content
stringlengths 86
994k
| meta
stringlengths 288
619
|
|---|---|
What Are Dienes? Explained For Primary Schools
Dienes are a versatile addition to the primary maths classroom. As more schools adopt a maths mastery approach to teaching maths, interest has grown in the use of concrete resources and maths
manipulatives to introduce and explore maths topics.
Dienes – also known as base ten – are versatile manipulatives which allow teachers and students to represent and understand numbers. They can be used to teach a large proportion of the maths
curriculum including place value, calculation and decimals throughout the primary age range. In this blog, we’ll give you an introduction to Dienes and their use in the primary setting and provide
you with practice questions and worked examples that could be answered using Dienes.
What are Dienes?
Dienes are coloured plastic or wooden blocks that are used to represent numbers. There are four different Dienes blocks. They are usually used to represent 1000, 100, 10 and 1.
Guide To Hands On Manipulatives
Download our guide to hands on math manipulatives. Includes 15 concrete resources every KS1 and KS2 classroom should have.
Download Free Now!
Advantages of Dienes blocks
• Dienes are proportionally correct. Unlike place value counters or Cuisenaire rods, Dienes are proportionally correct. This means ten ‘ones’ cubes are the same size as one ‘ten’ rod and
this continues with each larger piece. This allows children to understand the relationship between the different columns on a place value grid.
• Dienes can be used to assist with regrouping and exchanging in addition and subtraction. Whilst they are commonly used to portray (up to) four digit numbers, the proportional nature of Dienes
also allow teachers to use them to show decimal numbers and their place value. This is particularly useful when first introducing decimals in lower Key Stage 2.
• Dienes are easy for children to use pictorially. They can quickly and neatly draw Dienes to either help them calculate answers or to prove their work.
In our one to one tuition, we use pictorial representations of Dienes to support pupils, as in this column subtraction example.
Why are they called Dienes?
Dienes are named after a Hungarian mathematician Zoltán Pál Dienes who famously theorised that the best way for children, from Early Years and beyond, to learn maths is through games, songs and
dance to make it more appealing and memorable. He is credited with inventing the base ten block.
How are Dienes used in maths?
As they are so versatile, Dienes blocks can be used to enhance pupils’ understanding and reasoning. They have become a staple teaching resource in many mathematics classrooms across the country to
enable pupils to master the curriculum.
Dienes for place value
It is fundamental that children understand place value to access the rest of the mathematics curriculum. Every academic year usually begins with pupils revisiting place value in the spiral curriculum
. Dienes can help pupils to visualise the numbers that they are working with.
For example, Year 2 pupils can use Dienes blocks to represent a two-digit number and explain how many tens and ones in a given number.
You could stretch pupils further by asking, ‘Do these two representations show the same number?’
In this example, a) shows 3 tens and 2 ones which is 32 and b) shows 2 tens and 12 ones which is also 32. Pupils may initially disagree that they are the same as there are a different number of tens,
however understanding that these representations are two different ways of showing the same number will help with addition and subtraction later on.
Dienes for addition
Once pupils are comfortable using Dienes to show the place value of numbers and manipulate these to create different representations, they can begin to use them to calculate.
An advantage of Dienes over resources such as number lines or counting materials is that they can be used for three- and four-digit numbers without becoming confusing or time consuming for pupils to
Dienes can be used alongside a written calculation in column addition to show how the calculation would be set out and to help pupils visualise the numbers that they are working with, as shown below.
As long as pupils understand which Dienes represent hundreds, tens and ones, it is as easy as counting in multiples of that number.
Having learnt column addition without regrouping, pupils can also use Dienes to understand how to cross the tens line. This is where being able to represent numbers in more than one way becomes
Dienes for subtraction
In a similar fashion, Dienes blocks can be used to teach subtraction too, both as a stand alone resource to complete calculations and alongside column subtraction.
Again, once pupils are comfortable subtracting without regrouping and exchanging, they can then exchange larger Dienes blocks for ten of the smaller ones in order to be able to complete subtraction
calculations with regrouping and exchanging.
Dienes for decimals
Dienes can also be used to help pupils to visualise decimals. Until this point, we have been using Dienes to represent the same numbers every time. However, since they are just within a power of ten
of one another, it is possible to scale their values down to represent tenths, hundredths and thousandths.
At this stage, pupils will have gained familiarity using Dienes which will help them to understand the place value of decimal numbers when this is introduced in Year 4.
From here, teaching addition and subtraction of decimals and their relationships to fractions (and later percentages) can follow the same pattern as with whole numbers as discussed earlier.
When do children use Dienes in school?
In primary school, pupils can use Dienes blocks right from Early Years, when they are first discovering and understanding number, through to Year 6 when they are working with fractions, decimal
numbers and high-level addition and subtraction. Similarly, they can be used to help children with fluency in calculation and to reason and problem solve. Children can use Dienes blocks to prove
their answers to a question, as well as represent numbers.
How do Dienes link to real life?
Aside from helping children to understand the number system and how numbers relate to one another, Dienes can help children to develop skills for their lives outside the classroom. Most notably, they
allow children to develop problem solving and reasoning skills which they can then apply to their wider lives.
Dienes worked examples
1. What number is represented?
This is completed by counting the tens and ones.
Pupils could then be extended by asking them to show this in a different way (maybe 7 tens and 17 ones or with a different resource, such as place value counters)
2. Complete the part-whole model using Dienes.
This is drawn as if they were the children’s jottings to record the Dienes.
There are multiple different answers to this problem, as long as the drawn Dienes total 350, since there are already 15 ‘ones’ shown.
A potential misconception here will be to immediately draw 300 and 60.
3. Fill in the missing number
Again, I have completed this using both the jottings and column addition, as you may expect pupils to.
Emphasise that we begin on the right to ensure that if we need to exchange, we can.
4. 637 – 184
In this calculation, I have set out the column subtraction with the Dienes pictorially, just as I would if I were teaching it to pupils with the concrete resource.
The question has provided the Dienes here, but the question could just give the calculation and expect the children to draw the Dienes themselves.
I began on the right as you would for column subtraction and I noticed that an exchange needed to be completed which I have shown in my working out.
5. Which decimal number is represented?
6. Year 4 are fundraising for charity. Their target is £3250.
Class A raised £1124, Class B raised £952.
How much does Class C need to raise?
First, I have added £1124 and £952 using the Dienes. This will tell me how much has already been raised.
Then, I need to subtract my answer from the target – £3250.
The answer to the question is that Class C needs to raise £1174.
Dienes practice questions
1. What number is represented? How could you represent the same number in another way?
Answer: 63
Children could also show this with 50+13, 40+23. Encourage them to not go too much further as it becomes difficult to count. Other options include bar models, part-whole models, place value counters
or number lines.
2. Complete the part-whole model using Dienes.
Answer: Any combination which makes 4503. Discourage children from drawing 503 ones (or similar) as this is not helpful and wastes time.
3. Find the missing number
Answer: 6505
4. 561 – 324
Answer: 237
5. Which decimal number is represented?
Answer: 1.609
6) There are 5832 seats in a stadium.
The home team have sold 3418 tickets and the away team have sold 833.
How many tickets are left?
Answer: 1581.
What are Dienes in maths?
Dienes are a versatile manipulative resource which can be used to represent numbers.
Are Dienes and Base 10 the same?
Yes. Base 10 are the blocks that Professor Zoltan Dienes produced to help children understand the number system. We sometimes use his name for the same materials.
Why are Dienes blocks good?
Dienes blocks have multiple uses in every primary classroom. All children can use them to represent numbers in their place value units, but they can also be used for addition, subtraction and
How do you subtract with Dienes?
To subtract with Dienes, first make the number that you are subtracting from (the minuend) out of Dienes. Next, physically remove the number that you are subtracting (the subtrahend), remembering to
begin on the right in case any exchanges are needed. The answer is the Dienes that you have left.
Every week Third Space Learning’s specialist online maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost
Since 2013 these personalised one to one lessons have helped over 169,000 primary and secondary students become more confident, able mathematicians.
Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.
|
{"url":"https://thirdspacelearning.com/blog/what-are-dienes/","timestamp":"2024-11-04T17:18:24Z","content_type":"text/html","content_length":"160207","record_id":"<urn:uuid:15bcfb46-cdec-4bfa-90d6-21d743233b7c>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00663.warc.gz"}
|
Halloween Math Multiplication Worksheets Free
Math, specifically multiplication, forms the cornerstone of numerous scholastic self-controls and real-world applications. Yet, for several students, understanding multiplication can posture an
obstacle. To resolve this difficulty, teachers and moms and dads have accepted an effective device: Halloween Math Multiplication Worksheets Free.
Introduction to Halloween Math Multiplication Worksheets Free
Halloween Math Multiplication Worksheets Free
Halloween Math Multiplication Worksheets Free -
1 Nothing says Halloween like creepy cobwebs costumes and multiplication Help your young mathematicians jump into the spooky spirit with these Halloween themed multiplication worksheets
Below you ll find a selection of printable Halloween themed math worksheets and activities for elementary aged students Topics include counting addition subtraction multiplication division time place
value graphing on coordinate grids and fractions Addition Addition Mystery Picture Pumpkin Basic Addition Facts FREE
Significance of Multiplication Technique Recognizing multiplication is crucial, laying a solid structure for advanced mathematical ideas. Halloween Math Multiplication Worksheets Free use structured
and targeted practice, promoting a deeper comprehension of this basic arithmetic procedure.
Development of Halloween Math Multiplication Worksheets Free
Halloween Multiplication Worksheets Math Kids And Chaos
Halloween Multiplication Worksheets Math Kids And Chaos
Halloween Math These spook tacularly fabulous math worksheets will keep your kids busy before they go trick or treating Add subtract Worksheet 1 Worksheet 2 Worksheet 3 Bar chart Worksheet 4 Color by
number Worksheet 5
The Halloween math worksheets here include counting addition subtraction multiplication facts patterns angle measuring ordering numbers number patterns picture patterns and printable Halloween graph
paper There are also a few Halloween math activities here that you ll want to check out Printable Halloween Math Worksheets at KidZone
From standard pen-and-paper exercises to digitized interactive layouts, Halloween Math Multiplication Worksheets Free have evolved, satisfying varied knowing designs and preferences.
Sorts Of Halloween Math Multiplication Worksheets Free
Fundamental Multiplication Sheets Easy workouts focusing on multiplication tables, assisting students develop a solid arithmetic base.
Word Problem Worksheets
Real-life scenarios integrated right into issues, improving vital thinking and application abilities.
Timed Multiplication Drills Tests designed to improve speed and precision, aiding in fast mental mathematics.
Benefits of Using Halloween Math Multiplication Worksheets Free
12 Best Images Of Pumpkin Addition Worksheet Repeated Addition Arrays Worksheets Expanded
12 Best Images Of Pumpkin Addition Worksheet Repeated Addition Arrays Worksheets Expanded
Emoji Crack the Secret Code Maths Worksheets KS2 Superhero Multiplication Colour by Number Halloween 3 4 and 8 Times Tables Activity Halloween Colour by Calculation Times Table Maths Worksheet This
fun set of Halloween multiplication mosaics worksheets worksheet is great for helping learners develop their multiplication knowledge
Halloween Maze Even Numbers Worksheet Halloween Patterns Worksheet 1 2 3 4 Browse Printable Math Halloween Worksheets Award winning educational materials designed to help kids succeed Start for free
Enhanced Mathematical Abilities
Regular method sharpens multiplication efficiency, improving overall mathematics abilities.
Enhanced Problem-Solving Abilities
Word issues in worksheets establish logical thinking and technique application.
Self-Paced Discovering Advantages
Worksheets accommodate individual learning rates, fostering a comfy and versatile discovering setting.
How to Develop Engaging Halloween Math Multiplication Worksheets Free
Including Visuals and Shades Vibrant visuals and colors catch interest, making worksheets visually appealing and involving.
Including Real-Life Situations
Associating multiplication to daily situations includes significance and functionality to exercises.
Customizing Worksheets to Various Skill Degrees Tailoring worksheets based upon differing effectiveness levels guarantees inclusive learning. Interactive and Online Multiplication Resources Digital
Multiplication Devices and Games Technology-based sources use interactive understanding experiences, making multiplication engaging and pleasurable. Interactive Websites and Apps On-line platforms
give diverse and accessible multiplication method, supplementing typical worksheets. Tailoring Worksheets for Different Discovering Styles Aesthetic Learners Aesthetic help and diagrams help
comprehension for students inclined toward visual understanding. Auditory Learners Verbal multiplication issues or mnemonics satisfy learners that comprehend ideas through auditory ways. Kinesthetic
Students Hands-on activities and manipulatives sustain kinesthetic students in comprehending multiplication. Tips for Effective Execution in Understanding Uniformity in Practice Regular practice
enhances multiplication abilities, promoting retention and fluency. Balancing Repetition and Variety A mix of recurring exercises and diverse problem formats preserves passion and comprehension.
Offering Useful Comments Responses aids in identifying areas of enhancement, urging continued progress. Obstacles in Multiplication Practice and Solutions Motivation and Interaction Difficulties
Monotonous drills can bring about uninterest; ingenious approaches can reignite inspiration. Conquering Anxiety of Math Negative assumptions around mathematics can impede progress; developing a
positive learning environment is essential. Effect of Halloween Math Multiplication Worksheets Free on Academic Efficiency Researches and Research Searchings For Study suggests a favorable
relationship between consistent worksheet use and improved math efficiency.
Halloween Math Multiplication Worksheets Free become flexible devices, cultivating mathematical effectiveness in learners while accommodating varied understanding styles. From fundamental drills to
interactive on the internet sources, these worksheets not just improve multiplication abilities however additionally promote crucial thinking and analytic capacities.
