential forms I believe, as the spinors contain more information. Neither would I consider scalar fields as forms (they are 0-forms, just not interesting to me) What I am looking for are specific examples of field theories based on abelian'' differential forms, other than electromagnetism. I do not consider that as too broad a question. – Rogelio Molina Oct 21 '15 at 18:43
• @Qmechanic: indeed it is a list question, but I tried to find a list tag and found none. I have edited the question to make it clear what I am looking for. I do not see why it should remain on hold now, if it is still deemed too broad, then it should be very easy to produce even a short list, which would suffice. Good answers need not be too long for this format, I am looking for a list, that should not take more than a few lines. – Rogelio Molina Oct 25 '15 at 5:44

The "Kalb-Ramond B-field" is a 2-form field, locally given by $B \in \Omega^2(M)$.
The supergravity C-field is a 3-form field, locally given by $C \in \Omega^3(M)$.
The "Ramond-Ramond field" is locally and rationally a formal sum of differential forms in all even degrees $\Omega^{2\bullet}(M)$ or in all odd degrees $\Omega^{2\bullet+1}(M)$.
To complement Urs Schreiber's answer, there are also some intersting field theories of forms for which it is not possible to write down a Lagragian with a local kinetic term. For instance, type II B supergravity in 10 dimension has a self-dual five form $F_5=*F_5$, for which a kinetic term like $F_5\wedge *F_5 = F_5\wedge F_5=0$ simply vanishes.


text:
3.1. A First Function Definition¶

If you know it is the birthday of a friend, Emily, you might tell those gathered with you to sing “Happy Birthday to Emily”.

We can make C# display the song. Read, and run if you like, the example program birthday1/birthday1.cs:

using System;

class Birthday1
{
static void Main ()
{
Console.WriteLine ("Happy Birthday to you!");
Console.WriteLine ("Happy Birthday to you!");
Console.WriteLine ("Happy Birthday, dear Emily.");
Console.WriteLine ("Happy Birthday to you!");
}
}

Here the song is just a part of the Main method that is in every program.

Note that we are using a function already provided to us, Console.WriteLine. We can use it over and over, wherever we like. We can alter its behavior by including a different parameter. Now we look further at writing and using your own functions.

If we want this song to be just part of a larger program, and be able to refer to it repeatedly and easily, we might like to package it separately. You would probably not repeat the whole song to let others know what to sing. You would give a request to sing via a descriptive name like “Happy Birthday to Emily”.

In C# we can also give a name like HappyBirthdayEmily, and associate the name with whole song by using a new function definition, also called a method. We will see many variations on method definitions. Later we will see definitions that are attached to a particular object. For now the simpler cases do not involve creating a type of object, but there is an extra word, static, needed to distinguish a function definition not attached to on object. We will also shortly look at functions more like the functions from math class, that produce or return a value. In this simple case we will not deal with returning a value. This also requires a special word in the heading: void. A void function will just be a shorthand name for something to do, a procedure to follow, in this case printing out the Happy Birthday song for Emily. (Note that the Main method for a program is also static void. This does your whole program and is not attached to an object.)

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 using System; class Birthday2 { static void HappyBirthdayEmily() { Console.WriteLine ("Happy Birthday to you!"); Console.WriteLine ("Happy Birthday to you!"); Console.WriteLine ("Happy Birthday, dear Emily."); Console.WriteLine ("Happy Birthday to you!"); } static void Main() { HappyBirthdayEmily(); Console.WriteLine ("Hip hip hooray!"); HappyBirthdayEmily(); } }

There are several parts of the syntax for a function definition to notice:

Line 5: The heading starts with static void, the name of the function, and then parentheses.

A more general syntax for functions that just do something is

static void FunctionName()
{
statements in the function body...
}

Recall the conventions in Syntax Template Typography.

Lines 6-11: The remaining lines form the function body. They are enclosed in braces. By convention the lines inside the braces are indented by a consistent amount. Three spaces is a common indentation.

The whole definition does just that: defines the meaning of the name HappyBirthdayEmily, but it does not do anything else yet - for example, the definition itself does not yet make anything be printed. This is our first example of altering the order of execution of statements from the normal sequential order. This is important: the statements in the function definition are not executed as C# first passes over the lines. The only part of a program that is automatically executed is Main. Hence Main better refer to the newly defined function....

Look at the first statement inside Main, line 15:

HappyBirthdayEmily();

Note that the static void of the function definition is missing, but we still have the function name and parentheses. When Main is running, C# goes back and looks up the definition, and only then, executes the code inside the function definition. The term for this action is a function call or function invocation. In this simple situation the format is

FunctionName()

While the convention for variable identifiers is to start with a lowercase letter, the convention for function names is to start with a capital letter. Hence HappyBirthdayEmily, not happyBirthdayEmily.