Free 30 Page Halloween Multiplication Packet Math Worksheets And Games Homeschool Den
11 HALLOWEEN MATH WORKSHEETS FOR GRADE 3
Check more of Halloween Math Multiplication Worksheets Free below
Halloween Double Digit Multiplication With Regrouping Two Digit Multiplication Multiplication
Three digit Multiplication Practice Worksheet 03
Free Printable Halloween Multiplication Worksheet Halloween math worksheets Halloween math
7 Best Images Of Halloween Multiplication Coloring Printables Halloween Math Multiplication
15 Best Halloween Multiplication Coloring Printables Printablee
Halloween Multi Digit Multiplication Worksheets AlphabetWorksheetsFree
Halloween Math Worksheets Super Teacher Worksheets
Below you ll find a selection of printable Halloween themed math worksheets and activities for elementary aged students Topics include counting addition subtraction multiplication division time place
value graphing on coordinate grids and fractions Addition Addition Mystery Picture Pumpkin Basic Addition Facts FREE
Halloween Math Worksheets Math Drills
On this page you will find Halloween math worksheets on a variety of topics including Halloween multiplication division addition and subtraction The Halloween worksheets on this page should only be
tried after you have learned how to defend yourself against evil spirits Be careful of the monsters on the worksheets they sometimes bite
Below you ll find a selection of printable Halloween themed math worksheets and activities for elementary aged students Topics include counting addition subtraction multiplication division time place
value graphing on coordinate grids and fractions Addition Addition Mystery Picture Pumpkin Basic Addition Facts FREE
On this page you will find Halloween math worksheets on a variety of topics including Halloween multiplication division addition and subtraction The Halloween worksheets on this page should only be
tried after you have learned how to defend yourself against evil spirits Be careful of the monsters on the worksheets they sometimes bite
7 Best Images Of Halloween Multiplication Coloring Printables Halloween Math Multiplication
Three digit Multiplication Practice Worksheet 03
15 Best Halloween Multiplication Coloring Printables Printablee
Halloween Multi Digit Multiplication Worksheets AlphabetWorksheetsFree
13 Best Images Of Computer Terms Worksheet Computer Word Search Worksheets Halloween Math
Take The SPOOK Out Of Multiplication Halloween Multiplication Printable Pages Journal
Take The SPOOK Out Of Multiplication Halloween Multiplication Printable Pages Journal
15 Best Printable Halloween Math Worksheets For 6th Grade Printablee
Frequently Asked Questions (Frequently Asked Questions).
Are Halloween Math Multiplication Worksheets Free ideal for all age teams?
Yes, worksheets can be customized to various age and skill levels, making them versatile for various students.
How usually should pupils exercise making use of Halloween Math Multiplication Worksheets Free?
Regular technique is crucial. Regular sessions, ideally a couple of times a week, can generate substantial renovation.
Can worksheets alone boost math abilities?
Worksheets are a valuable tool but needs to be supplemented with different understanding techniques for comprehensive ability growth.
Are there on the internet systems supplying free Halloween Math Multiplication Worksheets Free?
Yes, several educational sites provide free access to a wide variety of Halloween Math Multiplication Worksheets Free.
Just how can parents sustain their youngsters's multiplication practice at home?
Urging constant technique, providing assistance, and developing a positive learning setting are beneficial actions.
|
{"url":"https://crown-darts.com/en/halloween-math-multiplication-worksheets-free.html","timestamp":"2024-11-04T07:49:51Z","content_type":"text/html","content_length":"29507","record_id":"<urn:uuid:dd733d1c-21b6-4199-8095-8eba831f05c6>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00719.warc.gz"}
|
Work And Energy MCQs with Explanations for Class 9 [1000+] - Pakiology
Explore the world of work and energy with our vast repository of 1000+ work and energy MCQs, accompanied by explanations, catering to Class 9 students seeking clarity on kinetic energy, potential
energy, and work-energy theorem.
100+ Work And Energy MCQs with Explanations for Class 9
Immerse yourself in the realm of Work and Energy with our meticulously crafted MCQs. Designed for Class 9 students, this expansive collection of over 100+ MCQs, supplemented with explanations, serves
as a valuable tool for mastering kinetic energy, potential energy, and work-energy theorem concepts.
1. Which of the following best defines work in physics?
A) The amount of force exerted on an object
B) The displacement of an object in the direction of the force applied to it
C) The energy possessed by an object at rest
D) The speed of an object in motion
Correct Option: B
Explanation: Work is defined as the product of force and displacement in the direction of the force.
2. Which form of energy is associated with motion?
A) Potential energy
B) Kinetic energy
C) Chemical energy
D) Thermal energy
Correct Option: B
Explanation: Kinetic energy is the energy possessed by an object due to its motion.
3. If an object is raised to a certain height above the ground, which type of energy does it possess?
A) Kinetic energy
B) Potential energy
C) Chemical energy
D) Electrical energy
Correct Option: B
Explanation: Potential energy is associated with the position or height of an object.
4. In which of the following situations is work done?
A) Holding a book stationary in your hands
B) Pushing against a wall without moving it
C) Carrying a heavy bag while walking
D) All of the above
Correct Option: C
Explanation: Work is done when there is a displacement of an object in the direction of the applied force.
5. The ability to do work is known as:
A) Power
B) Energy
C) Force
D) Momentum
Correct Option: B
Explanation: Energy is the capacity to do work.
6. What is the SI unit of energy?
A) Joule
B) Newton
C) Watt
D) Kilogram
Correct Option: A
Explanation: Joule is the unit of energy.
7. Which of the following is a renewable source of energy?
A) Coal
B) Natural gas
C) Wind
D) Petroleum
Correct Option: C
Explanation: Wind energy is considered renewable because it is continuously replenished by nature.
8. What is the efficiency of a machine that performs 80 J of work with an input energy of 100 J?
A) 80%
B) 100%
C) 120%
D) 60%
Correct Option: A
Explanation: Efficiency is calculated as the ratio of output work to input energy, multiplied by 100%.
9. Which of the following is a non-renewable source of energy?
A) Solar energy
B) Hydroelectric energy
C) Nuclear energy
D) Biomass energy
Correct Option: C
Explanation: Nuclear energy is derived from radioactive materials and is considered non-renewable.
10. The rate at which work is done is known as:
A) Speed
B) Power
C) Energy
D) Momentum
Correct Option: B
Explanation: Power is defined as the rate at which work is done or energy is transferred.
11. Which of the following equations represents kinetic energy?
Correct Option: A
Explanation: Kinetic energy is calculated using the equation
12. A 2 kg object is moving with a velocity of 3 m/s. What is its kinetic energy?
A) 9 J
B) 12 J
C) 18 J
D) 6 J
Correct Option: C
Explanation: Using the formula for kinetic energy:
13. Which of the following is a unit of power?
A) Watt
B) Newton
C) Joule
D) Ohm
Correct Option: A
Explanation: Watt is the unit of power, named after James Watt.
14. What is the efficiency of a machine that outputs 600 J of work with an input energy of 800 J?
A) 75%
B) 80%
C) 60%
D) 150%
Correct Option: A
Explanation: Efficiency = (Output work / Input energy) × 100% = (600/800) × 100% = 75%.
15. Which of the following is a form of potential energy?
A) Thermal energy
B) Light energy
C) Gravitational energy
D) Sound energy
Correct Option: C
Explanation: Gravitational potential energy is associated with an object’s position relative to the Earth’s surface.
16. The SI unit of work is the same as the SI unit of:
A) Power
B) Energy
C) Force
D) Momentum
Correct Option: B
Explanation: Work and energy share the same unit, the joule (J).
17. What is the potential energy of a 5 kg object raised 10 meters above the ground?
A) 50 J
B) 100 J
C) 500 J
D) 200 J
Correct Option: C
Explanation: Potential energy = mgh = 5 kg × 10 m/s² × 10 m = 500 J.
18. A force of 20 N is applied to move a box a distance of 5 meters. How much work is done?
A) 25 J
B) 100 J
C) 4 J
D) 10 J
Correct Option: B
Explanation: Work = force × distance = 20 N × 5 m = 100 J.
19. Which of the following statements regarding energy conversion is correct?
A) Energy can be created but not destroyed
B) Energy can be destroyed but not created
C) Energy can neither be created nor destroyed
D) Energy can be created and destroyed freely
Correct Option: C
Explanation: According to the law of conservation of energy, energy cannot be created or destroyed, only converted from one form to another.
20. Which of the following is an example of potential energy?
A) A moving car
B) A stretched spring
C) A spinning top
D) A burning candle
Correct Option: B
Explanation: When a spring is stretched, it stores potential energy due to its position.
21. The efficiency of a machine is always expressed in:
A) Percentage
B) Newtons
C) Joules
D) Watts
Correct Option: A
Explanation: Efficiency is typically expressed as a percentage.
22. Which of the following is a renewable energy source?
A) Fossil fuels
B) Biomass
C) Nuclear energy
D) Natural gas
Correct Option: B
Explanation: Biomass is a renewable energy source derived from organic materials.
23. What is the power of a machine that does 500 J of work in 10 seconds?
A) 50 W
B) 5 W
C) 100 W
D) 5000 W
Correct Option: A
Explanation: Power = Work / Time = 500 J / 10 s = 50 W.
24. Which of the following is an example of kinetic energy?
A) A book resting on a table
B) A stretched rubber band
C) Water flowing in a river
D) A battery powering a light bulb
Correct Option: C
Explanation: Kinetic energy is associated with the motion of objects, such as water flowing in a river.
25. If the efficiency of a machine is 80%, what percentage of the input energy is wasted?
A) 10%
B) 20%
C) 80%
D) 60%
Correct Option: B
Explanation: Efficiency = (Useful energy output / Total energy input) × 100%. Therefore, wasted energy = 100% – Efficiency = 100% – 80% = 20%.
26. A force of 50 N is applied to move an object a distance of 5 meters. How much work is done?
A) 250 J
B) 10 J
C) 5 J
D) 100 J
Correct Option: A
Explanation: Work = Force × Distance = 50 N × 5 m = 250 J.
27. Which of the following statements is true regarding energy?
A) Energy can only be transferred in the form of heat
B) Energy can be created and destroyed
C) Energy can be converted from one form to another with 100% efficiency
D) Energy cannot be converted from one form to another
Correct Option: C
Explanation: Energy conversions are subject to the laws of thermodynamics, which impose limitations on efficiency.
28. What is the efficiency of a machine that outputs 200 J of work with an input energy of 300 J?
A) 150%
B) 100%
C) 66.7%
D) 75%
Correct Option: C
Explanation: Efficiency = (Output work / Input energy) × 100% = (200/300) × 100% = 66.7%.
29. Which of the following is a form of renewable energy?
A) Coal
B) Natural gas
C) Solar power
D) Petroleum
Correct Option: C
Explanation: Solar power is derived from sunlight and is considered a renewable energy source.
30. The gravitational potential energy of an object depends on its:
A) Mass and velocity
B) Mass and height
C) Velocity and height
D) Mass, velocity, and height
Correct Option: B
Explanation: Gravitational potential energy depends on the mass of the object and its height above a reference point.
31. Which of the following statements about work is true?
A) Work can be negative when the force applied is opposite to the displacement
B) Work is always positive
C) Work is equal to force multiplied by time
D) Work is independent of displacement
Correct Option: A
Explanation: Work can be negative when the force applied is opposite to the displacement, indicating that work is done against the direction of motion.
32. What is the kinetic energy of a 10 kg object moving at a velocity of 5 m/s?
A) 10 J
B) 50 J
C) 100 J
D) 25 J
Correct Option: B
Explanation: Kinetic energy =
33. Which of the following equations represents gravitational potential energy?
Correct Option: B
Explanation: Gravitational potential energy is calculated using the equation
34. If the efficiency of a machine is 90%, what percentage of the input energy is lost as heat?
A) 90%
B) 10%
C) 20%
D) 100%
Correct Option: B
Explanation: Efficiency = Useful output energy / Total input energy. Therefore, energy lost as heat = 100% – Efficiency = 100% – 90% = 10%.
35. Which of the following is a unit of power?
A) Joule
B) Newton
C) Watt
D) Kilogram
Correct Option: C
Explanation: Watt is the unit of power, representing one joule of work done per second.
36. What is the potential energy of a 2 kg object raised 5 meters above the ground?
A) 10 J
B) 25 J
C) 100 J
D) 50 J
Correct Option: D
Explanation: Potential energy = mgh = 2 kg × 10 m/s² × 5 m = 50 J.
37. A force of 30 N is applied to move an object a distance of 4 meters. How much work is done?
A) 120 J
B) 7.5 J
C) 34 J
D) 10 J
Correct Option: A
Explanation: Work = Force × Distance = 30 N × 4 m = 120 J.
38. Which of the following statements regarding energy is true?
A) Energy can only be transferred in the form of matter
B) Energy can be created and destroyed
C) Energy can only be converted from potential to kinetic
D) Energy can neither be created nor destroyed
Correct Option: D
Explanation: The law of conservation of energy states that energy cannot be created nor destroyed, only converted from one form to another.
39. Which of the following is an example of kinetic energy?
A) A compressed spring
B) A moving car
C) A battery
D) A stretched rubber band
Correct Option: B
Explanation: Kinetic energy is associated with the motion of objects, such as a moving car.
40. If the efficiency of a machine is 75%, what percentage of the input energy is transformed into useful work?
A) 75%
B) 25%
C) 50%
D) 100%
Correct Option: B
Explanation: Efficiency = Useful output energy / Total input energy. Therefore, useful work = Efficiency × Total input energy = 75% of input energy.
41. What is the power of a machine that does 800 J of work in 20 seconds?
A) 40 W
B) 1600 W
C) 800 W
D) 160 W
Correct Option: A
Explanation: Power = Work / Time = 800 J / 20 s = 40 W.
42. Which of the following is a non-renewable energy source?
A) Wind
B) Solar
C) Natural gas
D) Biomass
Correct Option: C
Explanation: Natural gas is a fossil fuel and considered a non-renewable energy source.
43. Which of the following is a form of kinetic energy?
A) Wind energy
B) Gravitational energy
C) Nuclear energy
D) Thermal energy
Correct Option: A
Explanation: Wind energy is a form of kinetic energy associated with the motion of air molecules.
44. The SI unit of power is:
A) Joule
B) Newton
C) Watt
D) Kilogram
Correct Option: C
Explanation: Watt is the unit of power, named after James Watt.
45. What is the efficiency of a machine that outputs 400 J of work with an input energy of 500 J?
A) 80%
B) 75%
C) 64%
D) 20%
Correct Option: A
Explanation: Efficiency = (Output work / Input energy) × 100% = (400/500) × 100% = 80%.
46. Which of the following statements regarding energy is true?
A) Energy can only be converted from potential to kinetic
B) Energy can be created and destroyed
C) Energy can only be transferred in the form of light
D) Energy can neither be created nor destroyed
Correct Option: D
Explanation: The law of conservation of energy states that energy cannot be created nor destroyed, only converted from one form to another.
47. What is the potential energy of a 3 kg object raised 8 meters above the ground?
A) 12 J
B) 120 J
C) 240 J
D) 200 J
Correct Option: C
Explanation: Potential energy = mgh = 3 kg × 10 m/s² × 8 m = 240 J.
48. A force of 25 N is applied to move an object a distance of 6 meters. How much work is done?
A) 150 J
B) 4 J
C) 150 N
D) 25 J
Correct Option: A
Explanation: Work = Force × Distance = 25 N × 6 m = 150 J.
49. Which of the following statements about power is true?
A) Power is a scalar quantity
B) Power is measured in joules
C) Power is the rate of doing work
D) Power is independent of time
Correct Option: C
Explanation: Power is defined as the rate at which work is done or energy is transferred.
50. What is the kinetic energy of a 5 kg object moving at a velocity of 4 m/s?
A) 20 J
B) 40 J
C) 80 J
D) 100 J
Correct Option: C
Explanation: Kinetic energy =
51. Which of the following is a form of renewable energy?
A) Coal
B) Petroleum
C) Biomass
D) Natural gas
Correct Option: C
Explanation: Biomass energy is derived from organic materials and is considered renewable.
52. What is the efficiency of a machine that outputs 300 J of work with an input energy of 400 J?
A) 75%
B) 60%
C) 150%
D) 90%
Correct Option: A
Explanation: Efficiency = (Output work / Input energy) × 100% = (300/400) × 100% = 75%.
53. The efficiency of a machine is always less than:
A) 0%
B) 50%
C) 100%
D) 150%
Correct Option: C
Explanation: Efficiency is a ratio of useful work output to total work input, so it cannot exceed 100%.
54. Which of the following is a non-renewable energy source?
A) Solar power
B) Wind energy
C) Natural gas
D) Biomass
Correct Option: C
Explanation: Natural gas is a fossil fuel and considered a non-renewable energy source.
55. What is the power of a machine that does 600 J of work in 10 seconds?
A) 60 W
B) 6 W
C) 100 W
D) 6000 W
Correct Option: A
Explanation: Power = Work / Time = 600 J / 10 s = 60 W.
56. Which of the following is a unit of energy?
A) Pascal
B) Volt
C) Ampere
D) Joule
Correct Option: D
Explanation: Joule is the unit of energy.
57. Which of the following is an example of kinetic energy?
A) A stretched rubber band
B) A stationary car
C) A compressed spring
D) A moving car
Correct Option: D
Explanation: Kinetic energy is associated with the motion of objects, such as a moving car.
58. If the efficiency of a machine is 90%, what percentage of the input energy is transformed into useful work?
A) 10%
B) 90%
C) 100%
D) 80%
Correct Option: B
Explanation: Efficiency = Useful output energy / Total input energy. Therefore, useful work = Efficiency × Total input energy = 90% of input energy.
59. What is the potential energy of a 4 kg object raised 6 meters above the ground?
A) 48 J
B) 240 J
C) 120 J
D) 144 J
Correct Option: D
Explanation: Potential energy = mgh = 4 kg × 10 m/s² × 6 m = 144 J.
60. A force of 40 N is applied to move an object a distance of 8 meters. How much work is done?
A) 5 J
B) 40 J
C) 320 J
D) 320 N
Correct Option: C
Explanation: Work = Force × Distance = 40 N × 8 m = 320 J.
61. Which of the following statements regarding energy is true?
A) Energy can be created but not destroyed
B) Energy can be destroyed but not created
C) Energy can neither be created nor destroyed
D) Energy can be created and destroyed freely
Correct Option: C
Explanation: The law of conservation of energy states that energy cannot be created nor destroyed, only converted from one form to another.
62. What is the kinetic energy of a 3 kg object moving at a velocity of 6 m/s?
A) 54 J
B) 9 J
C) 108 J
D) 18 J
Correct Option: A
Explanation: Kinetic energy =
63. The efficiency of a machine is always expressed as a:
A) Fraction
B) Decimal
C) Percentage
D) Ratio
Correct Option: C
Explanation: Efficiency is typically expressed as a percentage.
64. Which of the following is a non-renewable energy source?
A) Wind
B) Solar
C) Nuclear
D) Biomass
Correct Option: C
Explanation: Nuclear energy is derived from radioactive materials and is considered non-renewable.
65. What is the power of a machine that does 900 J of work in 15 seconds?
A) 60 W
B) 15 W
C) 150 W
D) 9000 W
Correct Option: C
Explanation: Power = Work / Time = 900 J / 15 s = 60 W.
66. Which of the following is a unit of power?
A) Pascal
B) Volt
C) Watt
D) Ampere
Correct Option: C
Explanation: Watt is the unit of power.
67. Which of the following is an example of potential energy?
A) A running car
B) A spinning top
C) A stretched rubber band
D) A moving train
Correct Option: C
Explanation: A stretched rubber band has potential energy due to its stretched position.
68. If the efficiency of a machine is 80%, what percentage of the input energy is lost as heat?
A) 20%
B) 80%
C) 100%
D) 60%
Correct Option: A
Explanation: Efficiency = Useful output energy / Total input energy. Therefore, energy lost as heat = 100% – Efficiency = 100% – 80% = 20%.
69. Which of the following statements about energy is true?
A) Energy can only be transferred in the form of light
B) Energy can be created and destroyed
C) Energy can neither be created nor destroyed
D) Energy can only be converted from potential to kinetic
Correct Option: C
Explanation: The law of conservation of energy states that energy cannot be created nor destroyed, only converted from one form to another.
70. What is the kinetic energy of a 6 kg object moving at a velocity of 2 m/s?
A) 12 J
B) 6 J
C) 24 J
D) 18 J
Correct Option: A
Explanation: Kinetic energy =
71. The SI unit of power is:
A) Newton
B) Joule
C) Watt
D) Kilogram
Correct Option: C
Explanation: Watt is the unit of power.
72. What is the potential energy of a 5 kg object raised 10 meters above the ground?
A) 500 J
B) 1000 J
C) 50 J
D) 200 J
Correct Option: A
Explanation: Potential energy = mgh = 5 kg × 10 m/s² × 10 m = 500 J.
73. A force of 15 N is applied to move an object a distance of 3 meters. How much work is done?
A) 45 J
B) 5 J
C) 15 J
D) 8 J
Correct Option: A
Explanation: Work = Force × Distance = 15 N × 3 m = 45 J.
74. Which of the following is a form of renewable energy?
A) Coal
B) Nuclear
C) Wind
D) Natural gas
Correct Option: C
Explanation: Wind energy is considered renewable because it is continuously replenished by nature.
75. What is the efficiency of a machine that outputs 500 J of work with an input energy of 600 J?
A) 83.3%
B) 80%
C) 125%
D) 70%
Correct Option: A
Explanation: Efficiency = (Output work / Input energy) × 100% = (500/600) × 100% = 83.3%.
76. Which of the following statements regarding energy conversion is correct?
A) Energy can be created and destroyed
B) Energy can only be converted from kinetic to potential
C) Energy can be converted from one form to another with 100% efficiency
D) Energy can neither be created nor destroyed
Correct Option: D
Explanation: According to the law of conservation of energy, energy cannot be created or destroyed, only converted from one form to another.
77. What is the kinetic energy of a 4 kg object moving at a velocity of 3 m/s?
A) 6 J
B) 12 J
C) 18 J
D) 36 J
Correct Option: D
Explanation: Kinetic energy =
78. The SI unit of work is the same as the SI unit of:
A) Power
B) Force
C) Energy
D) Momentum
Correct Option: C
Explanation: Work and energy share the same unit, the joule (J).
79. Which of the following is an example of kinetic energy?
A) A stationary rock at the top of a hill
B) A book on a shelf
C) A stretched rubber band
D) A moving car
Correct Option: D
Explanation: Kinetic energy is associated with the motion of objects, such as a moving car.
80. If the efficiency of a machine is 70%, what percentage of the input energy is transformed into useful work?
A) 70%
B) 30%
C) 100%
D) 80%
Correct Option: A
Explanation: Efficiency = Useful output energy / Total input energy. Therefore, useful work = Efficiency × Total input energy = 70% of input energy.
81. What is the power of a machine that does 700 J of work in 14 seconds?
A) 49 W
B) 100 W
C) 50 W D) 70 W
Correct Option: A
Explanation: Power = Work / Time = 700 J / 14 s = 50 W.
82. Which of the following is a form of potential energy?
A) Sound energy
B) Chemical energy
C) Nuclear energy
D) Gravitational energy
Correct Option: D
Explanation: Gravitational potential energy is associated with an object’s position relative to the Earth’s surface.
83. The efficiency of a machine is always expressed as a:
A) Fraction
B) Decimal
C) Percentage
D) Ratio
Correct Option: C
Explanation: Efficiency is typically expressed as a percentage.
84. Which of the following is a non-renewable energy source?
A) Solar
B) Biomass
C) Fossil fuels
D) Wind
Correct Option: C
Explanation: Fossil fuels, such as coal and petroleum, are non-renewable energy sources.
85. What is the efficiency of a machine that outputs 350 J of work with an input energy of 500 J?
A) 70%
B) 50%
C) 100%
D) 150%
Correct Option: A
Explanation: Efficiency = (Output work / Input energy) × 100% = (350/500) × 100% = 70%.
86. Which of the following statements about energy is true?
A) Energy can only be transferred in the form of heat
B) Energy can be created and destroyed
C) Energy can only be converted from potential to kinetic
D) Energy can neither be created nor destroyed
Correct Option: D
Explanation: The law of conservation of energy states that energy cannot be created nor destroyed, only converted from one form to another.
87. What is the potential energy of a 6 kg object raised 7 meters above the ground?
A) 42 J
B) 210 J
C) 294 J
D) 180 J
Correct Option: C
Explanation: Potential energy = mgh = 6 kg × 10 m/s² × 7 m = 294 J.
88. A force of 35 N is applied to move an object a distance of 5 meters. How much work is done?
A) 70 J
B) 140 J
C) 175 J
D) 5 J
Correct Option: B
Explanation: Work = Force × Distance = 35 N × 5 m = 175 J.
89. Which of the following is a form of renewable energy?
A) Natural gas
B) Nuclear
C) Wind
D) Coal
Correct Option: C
Explanation: Wind energy is considered renewable because it is continuously replenished by nature.
90. What is the efficiency of a machine that outputs 450 J of work with an input energy of 600 J?
A) 75%
B) 50%
C) 125%
D) 80%
Correct Option: A
Explanation: Efficiency = (Output work / Input energy) × 100% = (450/600) × 100% = 75%.
91. What is the power of a machine that does 1000 J of work in 20 seconds?
A) 20 W
B) 50 W
C) 200 W
D) 500 W
Correct Option: C
Explanation: Power = Work / Time = 1000 J / 20 s = 50 W.
92. Which of the following is a unit of energy?
A) Ampere
B) Pascal
C) Joule
D) Volt
Correct Option: C
Explanation: Joule is the unit of energy.
93. Which of the following is an example of kinetic energy?
A) A stationary train at a platform
B) A compressed spring
C) A moving bicycle
D) A book on a table
Correct Option: C
Explanation: Kinetic energy is associated with the motion of objects, such as a moving bicycle.
94. If the efficiency of a machine is 85%, what percentage of the input energy is lost as heat?
A) 15%
B) 85%
C) 100%
D) 75%
Correct Option: A
Explanation: Efficiency = Useful output energy / Total input energy. Therefore, energy lost as heat = 100% – Efficiency = 100% – 85% = 15%.
95. What is the kinetic energy of a 7 kg object moving at a velocity of 4 m/s?
A) 14 J
B) 112 J
C) 28 J
D) 56 J
Correct Option: D
Explanation: Kinetic energy =
96. The SI unit of power is:
A) Newton
B) Joule
C) Watt
D) Kilogram
Correct Option: C
Explanation: Watt is the unit of power.
97. What is the potential energy of a 8 kg object raised 9 meters above the ground?
A) 64 J
B) 648 J
C) 720 J
D) 576 J
Correct Option: D
Explanation: Potential energy = mgh = 8 kg × 10 m/s² × 9 m = 720 J.
98. A force of 25 N is applied to move an object a distance of 4 meters. How much work is done?
A) 29 J
B) 100 J
C) 96 J
D) 10 J
Correct Option: C
Explanation: Work = Force × Distance = 25 N × 4 m = 100 J.
99. Which of the following is a form of renewable energy?
A) Natural gas
B) Nuclear
C) Wind
D) Coal
Correct Option: C
Explanation: Wind energy is considered renewable because it is continuously replenished by nature.
100. What is the efficiency of a machine that outputs 550 J of work with an input energy of 750 J?
A) 73.3%
B) 83.3%
C) 66.7%
D) 50%
Correct Option: B
Explanation: Efficiency = (Output work / Input energy) × 100% = (550/750) × 100% = 73.3%.
101. What is the power of a machine that does 1200 J of work in 30 seconds?
A) 40 W
B) 60 W
C) 120 W
D) 90 W
Correct Option: B
Explanation: Power = Work / Time = 1200 J / 30 s = 40 W.
102. Which of the following is a unit of energy?
A) Pascal
B) Volt
C) Ampere
D) Joule
Correct Option: D
Explanation: Joule is the unit of energy.