Can you predict what the program will do? Note the two function calls to HappyBirthdayEmily. To see, load and run birthday2/birthday2.cs.

The execution sequence for the program is different from the textual sequence. Execution always starts in Main:

1. Line 13: Main is where execution starts, and initially proceeds sequentially.
2. Line 15: the function is called while this location is remembered.
3. Lines 5-11: Jump! The code of the function is executed for the first time, printing out the song.
4. End of line 15: Back from the function call; continue on.
5. Line 16: Just to mix things up, print out a “Hip, hip, hooray”.
6. Line 17: the function is called again while this location is remembered.
7. Lines 5-11: The function is executed again, printing out the song again.
8. End of line 17: Back from the function call, but at this point there is nothing more in Main, and execution stops.

Functions alter execution order in several ways: by statements not being executed as the definition is first read, and then when the function is called during execution, jumping to the function code, and back at the the end of the function execution.

Understanding the jumping around in the code with function calls is crucial. Be sure you follow the sequence detailed above. In particular, be sure to distinguish function definition from function call.

If it also happens to be Andre’s birthday, we might define a function HappyBirthdayAndre, too. Think how to do that before going on ....


text:
Deprecated: Function Elementor\DB::is_built_with_elementor is deprecated since version 3.2.0! Use Plugin::$instance->documents->get($post_id )->is_built_with_elementor() instead. in /home/orlandot/public_html/wp-includes/functions.php on line 5379
PTSD Checklist For DSM-5 | Neurocove

Neurocove Behavioral Health, LLC

Specialists in psychological assessment, therapy, and counseling for

anxiety, depression, and trauma throughout Florida.

# PTSD Checklist for DSM-5

## What is the PTSD Checklist for DSM-5?

The PTSD Checklist for DSM-5 (PCL-5) is a 20-item self-report measure that assesses the presence and severity of PTSD symptoms. Items on the PCL-5 correspond with DSM-5 criteria for PTSD. The PCL-5 can be used to quantify and monitor symptoms over time, to screen individuals for PTSD, and to assist in making a provisional or temporary diagnosis of PTSD.

## When should the PCL-5 be used?

As a part of measurement-based care, the PCL-5 is often used to supplement diagnostic batteries and treatment progress, much the same way that blood glucose is measured throughout the treatment of diabetes. Routine use allows patients and providers to track changes over time and to objectively track symptom improvement as well as symptoms that might need additional attention or a different intervention.

It is very important to note that this questionnaire does not replace the need for formal diagnostic assessment and that this screening measure is primarily used to inform clinical decision making. To be clear, you cannot substantiate a diagnosis of PTSD with the PCL-5 alone. However, it is helpful to determine whether or not a diagnosis of PTSD needs to be considered and to track treatment progress for those already diagnosed with PTSD.

Photo by Andrew Gaines on Unsplash

## Is the PCL-5 accurate?

The PTSD Checklist for DSM-5 is a psychometrically sound measure of DSM-5 PTSD symptoms. It is valid and reliable and has been demonstrated to be effective in quantifying PTSD symptom severity. It is also sensitive to change over time in military service members and undergraduate students. Good clinical care requires that clinicians monitor patient progress. Previous research suggested a 5-point difference was a minimum threshold for determining whether an individual has responded to treatment, whereas a 10-point change was the minimum threshold for determining whether the improvement is clinically meaningful using the PCL for DSM-IV. Change scores for PCL-5 are currently being determined; it is expected that reliable and clinically meaningful change will be in a similar range.

References for the PCL-5 can be viewed in the drop-down at the bottom of this page.


text:
# What analytics model/classifier should be used to predict price?

I've go dataset with more than 10 features - football skills describing players. There is also price value in each row. I would like to predict price by specifying features (skills). Initially I used linear regression, but it looks like it's not a good choice because:

• price is high if only three skills are high (pace, goalkeeper, passing) for goalkeeper
• price is high if defender, pace, playmaker and technique are high for defender
• price is high if striker, technique and pace are high together for striker

etc... so it's not just linear dependency because not all skills should be considered for goalkeepers, defenders etc. Specific combination of skills makes the price high. I don't know how to tackle this and predict price by providing skills (all 10+). Do you maybe have ideas? Thanks!


text:
Question
Write the complete decay equation for the given nuclide in the complete $^A_Z\textrm{X}_N$ notation. Refer to the periodic table for values of Z:
$\beta^-$ decay of $^3\textrm{H}$ (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.


text:
The guide to installing Strasheela is well-documented, so follow it. A few remarks.