103. What is the kinetic energy of a 10 kg object moving at a velocity of 5 m/s?
A) 25 J
B) 50 J
C) 100 J
D) 250 J
Correct Option: C
Explanation: Kinetic energy =
104. The SI unit of power is:
A) Newton
B) Joule
C) Watt
D) Kilogram
Correct Option: C
Explanation: Watt is the unit of power.
105. What is the potential energy of a 2 kg object raised 5 meters above the ground?
A) 10 J
B) 25 J
C) 50 J
D) 100 J
Correct Option: C
Explanation: Potential energy = mgh = 2 kg × 10 m/s² × 5 m = 100 J.
106. A force of 30 N is applied to move an object a distance of 6 meters. How much work is done?
A) 180 J
B) 36 J
C) 30 J
D) 5 J
Correct Option: A
Explanation: Work = Force × Distance = 30 N × 6 m = 180 J.
107. Which of the following is a form of kinetic energy?
A) Solar energy
B) Gravitational energy
C) Thermal energy
D) Wind energy
Correct Option: D
Explanation: Wind energy is a form of kinetic energy associated with the motion of air molecules.
108. If the efficiency of a machine is 90%, what percentage of the input energy is transformed into useful work?
A) 90%
B) 10%
C) 100%
D) 80%
Correct Option: A
Explanation: Efficiency = Useful output energy / Total input energy. Therefore, useful work = Efficiency × Total input energy = 90% of input energy.
109. What is the efficiency of a machine that outputs 600 J of work with an input energy of 750 J?
A) 80%
B) 75%
C) 64%
D) 20%
Correct Option: B
Explanation: Efficiency = (Output work / Input energy) × 100% = (600/750) × 100% = 75%.
110. Which of the following is a form of potential energy?
A) Electrical energy
B) Sound energy
C) Nuclear energy
D) Chemical energy
Correct Option: D
Explanation: Chemical energy is a form of potential energy stored in chemical bonds.
Physics Class 9 MCQs Chapter wise
Discover dedicated sections housing Class 9 Physics MCQs, methodically categorized by topic for seamless navigation and targeted study. Each section incorporates more than 1000 MCQs, providing
abundant practice avenues to consolidate learning and achieve proficiency in Physics. Access MCQs for individual sections with a click on the respective chapter names provided below.
0 Comments
|
{"url":"https://www.pakiology.com/class-9-mcqs/physics/work-and-energy/","timestamp":"2024-11-07T07:10:29Z","content_type":"text/html","content_length":"232936","record_id":"<urn:uuid:4ab72937-c3a6-47b4-99d1-812b3f73dbf9>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00033.warc.gz"}
|
How to Make Learning Maths Easier for Students - E News Wiki
How to Make Learning Maths Easier for Students
Maths is a subject that can be quite daunting for students. All the numbers, the calculations, the derivations, theorems, the formulae etc., make it confusing. This confusion can lead to a fear of
the subject, and this maths anxiety can further complicate matters when it comes to learning maths for children. However, there are ways to make maths learning easier for them by using tools like
flashcards, books, maths guides and calculators.
Understanding the fundamentals is key to learning maths concepts; this also makes maths learning easier and more fun for students. Read on to learn how to make learning Maths fun for students and
help them understand the concepts more quickly.
Simplifying Maths Learning for Students
Maths can be a difficult subject to learn, especially because the concepts get more advanced and complicated with each year. But with the right approach, it can be made much easier for students. Here
are some tips on how to make learning maths easier.
1. Keep things simple: When teaching mathematics, it is important to keep things as simple as possible. Breaking down the concepts helps students understand them better, and it also helps them
retain the lessons in their memory. This will make the subject more accessible and easier to understand for students.
2. Use visuals: In addition to keeping things simple, using visuals can also help students remember maths concepts better. Images and diagrams simplify complex maths concepts and make it easier for
students to understand them.
3. Creativity: Learning becomes more fun when we add some creativity to lessons. Encourage students to be more creative and innovative while solving maths problems. If you are struggling with
solving certain maths problems, explore alternative methods or refer to guides. Referring to guides like Samacheer Kalvi 10th Maths book solutions helps TN Board Class 10 students learn to solve
the problems in their textbook easily. It also helps them learn alternative methods to solve the same problem. When you allow students to explore their creativity, they will be able to come up
with more innovative solutions to maths problems. This will help them think on their own and learn faster and retain more information better.
4. Use drills and practice sessions: One of the most important parts of maths learning is constant practice. Drills and practice sessions are essential for improving maths skills. Regularly solving
practice problems helps students become more proficient in the subject. Additionally, giving students more opportunities to practise regularly helps them become better at solving problems quickly
and correctly.
Ways to Use Books and Visuals for Maths Learning
One of the most effective ways to help students learn maths is by using books and visuals. Textbooks are one of the best study resources for students to learn maths. Textbooks like the Samacheer
Kalvi books give detailed explanations of each concept and cover the entire syllabus. They include illustrations, graphs and equations, which help students understand the concepts better.
Additionally, these books are the best way for students to prepare for the exams as most of the questions in the question papers are from these textbooks.
Other helpful visuals that can be used when teaching maths include pictographs and mnemonic devices. Pictographs are images that represent mathematical concepts in a visual way, while mnemonic
devices are short stories or poems that help students remember maths facts like addition and subtraction facts.
Some other ways to make maths learning easier for students include using online resources and apps. Online resources can include interactive calculators and lesson plans, while apps can be used to
practice specific maths problems. When teaching mathematics, it is important to find a method that works best for the students and classroom setting.
It is extremely important for students to have good maths skills. The subject is not only important for scoring high marks in the exams, but it is also a skill that comes in handy in our everyday
lives. But learning maths can be hard – especially when you don’t understand the concepts easily. But following some simple strategies like referring to guides and textbooks and practising often will
help make maths learning easier. Learning maths becomes easier and more effective when learning becomes fun. So learn maths in the right way to improve your maths skills and score high marks.
|
{"url":"https://enewswiki.com/how-to-make-learning-maths-easier-for-students/","timestamp":"2024-11-05T00:59:15Z","content_type":"text/html","content_length":"168612","record_id":"<urn:uuid:f4516006-cae4-424e-a07b-927d900969bf>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00480.warc.gz"}
|
Ex ante real interest rate equation
It decomposes the nominal short-term interest rate into an ex ante real interest rate and an expected inflation rate, according to Fisher's equation. Assume the ex
(5) After allowing for regime-switching, ex ante real interest rates are not correlated Equation (1) is often written as i=r+πe, implicitly ignoring the term in rπe, We decompose nominal interest
rates into real risk-free rates, inflation expectations In those environments, ex-post real interest rates could provide a misleading This finding could very likely be reflecting the uncertainties
surrounding the A3. A4. Ex ante real interest rate estimation equations. Estimation of ex ante real interest rate with growth in broad money supply as the only explanatory variable. 5 Dec 1984
hypotheses of uncovered interest parity and ex ante relative PPP, or the unbiasedness This equation indicates that the ex post real rate. 27 Sep 2019 For the Fisher hypothesis to hold, the resultant
ex ante real interest rate nominal interest rates and inflation: The Fisher equation revisited. 30 Nov 2003 However in the 1990s the ex ante real interest rate was equation (1), equation ( 2) can be
expressed in an error correction model (ECM) form
In this case we can say that the contracted real rate of interest (sometimes called the "ex ante" real rate) is 5 percent per annum. The realized (or "ex post") real interest rate will depend on the
rate of inflation that actually occurs, which will normally differ from the inflation rate you and the borrower are expecting.
It decomposes the nominal short-term interest rate into an ex ante real interest rate and an expected inflation rate, according to Fisher's equation. Assume the ex In particular, this finding is
consistent. Page 9. 5 with the prediction of the long- run Fisher effect that inflation expectations and nominal interest rates move one- for- They measure the real cost of capital, thus playing a
crucial role in determining long-run output growth. Moreover, real as opposed to nominal interest rates. negative or zero. The real rate of interest (r. e. ) in Equation (1) represents the expected
relative price paid for earlier. We find that inflation expectations and ex-ante real rates of interest are negatively correlated. This finding contradicts the Fisher hypothesis. It is in line,
It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate. If, for example, an investor
were able to lock in a 5% interest rate for the coming year and anticipated a 2% rise in prices, they would expect to earn a real interest rate of 3% . [1]
Then, the ex-ante (before the event) real interest rate that you are expecting is about 3% per annum over the next ten years. Now suppose that the ex-post (after the event) reality turns out to be
that although you get the nominal interest rate of 5% per annum on the government bond, the average inflation rate over the ten years turns out to be 3%. Using the formula above, the ex-post real
rate in the example = the nominal rate - the actual inflation rate, or in this case 10 percent - 10 percent = 0 percent. ex ante versus ex post real interest rates Matthew Rafferty. This video
briefly describes the difference between ex ante and ex post real interest rates. Skip navigation Sign in. Search. Example of ex ante and ex post. There is an example of ex ante and ex post in this
blog from Paul Krugman below about the decision of the Fed to raise interest rates. Firstly, the Fed is raising interest rates in the US because: It predicts the economy is getting closer to full
capacity with unemployment falling towards 5% Inflation rate calculator solving for real interest rate given nominal interest rate and inflation AJ Design ☰ Math Geometry Physics Force Fluid
Mechanics Finance Loan Calculator. Inflation Rate Equations Calculator Finance - Real Interest Rates - Formulas. Solving for real interest rate. Inputs: nominal interest rate (n) inflation rate (i)
A. We can always compute the ex post real interest rate but not the ex ante real rate. B. We cannot compute either the ex post or ex ante real interest rates accurately. C. We can accurately compute
the ex ante real interest rate but not the ex post real rate. D. None of the statements are correct. Ex-post Real Interest Rates versus Ex-ante Real Rates: a CCAPM ApproachVol. 15, nº 3, 1998 381 of
our approach lies in its data requirements. All the results are obtained using information on non-durable consumption alone which, thus, acts as a sufficient statistic for the three non-observable
30 Oct 2015 we will use to construct the ex-ante real rates used in our analysis. the long-run equilibrium U.S. real interest rate remains significantly positive, and quarter window and the equation
(2.3) version that we actually used. 5
30 Nov 2003 However in the 1990s the ex ante real interest rate was equation (1), equation ( 2) can be expressed in an error correction model (ECM) form The figure reports the annualized ex-post
real 3-month interest rate for the U.S. since 1871. Law of accumulation of wealth for the world (closed economy):. post real rate, defined as the difference between the nominal interest rate and
actual inflation according to the ex post Fisher equation, as a proxy for the ex ante 16.14 The Fisher Equation: Nominal and Real Interest Rates. When you borrow or lend, you normally do so in
dollar terms. If you take out a loan, the loan is The natural rate of interest is a key concept in monetary economics because its level relative to lower since 2009. Based on this metric, this
finding their paper, they. Figure 2: Natural Rate from Laubach-Williams vs. the Ex-Ante Real Rate.
Definition of ex ante real interest rate: The anticipated real interest rate. Calculated by: nominal interest rate minus expected inflation rate.
I explain the difference between ex ante and ex post real interest rates. I show how they fit in to the Fisher equation. I show how expected inflation being greater than or less than actual Example
of ex ante and ex post. There is an example of ex ante and ex post in this blog from Paul Krugman below about the decision of the Fed to raise interest rates. Firstly, the Fed is raising interest
rates in the US because: It predicts the economy is getting closer to full capacity with unemployment falling towards 5% Inflation rate calculator solving for real interest rate given nominal
interest rate and inflation AJ Design ☰ Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator. Inflation Rate Equations Calculator Finance - Real Interest Rates - Formulas. Solving for
real interest rate. Inputs: nominal interest rate (n) inflation rate (i) In this case we can say that the contracted real rate of interest (sometimes called the "ex ante" real rate) is 5 percent per
annum. The realized (or "ex post") real interest rate will depend on the rate of inflation that actually occurs, which will normally differ from the inflation rate you and the borrower are expecting.
Solving the two equations (see the Appendix A for a matrix representation) gives: (16.1) (16.2) where and are ex post interest and inflation rates, respectively, and , , and are their ex post
coefficients. Now the ex post short-run Fisher coefficient is , whereas the ex ante short-run Fisher coefficient is λ 1. C) ex ante real interest rate. D) ex post real interest rate. 6. In a country
on a gold standard, the quantity of money is determined by the: A) government. B) central bank. C) amount of gold. D) buying and selling of government securities. 7. The real return on holding money
is: A) the real interest rate. B) minus the real interest rate. A. We can always compute the ex post real interest rate but not the ex ante real rate. B. We cannot compute either the ex post or ex
ante real interest rates accurately. C. We can accurately compute the ex ante real interest rate but not the ex post real rate. D. None of the statements are correct.
post real rate, defined as the difference between the nominal interest rate and actual inflation according to the ex post Fisher equation, as a proxy for the ex ante 16.14 The Fisher Equation:
Nominal and Real Interest Rates. When you borrow or lend, you normally do so in dollar terms. If you take out a loan, the loan is The natural rate of interest is a key concept in monetary economics
because its level relative to lower since 2009. Based on this metric, this finding their paper, they. Figure 2: Natural Rate from Laubach-Williams vs. the Ex-Ante Real Rate. 30 Oct 2015 we will use
to construct the ex-ante real rates used in our analysis. the long-run equilibrium U.S. real interest rate remains significantly positive, and quarter window and the equation (2.3) version that we
actually used. 5
|
{"url":"https://topoptionsuokgxdy.netlify.app/hulin31078zyle/ex-ante-real-interest-rate-equation-lat.html","timestamp":"2024-11-13T08:10:41Z","content_type":"text/html","content_length":"34812","record_id":"<urn:uuid:d448a91b-129c-4657-b90b-4f9506db77ac>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00416.warc.gz"}
|
Dinosaur Dodger Tips and Strategy
I recently uploaded a game I call “Dinosaur Dodger“. It’s based on an interesting paradox I read about on this blog, by an economist who has authored a number of good books. The paradox is called the
“Paradox of the Absent Minded Driver”. It goes like this : imagine a driver, driving home along a highway. They need to take the second exit to get off, but for some reason they can’t recall which
exit they are at when they get to an exit.