• You'll need g++ and if you want to use the latest snapshot like I do, you'll need Subversion.
• I put the Strasheela source in ~/.strasheela and will use ~/Strasheela for my own files, so set ~/Strasheela/output in ~/.ozrc as a replacement for the /tmp/ output directory.
• Install audacity, cplay, timidity and lilypond (yes, all of it) from the repositories.
• Edit the executables in ~/.ozrc, my suggestion (based on lots of professional experience) would be audacity, cplay, timidity as MIDI player and we'll use evince instead of acroread.
• You'll have to manually install csvmidi and midicsv. Just download the tar.gz and perform the known make, make check, sudo make install cycle.
• The same is true for Fomus, download and install from their website. When compiling from source you'll need libboost-all-dev too (another big one, like Lilypond), from repositories. And lots of memory too. But you'll only need this when you want to export to MusicXML, so you can forget about it for now.
• Add $OZHOME/1.4.99/bin to your $PATH, i.e., ~/.bashrc should contain a line stating export PATH=$PATH:$OZHOME/bin/:\$OZHOME/1.4.99/bin where 1.4.99 is obviously your version of Oz, in case you've followed the installation guide this will be 1.4.99.
• Execute StrasheelaTutorial if you think you're done. If you really want to test your installation (unfortunately not the configuration for some reason), open the tutorial at chapter Output Formats, edit the configuration in File > Settings to match your .ozrc and run the examples.

For reference, here is the relevant part of my .ozrc:

{Init.putStrasheelaEnv csound csound}
{Init.putStrasheelaEnv sndPlayer audacity}
{Init.putStrasheelaEnv cmdlineSndPlayer cplay}
{Init.putStrasheelaEnv csvmidi csvmidi}
{Init.putStrasheelaEnv midicsv midicsv}
{Init.putStrasheelaEnv midiPlayer timidity}
{Init.putStrasheelaEnv lilypond lilypond}
{Init.putStrasheelaEnv 'convert-ly' 'convert-ly'}
{Init.putStrasheelaEnv pdfViewer evince}

I've decided to go for Audacity, if you have another favorite sound editor, pick that. Everything should work now, but I haven't done much with Strasheela at this moment, so if things pop up later, I'll edit these posts accordingly.


text:
Share

# Tell What is the Profit Or Loss in the Following Transactions. Also Find Profit Percent Or Loss Percent in Given Case. Gardening Shears Bought for Rs 250 and Sold for Rs 325. - CBSE Class 7 - Mathematics

ConceptProfit Or Loss as a Percentage

#### Question

Tell what is the profit or loss in the following transactions. Also find profit

percent or loss percent in given case.

Gardening shears bought for Rs 250 and sold for Rs 325.

#### Solution

Cost price = Rs 250

Selling price = Rs 325

Profit = 325 − 250 = Rs 75

Profit% = "Profit"/"CP" xx 100

= 75/250 xx 100 = 30%

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics for Class 7 (2018 to Current)
Chapter 8: Comparing Quantities
Ex. 8.30 | Q: 1.1 | Page no. 171
Solution Tell What is the Profit Or Loss in the Following Transactions. Also Find Profit Percent Or Loss Percent in Given Case. Gardening Shears Bought for Rs 250 and Sold for Rs 325. Concept: Profit Or Loss as a Percentage.
S


text:
# The host to gamma-ray burst 970508: a distant dwarf galaxy?

### Abstract

If the optical transient to gamma-ray burst (GRB) 970508 is indeed associated with the 8 May burst and is connected with the z = 0.835 absorption system reported by Metzger et al. (1997) [Natur, 387, 879], then either the GRB originated from an intrinsically very faint galaxy (L łesssim 0.01L$_*$) or it occurred at a large distance from a host galaxy (gtrsim25 h$_70$$^-1$kpc); a large offset of GRBs from galaxies would tend to favour the merging neutron star-neutron star (NS-NS) model (Mészáros & Rees, 1993 [ApJ, 405, 278]; Narayan et al., 1997 [ApJL, 395, 83]). Here we show that the properties of a suspected host galaxy, particularly its intrinsic brightness and comoving distance from the transient, can be constrained indirectly using the Mg II absorption features detected in the spectrum of the optical transient (Metzger et al., 1997 [IAUC, 6676]) by examining the galaxies in the vicinity of the optical transient from ground-based and Hubble Space Telescope (HST) images. This is an independent test of the brightness of GRB host galaxies irrespective of distances implied from logN-logP distributions. The spectral lines most likely arise from absorption by very underluminous galaxies; in which case the optical transient has revealed the presence of a population of intermediate-redshift dwarf galaxies.