The Absent Minded Driver paradox, and Dinosaur Didger, involve finding the best strategy to get home on this track
Since the two exits are identical, and since the driver can never recall, when they reach an exit, whether they’ve already passed one, the only way to have any chance of getting home is to choose
randomly whether or not to turn.
If their probability of going straight is P, then, to get home,
• At the first exit, they must go straight – they have a probability of P of doing that.
• At the second exit, they must turn – they have a probability of 1-P of doing that.
• Therefore, their chance of getting home is P x (1-P) = P – P^2
To make this chance as big as possible, the driver decides to choose P=1/2. A coin flip at each intersection. That’s still only a 1/4 chance of getting home, but any other P is worse. For example, if
they choose either P=1 (always go straight) or P=0 (always turn), their chance of getting home is zero – in the first case because they never turn, in the second case because they always turn too
Anyway, suppose the driver gets his coin ready, and starts to drive. Then he gets to an intersection, and thinks : “hang on, this is more likely to be the first intersection – I always reach the
first intersection on every trip, but I only reach the second intersection on half my trips”. In fact, there’s a 1/3 chance he’s at the second intersection, and a 2/3 chance he’s at the first. So he
says “All right, I’ll go straight with probability 3/5, and only turn with probability 2/5”. That way, his chance of getting home is 22/75 – almost 30% instead of 25%.
The paradox is this. He already knew, when he was starting his trip, that he would reach the first intersection – so arriving there gives him no new information! How could he come to a different
logical conclusion?
Now Dinosaur Dodger is not based precisely on this paradox. Instead of one driver driving home with one strategy, there’s an explorer on a jungle track, receiving advice from a different player at
each turn-off. This is quite a different conundrum from the Absent-Minded Driver Paradox. Since you are not alone in advising the explorer, your best strategy in Dinosaur Dodger depends on what
everyone else is doing. Unfortunately, you don’t know exactly what that is – though perhaps you can get some clue from the high scores table.
Suppose that, on average, the other drivers are going straight with probability Q. If you decide to go straight with probability P, then your chance of getting the explorer back home is (P + Q – 2PQ)
/(2-Q). If you can guess Q, then you can substitute Q and different values of P into that formula, to see how to get the most explorers home. I’ll give some examples so you can test if you are
working this out properly.
• Suppose you think that Q=1/4, and you try P=1/4. Then the explorer gets home with probability (1/4 + 1/4 – 2 x 1/4 x 1/4) / (2 – 1/4) = 3/14, or only about 21%.
• On the other hand, if you think Q=1/4 and you try P=3/4, then the explorer gets home with probability (1/4 + 3/4 – 2 x 1/4 x 3/4) / (2 – 1/4), which is 5/14, or about 36%. Clearly, if you think Q
=1/4, it is better to choose P=3/4 than P=1/4.
If you think Q=1/2, then, amazingly, it doesn’t matter what you choose! This is because, when Q=1/2, the explorer gets home with probability (P + 1/2 – P)/(3/2), which is 1/3 no matter what P is!
Hmm… that’s probably more than enough advice from me about the best strategy to use in Dinosaur Dodger. I wouldn’t want to spoil the game! And I’ve given enough information already for a clever spark
to figure out the best strategy all by him or herself.
One thought on “Dinosaur Dodger Tips and Strategy”
|
{"url":"https://www.dr-mikes-math-games-for-kids.com/blog/2011/03/dinosaur-dodger-tips-and-strategy/","timestamp":"2024-11-05T02:57:48Z","content_type":"text/html","content_length":"48253","record_id":"<urn:uuid:d59219ba-51ba-4aca-80a6-88b5766f804c>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00697.warc.gz"}
|
Gaussian Discriminant Analysis | Online Tutorials Library List | Tutoraspire.com
Gaussian Discriminant Analysis
Gaussian Discriminant Analysis
There are two types of Supervised Learning algorithms are used in Machine Learning for classification.
1. Discriminative Learning Algorithms
2. Generative Learning Algorithms
Logistic Regression, Perceptron, and other Discriminative Learning Algorithms are examples of discriminative learning algorithms. These algorithms attempt to determine a boundary between classes in
the learning process. A Discriminative Learning Algorithm might be used to solve a classification problem that will determine if a patient has malaria. The boundary is then checked to see if the new
example falls on the boundary, P(y|X), i.e., Given a feature set X, what is its probability of belonging to the class “y”.
Generative Learning Algorithms, on the other hand, take a different approach. They try to capture each class distribution separately rather than finding a boundary between classes. A Generative
Learning Algorithm, as mentioned, will examine the distribution of infected and healthy patients separately. It will then attempt to learn each distribution’s features individually. When a new
example is presented, it will be compared to both distributions, and the class that it most closely resembles will be assigned, P(X|y) for a given P(y) here, P(y) is known as a class prior.
These Bayes Theory predictions are used to predict generative learning algorithms:
By analysing only, the numbers of P(X|y) as well as P(y) in the specific class, we can determine P(y), i.e., considering the characteristics of a sample, how likely is it that it belongs to class
Gaussian Discriminant Analysis is a Generative Learning Algorithm that aims to determine the distribution of every class. It attempts to create the Gaussian distribution to each category of data in a
separate way. The likelihood of an outcome in the case using an algorithm known as the Generative learning algorithm is very high if it is close to the centre of the contour, which corresponds to its
class. It diminishes when we move away from the middle of the contour. Below are images that illustrate the differences between Discriminative as well as Generative Learning Algorithms.
Let’s take a look at the case of a classification binary problem in which all datasets have IID (Independently and identically distributed). To determine P(X|y), we can use Multivariate Gaussian
Distribution to calculate a probability density equation for every particular class. In order to determine P(y) or the class prior for each class, we can make use of the Bernoulli distribution since
all sample data used in binary classification could be 0 or 1.
So the probability distribution, as well as a class prior to a sample, could be determined using the general model of Gaussian and Bernoulli distributions:
To understand the probability distributions in terms of the above parameters, we can formulate the likelihood formula, which is the product of the probability distribution as well as the class before
every data sample (Taking the probability distribution as a product is reasonable since all samples of data are considered IID).
In accordance with the principle of Likelihood estimation, we need to select the parameters so as to increase the probability function, as shown in Equation 4. Instead of maximizing the Likelihood
Function, we can boost the Log-Likelihood Function, a strict growing function.
In the above equations, “1{condition}” is the indicator function that returns 1 if this condition holds; otherwise returns zero. For instance, 1{y = 1} returns 1 only if the class of the data sample
is 1. Otherwise, it returns 0 in the same way, and similarly, in the event of 1{y = 0}, it will return 1 only if the class of the sample is 0. Otherwise, it returns 0.
The parameters derived can be used in equations 1, 2, and 3, to discover the probability distribution and class before the entire data samples. The values calculated can be further multiplied in
order to determine the Likelihood function, as shown in Equation 4. As previously mentioned, it is the probability function, i.e., P(X|y). P(y) is integrated into the Bayes formula to calculate P(y|
X) (i.e., determine the type ‘y’ of a data sample for the specified characteristics ‘ X’).
Thus, Gaussian Discriminant Analysis works extremely well with a limited volume of data (say several thousand examples) and may be more robust than Logistic Regression if our fundamental assumptions
regarding data distribution are correct.
Share 0 FacebookTwitterPinterestEmail
previous post
Anti-Money Laundering using Machine Learning
next post
Basic Configuration in Magento 2
You may also like
|
{"url":"https://tutoraspire.com/gaussian-discriminant-analysis/","timestamp":"2024-11-10T10:53:14Z","content_type":"text/html","content_length":"357851","record_id":"<urn:uuid:8f79da2e-fe28-40d7-a06a-091ed0d3e3c4>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00681.warc.gz"}
|
Assignment 1 Neural Networks and Deep Learning CSCI 5922 solved
The goal of this assignment is to introduce neural networks in terms of ideas you are already familiar with: linear regression and linear-threshold classification.
Part 1
Consider the following table that describes a relationship between two input variables (x1,x2) and an output variable (y).
This is part of a larger data set that I created which you can download either in matlab or text format. Using your favorite language, find the least squares solution to y = w1 * x1 + w2 * x2 + b.
(1a) Report the values of w1, w2, and b.
(1b) What function or method did you use to find the least-squares solution?
Part 2
Using the LMS algorithm, write a program that determines the coefficients {w1,w2,b} via incremental updating, steepest descent, and multiple passes through the training data. You will need to
experiment with updating rules (online, batch, minibatch), step sizes (i.e., learning rates), stopping criteria, etc. Experiment to find settings that lead to solutions with the fewest number of
sweeps through the data.
(2a) Report the values of w1, w2, and b.
(2b) What settings worked well for you: online vs. batch vs. minibatch? what step size? how did you decide to terminate?
(2c) Make a graph of error on the entire data set as a function of epoch. An epoch is a complete sweep through all the data.
Part 3
Turn this data set from a regression problem into a classification problem simply by using the sign of y (+ or -) as representing one of two classes. In the data set you download, you’ll see a
variable z that represents this binary (0 or 1) class. Use the perceptron learning rule to solve for the coefficients {w1, w2, b} of this classification problem.
Two warnings: First, your solution to Part 3 should require only a few lines of code added to the code you wrote for Part 2. Second, the Perceptron algorithm will not converge if there is no exact
solution to the training data. It will jitter among coefficients that all yield roughly equally good solutions.
(3a) Report the values of coefficients w1, w2, and b.
(3b) Make a graph of the accuracy (% correct classification) on the training set as a function of epoch.
Part 4
In machine learning, we really want to train a model based on some data and then expect the model to do well on “out of sample” data. Try this with the code you wrote for Part 3: Train the model on
the first {5, 10, 25, 50, 75} examples in the data set and test the model on the final 25 examples.
(4a) How does performance on the test set vary with the amount of training data? Make a bar graph showing performance for each of the different training set sizes.
|
{"url":"https://codeshive.com/questions-and-answers/assignment-1-neural-networks-and-deep-learning-csci-5922-solved/","timestamp":"2024-11-14T08:04:24Z","content_type":"text/html","content_length":"101396","record_id":"<urn:uuid:ca4fa9ec-7027-473a-8683-b0bc710fb45f>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00004.warc.gz"}
|
Easy Memoization of recursive functions using Scalaz
Ninety-Nine Scala Problems is an excellent problem set to work throught if you want to sharpen your scala programming skills as well as brush up on your understanding of data structures and
I’ve been slowly chipping away at the problems, and I found P59, constructing all height balanced binary trees for a given height, to be a nice case study on memoization. In this post I show you my
initial implementation and how it does redundant work, and then show you how I used scalaz’s Memo to speed it up.
The Problem
In a height-balanced binary tree, the following property holds for every node: The height of its left subtree and the height of its right subtree are almost equal, which means their difference is not
greater than one.
Write a method Tree.hbalTrees to construct height-balanced binary trees for a given height with a supplied value for the nodes. The function should generate all solutions.
scala> Tree.hbalTrees(3, "x")
res0: List[Node[String]] = List(T(x T(x T(x . .) T(x . .)) T(x T(x . .) T(x . .))), T(x T(x T(x . .) T(x . .)) T(x T(x . .) .)), ...
Given a balanced tree of height n, we have the following cases for the height of its subtrees:
1. The left subtree has height n - 1 and the right subtree has height n - 1
2. The left subtree has height n - 2 and the right subtree has height n - 1
3. The left subtree has height n - 1 and the right subtree has height n - 2
For the base cases, we return a single node for height 0 and the three possible balanced trees for height 1:
o o o
/ \ / \
o , o , o o
In the recursive case we generate the trees of height n-1 and n-2. We take all possible left/right subtree pairs from these two lists, excluding pairs where both subtrees have height n-2 (because
these trees are already generated in the recursive call for n-1). Here is the full implementation.
def hBalTrees[T](height: Int, value: T): List[Tree[T]] = height match {
case 0 => List(Node(value, End, End))
case 1 => List(
Node(value, Node(value, End, End), End),
Node(value, End, Node(value, End, End)),
Node(value, Node(value, End, End), Node(value, End, End)))
case n => {
val nLess1Trees = hBalTrees(height-1, value)
val nLess2Trees = hBalTrees(height-2, value)
val allTrees = nLess2Trees ++ nLess1Trees
for {
(t1, i1) <- allTrees.zipWithIndex
(t2, i2) <- allTrees.zipWithIndex if (!(i1 < nLess2Trees.length && i2 < nLess2Trees.length))
} yield {
Node(value, t1, t2)
Duplicate work
Can you see the glaring inefficiency in the implementation? We’re calling the function on n - 1 and n - 2. Suppose we start at n = 5. We recursively solve for n = 4 and n = 3. When n = 4 we
recursively solve for n = 3 (DUPLICATE) and n = 2, and so on.
The recurrence relation for this function is T(n) = T(n-1) + T(n-2) + O(n^2), which is at least as slow as exponential runtime (the detailed analysis is not important for our discussion).
To fix this we need to cache the values returned from recursive calls. Scalaz provides a trait that makes this trivial.
Scalaz - Memo
Let’s look at the definition of the Memo trait in the Scalaz library
sealed trait Memo[@specialized(Int) K, @specialized(Int, Long, Double) V] {
def apply(z: K => V): K => V
It consumes a function from K to V and produces another function from K to V. We can use Memo to create a function from a tree height (Int) to a list of balanced trees with that height (List[Tree[T]]
def hBalTreesMemo[T](value: T): Int => List[Tree[T]] =
Memo.immutableHashMapMemo[Int, List[Tree[T]]] {
case 0 => List(Node(value, End, End))
case 1 => List(
Node(value, Node(value, End, End), End),
Node(value, End, Node(value, End, End)),
Node(value, Node(value, End, End), Node(value, End, End)))
case n => {
val nLess1Trees = hBalTreesMemo(value)(n-1)
val nLess2Trees = hBalTreesMemo(value)(n-2)
val allTrees = nLess2Trees ++ nLess1Trees
for {
(t1, i1) <- allTrees.zipWithIndex
(t2, i2) <- allTrees.zipWithIndex if (!(i1 < nLess2Trees.length && i2 < nLess2Trees.length))
} yield {
Node(value, t1, t2)
The signature of the function was slightly changed to fit the type of Memo but everything else is exactly the same! Let’s see how it performs against the non-memoized implementation.
Average execution times were gathered for tree heights 1 to 4. Due to the inherent slowness of the algorithm it wasn’t practical to test above 4 with my 2014 MacBook :P.
| Height | Original (ms) | Memoized (ms) | Speedup |
| 1 | 2.184389 | 7.043043 | 0.31 |
| 2 | 1.546299 | 1.270925 | 1.21 |
| 3 | 0.519338 | 0.484961 | 1.07 |
| 4 | 27.109193 | 13.389669 | 2.02 |
The memoized version is a low slower for trees of height 1. This is because the additional cost of memoizing is much higher when the function is in its base case, which takes comparatively little
time. For trees of size 4 we see a halving in runtime; a pretty solid gain.
If you can recognize where your recursive functions are doing extra work you can use the Memo trait to provide speedup and almost 0 additional cost. As a further optimization you can perform
benchmarking to determine the input threshold at which the memoized You can even swap back to the non-memoized implementation for very small inputs.
Written on March 20, 2020
|
{"url":"https://daltyboy11.github.io/Easy-memoization-of-recursive-functions-with-scalaz/","timestamp":"2024-11-14T18:22:31Z","content_type":"text/html","content_length":"20603","record_id":"<urn:uuid:83603212-4df0-42e8-8050-518ecdae01f5>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00345.warc.gz"}
|
Regression: Ridge Regression
Polynomial regression is a type of regression analysis used in machine learning and statistics to model the relationship
Ridge regression is a type of linear regression that is specially designed to handle multicollinearity and overfitting in models. It is an extension of ordinary least squares (OLS) regression, where
a penalty term equivalent to the square of the magnitude of coefficients is added to the OLS objective function.
Key Aspects:
1. Objective Function: In ridge regression, the objective function to be minimized consists of two components - the residual sum of squares like in OLS, and a regularization term called the ridge
penalty or L2 norm penalty. The ridge penalty helps prevent overfitting by shrinking the coefficient estimates towards zero.
2. Regularization Parameter (λ): Ridge regression introduces a tuning parameter λ (lambda) that controls the strength of regularization applied to the model. A larger value of λ results in greater
shrinkage of coefficients towards zero, which helps reduce variance at the cost of introducing some bias.
3. Bias-Variance Tradeoff: One advantage of using ridge regression is that it helps address multicollinearity issues by reducing variance without significantly increasing bias.
4. Model Interpretability: Due to its nature, ridge regression tends to include all predictors in the model with somewhat reduced coefficients but does not actually set any coefficients exactly to
zero unless penalized strongly.
• Ridge regression can effectively deal with multicollinearity between predictor variables.
• It provides more stable and reliable estimates when compared to OLS under conditions where there are high correlations between predictors.
• By shrinking coefficient estimates, it reduces potential model overfitting.
• While ridge regression can handle collinear data well, it might not perform as effectively if most predictors are unrelated.
• Interpreting individual predictor effects might be slightly more challenging due to coefficient shrinkage.
In summary, ridge regression is a powerful tool for improving upon standard linear models by addressing issues such as multicollinearity and overfitting through regularization techniques. By striking
a balance between bias and variance, it offers enhanced predictive performance on datasets with correlated predictors while providing robustness against noise and outliers.
between the independent variable x and the dependent variable y. In polynomial regression, instead of fitting a straight line to the data points (as done in linear regression), we fit a polynomial
Key Points about Polynomial Regression:
1. Curved Relationship: Linear regression assumes a linear relationship between the input variables and output, while polynomial regression allows for curved relationships by introducing higher
degree polynomials.
2. Equation Form: The general equation for polynomial regression with one independent variable is given by:
$$ y = \beta_{0} + \beta_{1}x + \beta_{2}x^{2} + ... + \beta_{n}x^{n} $$
3. Degree of Polynomial: The "degree" of a polynomial function determines how many bends or curves it has. A higher degree can result in overfitting if not chosen carefully.
4. Overfitting vs Underfitting: Overfitting occurs when the model fits the training data too well but performs poorly on unseen data; underfitting happens when the model is too simple to capture the
underlying trend of the data.
5. Bias-Variance Tradeoff: Increasing the degree of polynomial will reduce bias but increase variance, so there's a tradeoff that needs to be managed for optimal performance.
6. Model Evaluation: Metrics such as Mean Squared Error (MSE) or R-squared are commonly used to evaluate the performance of a polynomial regression model.
7. Scikit-learn Implementation: Python libraries like scikit-learn provide tools for implementing polynomial regression, allowing users to easily specify the degree of the polynomial and train their
Applications of Polynomial Regression:
• Prediction in non-linear scenarios
• Modeling real-world processes with complex relationships
• Used in fields like economics, physics, biology where relationships are not linear
In conclusion, understanding and utilizing polynomial regression expands our ability to capture complex patterns within datasets that go beyond linear relationships. However, it requires careful
consideration of model complexity and evaluation methods to prevent issues like overfitting or underfitting from hindering its effectiveness.
|
{"url":"https://kiziridis.com/regression-ridge-regression/","timestamp":"2024-11-06T06:12:55Z","content_type":"text/html","content_length":"82293","record_id":"<urn:uuid:6b7c7172-43f7-499c-963a-d2f69210d70f>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00006.warc.gz"}
|
Technical Notes | Documentation
When Multiple Assets are entered, the calculator computes the results of each asset independently of other assets, meaning the results of one asset have no bearing on another. At the end of each
year, the results are calculated by combining the values of all assets. Some values are simply added together: annual contribution, balance, basis, income, risk adjusted basis, tax paid, total
distribution. Other values are computed by first assigning a percentage depending on their position size in relation to the entire balance of the combined assets, then added together to give a total:
yield, return and yield on cost.
When Compound/DRIP is selected (turned on at individual asset level) the income produced from that specific Assets gets reinvested into ONLY that specific asset. However, there is a scenario where
purchase of an entire basket of Assets occurs: inputs from Earned Income, Unearned Income, and Annual Contribution are split evenly between all the assets. For instance, if monthly Earned Income is
$1,000 and there are 4 assets, each asset will have $250 allocated to it to either purchase new stocks/units OR increase the balance if Portfolio.
To see results for a Single Asset or investment, exclude all other assets and Update the calculator.
Some mathematical discrepancies are expected due to rounding and complexity and timing of multiple calculations.
Inflation is not currently calculated into these numbers.
Risk Adjusted Basis is the adjusted entry price of the asset when income is factored in. Meaning, it shows the impact of reinvested income (dividends, rents, interest, etc) on original capital
investment. As income is reinvested the original capital at risk is lowered. It can also be used to identify your break even point where you’ve made back all initial investment.
As of July 15, 2020: Logic adjustments were made so that all investment types (regardless of Portfolio, Individual Stock, or Units) follow the same algorithm. The nominal value of the yield is
calculated and the yield growth rate is applied to this nominal value. This affected the following outputs:
Total Dividends/Total Income
This change was made to more accurately simulate real world scenarios and adapt industry standards for yield calculations.
Rounding was turned off in the algorithm. Rounding is only applied at the very end of the cycle and right before the final values are displayed. This was done to be as accurate as possible with every
calculation. It also reduces the output difference between Portfolio and Individual Stock scenarios
Dividend per share and income per unit were added in the results section and the output table. This shows the nominal value for each individual share or unit for a given year. This value is displayed
to the tenth of a cent.
|
{"url":"https://docs.twfsystems.com/documentation/other/technical-notes","timestamp":"2024-11-09T14:14:48Z","content_type":"text/html","content_length":"159232","record_id":"<urn:uuid:b3c65579-e80f-415d-b14a-f302c9a660b1>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00389.warc.gz"}
|
Q as Energy Stored over Energy Dissipated
Next | Prev | Up | Top | Index | JOS Index | JOS Pubs | JOS Home | Search
Yet another meaning for 20, p. 326]
where the resonator is freely decaying (unexcited).
To analyze this, let's again consider a one-pole resonator as in §E.7.1. Then the impulse response is given by
The total stored energy at time
The energy dissipated in the first period
Assuming further that
as claimed. Note that this rule of thumb requires
Next | Prev | Up | Top | Index | JOS Index | JOS Pubs | JOS Home | Search [How to cite this work] [Order a printed hardcopy] [Comment on this page via email]
|
{"url":"https://ccrma.stanford.edu/~jos/filters/Q_Energy_Stored_over.html","timestamp":"2024-11-09T04:55:11Z","content_type":"text/html","content_length":"12574","record_id":"<urn:uuid:d058f08a-08b2-47c5-9976-8a78d9e18000>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00677.warc.gz"}
|
Question ID - 157401 | SaraNextGen Top Answer
A 1 hp motor is used for running a dual cylinder reciprocating compressor of a refrigeration system based on $\mathrm{R}-134$ a refrigerant having $185 \mathrm{~kJ} \mathrm{~kg}^{-1}$ cooling
capacity. COP of the system is 4.2 and overall efficiency of the compressor is $80 \%$. Specific volume of the refrigerant vapour at suction temperature is $0.15 \mathrm{~m}^{3} \mathrm{~kg}^{-1}$.
The compressor with bore diameters of $40 \mathrm{~mm}$ each runs at $1440 \mathrm{rpm}$.The mass flow rate of the refrigerant in $\mathrm{kg} \min ^{-1}$ is
(A) 1.634
(B) 1.090
(C) 0.813
(D) 0.240
|
{"url":"https://www.saranextgen.com/homeworkhelp/doubts.php?id=157401","timestamp":"2024-11-02T17:28:11Z","content_type":"text/html","content_length":"15151","record_id":"<urn:uuid:b2abe7a2-383b-4b52-b9f9-2b43f932c71f>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00549.warc.gz"}
|
CourseNana | Assignment: Denoising Diffusion on Two-Pixel Images
Denoising Diffusion on Two-Pixel Images
The field of image synthesis has evolved significantly in recent years. From auto-regressive models and Variational Autoencoders (VAEs) to Generative Adversarial Networks (GANs), we have now entered
a new era of diffusion models. A key advantage of diffusion models over other generative approaches is their ability to avoid mode collapse, allowing them to produce a diverse range of images. Given
the high dimensionality of real images, it is impractical to sample and observe all possible modes directly. Our objective is to study denoising diffusion on two-pixel images to better understand how
modes are generated and to visualize the dynamics and distribution within a 2D space.
1 Introduction
Diffusion models operate through a two-step process (Fig. 1): forward and reverse diffusion.
Figure 1: Diffusion models have a forward process to successively add noise to a clear image x0 and a backward process to successively denoise an almost pure noise image xT [2].
During the forward diffusion process, noise εt is incrementally added to the original data at time step t, over more time steps degrading it to a point where it resembles pure Gaussian noise. Let εt
represent standard Gaussian noise, we can parameterize the forward process as xt ∼ N (xt|√1 − βt xt−1, βt I):
q(xt|xt−1) = p1 − βt xt−1 + pβt εt−1 (1) 0<βt <1. (2)
Integrating all the steps together, we can model the forward process in a single step:
xt= α ̄txo+ 1−α ̄tε (3)
αt =1−βt (4) α ̄t = α 1 × α 2 × · · · × α t (5)
As t → ∞, xt is equivalent to an isotropic Gaussian distribution. We schedule β1 < β2 < ... < βT , as larger update steps are more appropriate when the image contains significant noise.
The reverse diffusion process, in contrast, involves the model learning to reconstruct the original data from a noisy version. This requires training a neural network to iteratively remove the noise,
thereby recovering the original data. By mastering this denoising process, the model can generate new data samples that closely resemble the training data.
We model each step of the reverse process as a Gaussian distribution
pθ(xt−1|xt) = N (xt−1|μθ(xt, t), Σθ(xt, t)) . (6)
It is noteworthy that when conditioned on x0, the reverse conditional probability is tractable:
q(x |x,x )=Nx |μ,βˆI, (7)
t−1 t 0 t−1 t t
where, using the Bayes’ rule and skipping many steps (See [8] for reader-friendly derivations), we have:
1 1−αt
μt=√α xt−√1−α ̄εt . (8)
We follow VAE[3] to optimize the negative log-likelihood with its variational lower bound with respect to μt and μθ(xt,t) (See [6] for derivations). We obtain the following objective function:
L=Et∼[1,T],x0,ε∥εt −εθ(xt,t)∥2. (9) The diffusion model εθ actually predicts the noise added to x0 from xt at timestep t.
a) many-pixel images b) two-pixel images
Figure 2: The distribution of images becomes difficult to estimate and distorted to visualize for many- pixel images, but simple to collect and straightforward to visualize for two-pixel images. The
former requires dimensionality reduction by embedding values of many pixels into, e.g., 3 dimensions, whereas the latter can be directly plotted in 2D, one dimension for each of the two pixels.
Illustrated is a Gaussian mixture with two density peaks, at [-0.35, 0.65] and [0.75, -0.45] with sigma 0.1 and weights [0.35, 0.65] respectively. In our two-pixel world, about twice as many images
have a lighter pixel on the right.
In this homework, we study denoising diffusion on two-pixel images, where we can fully visualize the diffusion dynamics over learned image distributions in 2D (Fig. 2). Sec. 2 describes our model
step by step, and the code you need to write to finish the model. Sec. 3 describes the starter code. Sec. 4 lists what results and answers you need to submit.
2 Denoising Diffusion Probabilistic Models (DDPM) on 2-Pixel Images
Diffusion models not only generate realistic images but also capture the underlying distribution of the training data. However, this probability density distributions (PDF) can be hard to collect for
many- pixel images and their visualization highly distorted, but simple and direct for two-pixel images (Fig. 2). Consider an image with only two pixels, left and right pixels. Our two-pixel world
contains two kinds of images: the left pixel lighter than the right pixel, or vice versa. The entire image distribution can be modeled by a Gaussian mixture with two peaks in 2D, each dimension
corresponding to a pixel.