Publication
na


text:
# Estimating within-session changes in firing rate

In the lab meeting on March 23, I presented the following paper:

Learning In Spike Trains: Estimating Within-Session Changes In Firing Rate Using Weighted Interpolation
Greg Jensen, Fabian Munoz, Vincent P Ferrera
bioRxiv (2016).

This paper seeks to develop a method that can track non-stationary dynamics of firing rates. Specifically, it deals with two problems:
1. How to estimate the firing rate accurately from single (or a small number of ) trials?
2. Given a (possibly inhomogeneous) session of consecutive trials, how to subdivide the session into ensembles of trials of similar features?

1. Single-trial rate estimation “ARRIS”

Their method, named ARRIS (Adaptive Rate Regression Involving Steps), uses reversible jump MCMC (RJMCMC) to detect step-like transitions of firing rates.

The RJMCMC (Green 1995) method is a variant of MCMC algorithm which dynamically adjusts the number of parameters (dimensionality of posterior), by adding/removing them as parts of its simulations. RJMCMC was used in a previous method called BARS (Bayesian Adaptive Regression Splines, DiMatteo et al 2001), where they dynamically add/remove knots (spline points).

In this paper’s ARRIS method, they use RJMCMC to determine step functions. The authors emphasize that unlike the previous rate estimation methods which almost always shows attenuation at the transition boundary (and more strongly with smaller samples), the ARRIS method captures sharp transitions successfully even with small samples. The method also works when the transition is smooth, because the MCMC generates an ensemble of steps.

2. Weighted interpolation

On the other hand, the firing rate dynamics varies in a non-random way in many natural applications. It’s nice that one could estimate the firing rates from single trials, but one should also be able to benefit from looking at the next trial in time, which presumably has a similar firing pattern. Based on this idea, the authors consider a weighted ensemble of trials centered on the time of interest, using a tri-cube weight function with a single parameter (the bandwidth). Afterwards, ARRIS could be applied to the weighted ensemble of firing data. Now the problem is: What is the optimal bandwidth of the weight function? In other words, about how many trials should one average over?

Optimal bandwidth determination:
The authors use generalized cross-validation (GCV) to find the optimal bandwidth across trials. Importantly, the across-trial bandwidth is optimized by GCV at each trial $r$ separately. The resulting bandwidth $h(r)$ is itself a good representation of data variability.
More specifically, in order to find the optimal bandwidth $h(r)$ at a given trial $r$, one needs to iterate the following. Specify a fixed bandwidth $h$; Construct a weighted ensemble of spikes with across-trial width $h$ and centered at trial $r$; Calculate a generalized cross-validation score $\textrm{GCV}(h,r)$ by running ARRIS on this weighted ensemble while leaving one time-point out at a time.

Rapid evaluation of the bandwidth:
However, there is a practical difficulty in executing the optimization procedure described above. The most obvious reason is that MCMC is already computationally intensive, and that iterating over many candidate values of $h$ may be too expensive. But more fundamentally, the single-trial estimate of the firing rate would fluctuate, because it depends on a stochastic algorithm (RJMCMC). It means the optimization of $h(r)$ will not be robust, because the GCV score will turn out differently every time it is calculated.

To get around this problem the authors suggest using a kernel density approximation, where the ARRIS estimate is replaced by a box kernel with a fixed bandwidth (*note* this bandwidth is within-trial, not across-trial). This within-trial bandwidth is determined by a simple estimator that depends on spike interval median (rather than being optimized). The approximation is only used to evaluate the optimal bandwidth, then ARRIS can be used to obtain the final estimate at the optimal bandwidth.

Overall, this is a nice paper that provides a readily applicable method for learning non-stationary firing dynamics from small samples. It has two contributions: (1) the step-function-based ARRIS method for single-trial firing rate estimate, and (2) the weighted interpolation framework that involves the determination the optimal bandwidth $h(r)$ which captures data variability.

• For better representation, the authors suggest that the optimal bandwidth $h(r)$ can be smoothed once again with a “smoothing bandwidth $h_{s}$” (which is optimized by another round of GCV).
• There are three different uses of the term “bandwidth” in the paper, which may be confusing: the across-trial bandwidth $h(r)$ for the weighted ensemble construction which is at the core of the paper, the smoothing bandwidth that goes on top of $h(r)$, and finally the within-trial bandwidth that is introduced for the kernel density approximation.


text:
# Coth

## Description

The coth(x) function is the hyperbolic cotangent of x.

## Syntax

double coth(double x)

## Parameters

x

x is any non-zero real number. Note that numbers whose absolute value is greater than about 710 return 1/-1.

## Return

Returns the hyperbolic cotangent of x.

## Example

val = coth(-.909); // val will have a value of ~-1.3876