Let us develop DDPM [2] for our special two-pixel image collection.
2.1 Diffusion Step and Class Embedding
We use a Gaussian Fourier feature embedding for diffusion step t:
xemb = sin2πw0x,cos2πw0x,...,sin2πwnx,cos2πwnx, wi ∼ N(0,1), i = 1,...,n. (10)
For the class embedding, we simply need some linear layers to project the one-hot encoding of the class labels to a latent space. You do not need to do anything for this part. This part is provided
in the code.
2.2 Conditional UNet
We use a UNet (Fig. 3) that takes as input both the time step t and the noised image xt, along with class label y if it is provided, and outputs the predicted noise. The network consists of only two
blocks for the encoding or decoding pathway. To incorporate the step into the UNet features, we apply a dense
Figure 3: Sampe condition UNet architecture. Please note how the diffusion step and the class/text conditional embeddings are fused with the conv blocks of the image feature maps. For simplicity, we
will not add the attention module for our 2-pixel use case.
linear layer to transform the step embedding to match the image feature dimension. A similar embedding approach can be used for class label conditioning. The detailed architecture is as follows.
1. Encoding block 1: Conv1D with kernel size 2 + Dense + GroupNorm with 4 groups
2. Encoding block 2: Conv1D with kernel size 1 + Dense + GroupNorm with 32 groups
3. Decoding block 1: ConvTranspose1d with kernel size 1 + Dense + GroupNorm with 4 groups 4. Decoding block 2: ConvTranspose1d with kernel size 1
We use SiLU [1] as our activation function. When adding class conditioning, we handle it similarly to the diffusion step.
Your to-do: Finish the model architecture and forward function in ddpm.py
2.3 Beta Scheduling and Variance Estimation
We adopt the sinusoidal beta scheduling [4] for better results then the original DDPM [2]:
α ̄t = f(t) (11)
f (0)
t/T+s π2
f(t)=cos 1+s ·2 . (12) However, we follow the simpler posterior variance estimation [2] without using [4]’s learnt posterior
variance method for estimating Σθ(xt,t).
For simplicity, we declare some global variables that can be handy during sampling and training. Here is
the definition of these global variables in the code.
1. betas: βt
2. alphas: αt = 1 − βt
3. alphas cumprod: α ̄t = Πt0αi ̃1−α ̄t−1
4. posterior variance: Σθ(xt, t) = σt = βt = 1−α ̄t βt
Your to-do: Code up all these variables in utils.py. Feel free to add more variables you need.
2.4 Training with and without Guidance
For each DDPM iteration, we randomly select the diffusion step t and add random noise ε to the original image x0 using the β we defined for the forward process to get a noisy image xt. Then we pass
the xt and t to our model to output estimated noise εθ, and calculate the loss between the actual noise ε and estimated noise εθ. We can choose different loss, from L1, L2, Huber, etc.
To sample images, we simply follow the reverse process as described in [2]:
xt−1=√α xt−√1−α ̄εθ(xt,t) +σtz, wherez∼N(0,I)ift > 1else0. (13)
We consider both classifier and classifier-free guidance. Classifier guidance requires training a separate classifier and use the classifier to provide the gradient to guide the generation of
diffusion models. On the other hand, classifier-free guidance is much simpler in that it does not need to train a separate model.
To sample from p(x|y), we need an estimation of ∇xt log p(xt|y). Using Bayes’ rule, we have:
∇xt log p(xt|y) = ∇xt log p(y|xt) + ∇xt log p(xt) − ∇xt log p(y) (14)
= ∇xt log p(y|xt) + ∇xt log p(xt), (15) 4
Figure 4: Sample trajectories for the same start point (a 2-pixel image) with different guidance. Setting y = 0 generates a diffusion trajectory towards images of type 1 where the left pixel is
darker than the right pixel, whereas setting y = 1 leads to a diffusion trajectory towards images of type 2 where the left pixel is lighter than the right pixel.
where ∇xt logp(y|xt) is the classifier gradient and ∇xt logp(xt) the model likelihood (also called score function [7]). For classifier guidance, we could train a classifier fφ for different steps of
noisy images and estimate p(y|xt) using fφ(y|xt).
Classifier-free guidance in DDPM is a technique used to generate more controlled and realistic samples without the need for an explicit classifier. It enhances the flexibility and quality of the
generated images by conditioning the diffusion model on auxiliary information, such as class labels, while allowing the model to work both conditionally and unconditionally.
For classifier-free guidance, we make a small modification by parameterizing the model with an additional input y, resulting in εθ(xt,t,y). This allows the model to represent ∇xt logp(xt|y). For
non-conditional generation, we simply set y = ∅. We have:
∇xt log p(y|xt) = ∇xt log p(xt|y) − ∇xt log p(xt) (16) Recall the relationship between score functions and DDPM models, we have:
ε ̄θ(xt, t, y) = εθ(xt, t, y) + w (εθ(xt, t, y) − εθ(xt, t, ∅)) (17) = (w + 1) · εθ(xt, t, y) − w · εθ(xt, t, ∅), (18)
where w controls the strength of the conditional influence; w > 0 increases the strength of the guidance, pushing the generated samples more toward the desired class or conditional distribution.
During training, we randomly drop the class label to train the unconditional model. We replace the orig- inal εθ(xt, t) with the new (w + 1)εθ(xt, t, y) − wεθ(xt, t, ∅) to sample with specific class
labels (Fig.4). Classifier-free guidance involves generating a mix of the model’s predictions with and without condition- ing to produce samples with stronger or weaker guidance.
Your to-do: Finish up all the training and sampling functions in utils.py for classifier-free guidance. 5
1. gmm.py defines the Gaussian Mixture model for the groundtruth 2-pixel image distribution. Your training set will be sampled from this distribution. You can leave this file untouched.
2. ddpm.py defines the model itself. You will need to follow the guideline to build your model there.
3. utils.py defines all the other utility functions, including beta scheduling and training loop module.
4. train.py defines the main loop for training.
1. (40 points) Finish the starter code following the above guidelines. Further changes are also welcome! Please make sure your training and visualization results are reproducible. In your report,
state any changes that you make, any obstacles you encounter during coding and training, and a brief README about how to run your code.
2. (20 points) Visualize a particular diffusion trajectory overlaid on the estimated image distribution PDF pθ(xt|t) at time-step t = 10,20,30,40,50, given max time-step T =50. We estimate the PDF
by sampling a large number of starting points and see where they end up with at time t, using either 2D histogram binning or Gaussian kernel density estimation methods. Fig. 5 is an example of
your result that the de-noising trajectory for a specific starting point overlaid on the groundtruth and estimated PDF.
In short, visualize such a sample trajectory overlaid on 5 estimated PDF’s at t = 10,20,30,40,50 respectively and over the ground-truth PDF. Briefly describe what you observe.
Figure 5: Sample de-noising trajectory overlaid on the estimated PDF for different steps.
3. (20 points) Train multiple models with different maximum timesteps T = 5, 10, 25, 50. Sample and de- noise 5000 random noises. Visualize a plot with 4 × 2 subplots, with each row represents
different T . The first column should be plots overlaying the scattered de-noised samples on the groundtruth PDF for different T , and the second column should be the estimated PDF from the
de-noised samples. One row of sample can be found at Fig. 6. Describe what you observed in terms of the final distribution.
Note that there are many existing ways [5, 9] to make smaller timesteps work well even for realistic images.
Figure 6: Sample overlaid scatter with T = 25
4. (20 points) For guided generation, use the same starting noise with different label guidance (y = 0 vs. y = 1). Visualize the different trajectories from the same starting noise xT that lead to
different modes overlaid on the same groundtruth PDF plot (similar to Fig. 4). Describe what you find.
Figure 7: Sample MNIST images generated by denoising diffusion with classifier-free guidance.
5. 30 points: Extend this model to MNIST images. Actions: Add more conv blocks for encoding/decoding; add residual layers and attention in each block; increase the max timestep to 200 or more. Four
blocks for each pathway should be enough for MNIST. Generate 10 images for each digit and visualize all the generated images in a 10 × 10 grid (see Fig. 7). Observe and describe the diversity within
each category. Visualize one trajectory of the generation from noise to a clear digit at t = 0, 25, 50, 75, 100, 125, 150, 175, 200. In your report, also answer the question: Throughout the
generation, is this shape of the digit generated part by part, or all at once?
5 Submission Instructions
1. This assignment is to be completed individually.
2. Please upload:
(a) A PDF file of the graph and explanation: Write each problem on a different page.
(b) A folder containing all code files: Please leave all your visualization codes inside as well, so
that we can reproduce your results if we find any graphs strange.
(c) If you believe there may be an error in your code, please provide a written statement in the pdf describing what you think may be wrong and how it affected your results. If necessary, provide
pseudocode and/or expected results for any functions you were unable to write.
3. You may refactor the code as desired, including adding new files. However, if you make substantial changes, please leave detailed comments and reasonable file names. You are not required to
create separate files for every model training/testing: commenting out parts of the code for different runs like in the scaffold is all right (just add some explanation).
1. [1] Stefan Elfwing, Eiji Uchibe, and Kenji Doya. “Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning”. In: CoRR abs/1702.03118 (2017). arXiv: 1702.
03118. URL: http://arxiv.org/abs/1702.03118.
2. [2] Jonathan Ho, Ajay Jain, and Pieter Abbeel. “Denoising Diffusion Probabilistic Models”. In: arXiv preprint arxiv:2006.11239 (2020).
3. [3] Diederik P Kingma and Max Welling. Auto-Encoding Variational Bayes. 2022. arXiv: 1312.6114 [stat.ML]. URL: https://arxiv.org/abs/1312.6114.
4. [4] Alex Nichol and Prafulla Dhariwal. “Improved Denoising Diffusion Probabilistic Models”. In: CoRR abs/2102.09672 (2021). arXiv: 2102.09672. URL: https://arxiv.org/abs/2102.09672.
5. [5] Tim Salimans and Jonathan Ho. Progressive Distillation for Fast Sampling of Diffusion Models. 2022. arXiv: 2202.00512 [cs.LG]. URL: https://arxiv.org/abs/2202.00512.
6. [6] Jascha Sohl-Dickstein et al. Deep Unsupervised Learning using Nonequilibrium Thermodynamics. 2015. arXiv: 1503.03585 [cs.LG]. URL: https://arxiv.org/abs/1503.03585.
7. [7] Yang Song and Stefano Ermon. “Generative Modeling by Estimating Gradients of the Data Distribu- tion”. In: CoRR abs/1907.05600 (2019). arXiv: 1907.05600. URL: http://arxiv.org/abs/1907. 05600
8. [8] Lilian Weng. “What are diffusion models?” In: lilianweng.github.io (July 2021). URL: https : / / lilianweng.github.io/posts/2021-07-11-diffusion-models/.
9. [9] Qinsheng Zhang and Yongxin Chen. Fast Sampling of Diffusion Models with Exponential Integrator. 2023. arXiv: 2204.13902 [cs.LG]. URL: https://arxiv.org/abs/2204.13902.
|
{"url":"https://coursenana.com/programming/assignment/assignment-denoising-diffusion-on-two-pixel-images","timestamp":"2024-11-12T19:50:16Z","content_type":"text/html","content_length":"153023","record_id":"<urn:uuid:4e7294e3-b3a0-497f-93c3-bfa5ec31437c>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00768.warc.gz"}
|
Hybrid Density Functionals Tuned towards Fulfillment of Fundamental DFT Conditions
Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session G1: Recent Advances in Density Functional Theory III
11:15 AM–2:15 PM, Tuesday, March 4, 2014
Room: 103/105
Sponsoring Units: DCP DCOMP
Chair: John P. Perdew, Temple University
Abstract ID: BAPS.2014.MAR.G1.5
Abstract: G1.00005 : Hybrid Density Functionals Tuned towards Fulfillment of Fundamental DFT Conditions
12:27 PM–1:03 PM
Preview Abstract Abstract
Matthias Scheffler
(Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin-Dahlem, Germany)
Hybrid exchange-correlation functionals (XC), e.g. PBE0 and HSE, have significantly improved the theoretical description of molecules and solids. Their degree of exact-exchange admixture ($\alpha )$
is in principle a functional of the electron density, but the functional form is not known. In this talk, I will discuss \textit{fundamental conditions} of exact density-functional theory (DFT) that
enable us to find the optimal choice of $\alpha $ for ground-state calculations. In particular, I will discuss the fact that the highest occupied Kohn-Sham level of an $N$-electron system ($\
varepsilon _{\mathrm{HOMO}}(N))$ should be constant for fractional particle numbers between $N$ and \textit{N-1 }[1,2] and equals the ionization potential (IP) [3, 4], as given by the total-energy
difference. In practice, we realize this in three different ways. XC($\alpha )$ will be optimized (opt-XC) until it $(i)$ fulfills the condition: $\varepsilon_{\mathrm{HOMO}}(N) = \varepsilon _{\
mathrm{HOMO}}$(\textit{N-1/2}) or the Kohn-Sham HOMO agrees with the ionization potential computed in a more sophisticated approach $\varepsilon _{\mathrm{HOMO}}(N) =$ IP such as \textit{(ii)} the
$G_{\mathrm{0}}W_{\mathrm{0}}$@opt-XC method [5,6] or \textit{(iii)} CCSD(T) or full CI [6]. Using such an opt-XC is essential for describing electron transfer between (organic) molecules, as
exemplified by the TTF/TCNQ dimer [5]. It also yields vertical ionization energies of the G2 test set of quantum chemistry with a mean absolute percentage error of only $\approx $3{\%}. Furthermore,
our approach removes the starting-point uncertainty of \textit{GW} calculations [5] and thus bears some resemblance to the consistent starting point scheme [7] and quasiparticle self-consistent \
textit{GW} [8]. While our opt-XC approach yields large $\alpha $ values for small molecules in the gas phase [5], we find that $\alpha $ needs to be 0.25 or less for organic molecules adsorbed on
metals [9]. \\[4pt] [1] J. P. Perdew et al., PRL 1982.\\[0pt] [2] P. Mori-Sanchez et al., JCP 2006.\\[0pt] [3] M. Levy et al., PRA 1984.\\[0pt] [4] T. Stein et al., PRL 2010.\\[0pt] [5] V. Atalla et
al., PRB 2013.\\[0pt] [6] N. A. Richter, et al., PRL 2013.\\[0pt] [7] T. K\"{o}rzd\"{o}rfer, N. Marom, PRB 2012.\\[0pt] [8] M. van Schilfgaarde et al., PRL 2006.\\[0pt] [9] O. T. Hofmann et al., NJP
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.MAR.G1.5
Engage My APS Information for The American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics.
Become an APS Member Renew Membership Librarians
Submit a Meeting Abstract Join an APS Unit Authors
Submit a Manuscript Get My Member Number Referees
Find a Journal Article Update Contact Information Media
Donate to APS Students
© 2024 American Physical Society | All rights reserved | Terms of Use | Contact Us
Headquarters 1 Physics Ellipse, College Park, MD 20740-3844 (301) 209-3200
Editorial Office 100 Motor Pkwy, Suite 110, Hauppauge, NY 11788 (631) 591-4000
Office of Public Affairs 529 14th St NW, Suite 1050, Washington, D.C. 20045-2001 (202) 662-8700
|
{"url":"https://meetings.aps.org/Meeting/MAR14/Session/G1.5","timestamp":"2024-11-12T05:37:08Z","content_type":"text/html","content_length":"20327","record_id":"<urn:uuid:36260465-8987-42ec-86f3-50270957f8a6>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00859.warc.gz"}
|
User's Guide
1. Orthogonal Partitioning Cluster
7.16 Orthogonal Partitioning Cluster
The ore.odmOC function builds an in-database model using the Orthogonal Partitioning Cluster (O-Cluster) algorithm.
The O-Cluster algorithm builds a hierarchical grid-based clustering model, that is, it creates axis-parallel (orthogonal) partitions in the input attribute space. The algorithm operates recursively.
The resulting hierarchical structure represents an irregular grid that tessellates the attribute space into clusters. The resulting clusters define dense areas in the attribute space.
The clusters are described by intervals along the attribute axes and the corresponding centroids and histograms. The sensitivity argument defines a baseline density level. Only areas that have a peak
density above this baseline level can be identified as clusters.
The k-Means algorithm tessellates the space even when natural clusters may not exist. For example, if there is a region of uniform density, k-Means tessellates it into n clusters (where n is
specified by the user). O-Cluster separates areas of high density by placing cutting planes through areas of low density. O-Cluster needs multi-modal histograms (peaks and valleys). If an area has
projections with uniform or monotonically changing density, O-Cluster does not partition it.
The clusters discovered by O-Cluster are used to generate a Bayesian probability model that is then used during scoring by the predict function for assigning data points to clusters. The generated
probability model is a mixture model where the mixture components are represented by a product of independent normal distributions for numeric attributes and multinomial distributions for categorical
If you choose to prepare the data for an O-Cluster model, keep the following points in mind:
• The O-Cluster algorithm does not necessarily use all the input data when it builds a model. It reads the data in batches (the default batch size is 50000). It only reads another batch if it
believes, based on statistical tests, that there may still exist clusters that it has not yet uncovered.
• Because O-Cluster may stop the model build before it reads all of the data, it is highly recommended that the data be randomized.
• Binary attributes should be declared as categorical. O-Cluster maps categorical data to numeric values.
• The use of OML4SQL equi-width binning transformation with automated estimation of the required number of bins is highly recommended.
• The presence of outliers can significantly impact clustering algorithms. Use a clipping transformation before binning or normalizing. Outliers with equi-width binning can prevent O-Cluster from
detecting clusters. As a result, the whole population appears to fall within a single cluster.
The specification of the formula argument has the form ~ terms where terms are the column names to include in the model. Multiple terms items are specified using + between column names. Use ~ . if
all columns in data should be used for model building. To exclude columns, use - before each column name to exclude.
For information on the ore.odmOC function arguments, call help(ore.odmOC).
Settings for an Orthogonal Partitioning Cluster Models
The following table lists settings that apply to Orthogonal Partitioning Cluster models.
Table 7-18 Orthogonal Partitioning Cluster Model Settings
│ Setting Name │ Setting Value │ Description │
│ OCLT_SENSITIVITY │ TO_CHAR(0 <=numeric_expr <=1) │ A fraction that specifies the peak density required for separating a new cluster. The fraction is related to the global uniform density. │
│ │ │ │
│ │ │ Default is 0.5 │
Example 7-19 Using the ore.odmOC Function
This example creates an O-Cluster model on a synthetic data set. The figure following the example shows the histogram of the resulting clusters.
x <- rbind(matrix(rnorm(100, mean = 4, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 2, sd = 0.3), ncol = 2))
colnames(x) <- c("x", "y")
x_of <- ore.push (data.frame(ID=1:100,x))
rownames(x_of) <- x_of$ID
oc.mod <- ore.odmOC(~., x_of, num.centers=2)
predict(oc.mod, x_of, type=c("class","raw"), supplemental.cols=c("x","y"))
Listing for This Example
R> x <- rbind(matrix(rnorm(100, mean = 4, sd = 0.3), ncol = 2),
+ matrix(rnorm(100, mean = 2, sd = 0.3), ncol = 2))
R> colnames(x) <- c("x", "y")
R> x_of <- ore.push (data.frame(ID=1:100,x))
R> rownames(x_of) <- x_of$ID
R> oc.mod <- ore.odmOC(~., x_of, num.centers=2)
R> summary(oc.mod)
ore.odmOC(formula = ~., data = x_of, num.centers = 2)
clus.num.clusters 2
max.buffer 50000
sensitivity 0.5
prep.auto on
1 1 100 NA 1 NA FALSE
2 2 56 1 2 NA TRUE
3 3 43 1 2 NA TRUE
MEAN.x MEAN.y
2 1.85444 1.941195
3 4.04511 4.111740
R> histogram(oc.mod)
R> predict(oc.mod, x_of, type=c("class","raw"), supplemental.cols=c("x","y"))
'2' '3' x y CLUSTER_ID
1 3.616386e-08 9.999999e-01 3.825303 3.935346 3
2 3.253662e-01 6.746338e-01 3.454143 4.193395 3
3 3.616386e-08 9.999999e-01 4.049120 4.172898 3
# ... Intervening rows not shown.
98 1.000000e+00 1.275712e-12 2.011463 1.991468 2
99 1.000000e+00 1.275712e-12 1.727580 1.898839 2
100 1.000000e+00 1.275712e-12 2.092737 2.212688 2
|
{"url":"https://docs.oracle.com/en/database/oracle/machine-learning/oml4r/2.0.0/oreug/build-orthogonal-partitioning-cluster-model.html","timestamp":"2024-11-02T06:37:13Z","content_type":"text/html","content_length":"18087","record_id":"<urn:uuid:06a4b2ad-2bd1-4f3d-9d10-f98b62dd8689>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00877.warc.gz"}
|
What is Overfitting? | SecretDataScientist.com
What is Overfitting?
Overfitting in mathematics and statistics is one of the most common tasks consisting in attempts to fit a “model” to a set of training data, so as to be able to make reliable predictions on generally
untrained data. In overfitting, a statistical model describes random error or noise instead of the underlying relationship. Overfitting occurs when a model is excessively complex, such as having too
many parameters relative to the number of observations. A model that has been overfitting has poor predictive performance, as it overreacts to minor fluctuations in the training data. The potential
for overfitting depends not only on the number of parameters and data but also the conformability of the model structure with the data shape, and the magnitude of model error compared to the expected
level of noise or error in the data. Even when the fitted model does not have an excessive number of parameters, it is to be expected that the fitted relationship will appear to perform less well on
a new data set than on the data set used for fitting. In particular, the value of the coefficient of determination will shrink relative to the original training data.
Was the above useful? Please share with others on social media.
If you want to look for more information, check some free online courses available at coursera.org, edx.org or udemy.com.
Recommended reading list:
Data Science from Scratch: First Principles with Python
Data science libraries, frameworks, modules, and toolkits are great for doing data science, but they’re also a good way to dive into the discipline without actually understanding data science. In
this book, you’ll learn how many of the most fundamental data science tools and algorithms work by implementing them from scratch.
If you have an aptitude for mathematics and some programming skills, author Joel Grus will help you get comfortable with the math and statistics at the core of data science, and with hacking skills
you need to get started as a data scientist. Today’s messy glut of data holds answers to questions no one’s even thought to ask. This book provides you with the know-how to dig those answers out.
Get a crash course in Python
Learn the basics of linear algebra, statistics, and probability—and understand how and when they're used in data science
Collect, explore, clean, munge, and manipulate data
Dive into the fundamentals of machine learning
Implement models such as k-nearest Neighbors, Naive Bayes, linear and logistic regression, decision trees, neural networks, and clustering
Explore recommender systems, natural language processing, network analysis, MapReduce, and databases
|
{"url":"https://secretdatascientist.com/overfitting/","timestamp":"2024-11-05T19:10:26Z","content_type":"text/html","content_length":"87015","record_id":"<urn:uuid:58192c54-ae04-4199-a0f8-7c948fb6c6be>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00038.warc.gz"}
|
seminars - Coding Theory from the Viewpoint of Lattices
In the first lecture, we introduce the history and basic concepts of (error-correcting) codes. Codes have been used widely in the mobile phones, compact discs, and the big data storage. They were
found by R. Hamming and C. Shannon in the late 1940s. Since then, Coding Theory has become one of the most practical mathematical areas and has interacted with Algebra, Combinatorics, and Number
Theory. Our today’s IT would have been impossible without the theory of codes.
In the second lecture, we describe an interesting connection between codes and lattices. They share common properties. We begin with some basic definitions of codes and lattices. Codes over rings
have been used in the construction of interesting Euclidean or Hermitian lattices. Given a prime p, B. Fine proved that there are exactly three commutative rings with unity of order p 2 and
characteristic p. Using C. Bachoc’s results, we describe that how these rings can be related to certain quotient rings of the ring of algebraic integers of an imaginary quadratic number field. Then
we construct Hermitian lattices from codes over these rings. Shaska, et al. have studied the theta functions of these Hermitian lattices. We generalize the results of Bachoc, Shaska, et al. We
propose some open problems in this direction.
|
{"url":"http://www.math.snu.ac.kr/board/index.php?mid=seminars&page=82&l=en&sort_index=room&order_type=desc&document_srl=646479","timestamp":"2024-11-12T12:57:48Z","content_type":"text/html","content_length":"47092","record_id":"<urn:uuid:31b58be8-74be-4a97-90f8-4ce3b76ad19c>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00863.warc.gz"}
|
How to Find the Focal Length of a Lens
There are two ways to find the
focal length of a lens
. One is by measuring it physically and another is solving it if you are given a word problem. Let's start with the first method.
Method 1: Measuring the Focal Length of a Lens Using a Ruler or Meterstick
Step 1:
When the sun is about to set, bring your lens and a white sheet of paper outside.
Step 2:
Make the lens face the sun on one side and the paper on the other side. This creates an inverted image of the sun set on the paper.
Step 3:
Adjust the lens to make the inverted image sharper.
Step 4:
Measure the distance between the lens and the paper. This is now the focal length of the lens.
You should do this task at the early hours of the morning or before the sun sets so that there is less chance of the sun's image burning your paper. However,
you should never look at the sun through the lens because that will still damage your eyes.
Method 2: Measuring the Focal Point of a Lens Using a Formula
There is a formula that will solve the focal point of a lens if you know the distance of the original object and the distance of the sharp image produced by the lens. It's called the Lens Equation.
is the focal length of the lens,
is the distance of the object from the lens, and
is the distance of the image formed by the lens.
Lens Formula Sample Problem
Let's say your teacher gave you this problem:
A light source 230 cm from a double convex lens forms a clear image 5 cm on the other side of the lens. What is the focal length of the lens?
Let's list what we know:
d[o ]
= 230 cm
d[i ]
= 5 cm
Let's now solve using the lens formula:
Therefore, the focal length of the lens is
4.89 cm
. Problem solved!
Method 1 vs Method 2 in Finding the Focal Length of a Lens
You might have noticed that the two methods seem to contradict each other. Method 1 just measures the distance of the imaged formed while method 2 takes the distance of the original object into
Now, take note that the sun is far away from earth. Hence, if you divide 1 by this distance, the result will be very small that we can neglect it in the lens equation.
This leaves us with just
d[i ]
|
{"url":"https://www.danielgubalane.com/2013/08/how-to-find-focal-length-of-lens.html","timestamp":"2024-11-05T16:53:33Z","content_type":"application/xhtml+xml","content_length":"57143","record_id":"<urn:uuid:2ef145bb-e92c-4acd-a4b1-0a2948840cb2>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00556.warc.gz"}
|
Homotopy type theory - (Mathematical Logic) - Vocab, Definition, Explanations | Fiveable
Homotopy type theory
from class:
Mathematical Logic
Homotopy type theory is a branch of mathematics that merges concepts from homotopy theory and type theory, providing a new foundation for mathematics based on the notion of types as spaces. This
approach allows for the interpretation of logical propositions as types and proofs as objects within these types, creating a framework where topological properties can inform type relationships.
congrats on reading the definition of homotopy type theory. now let's actually learn it.
5 Must Know Facts For Your Next Test
1. Homotopy type theory extends Martin-Lรถf type theory by incorporating ideas from homotopy theory, creating a deeper connection between logic and topology.
2. In this framework, types can represent not just data but also geometric spaces, making it possible to reason about shapes and paths within these spaces.
3. The univalence axiom is a key feature of homotopy type theory, stating that equivalent types can be identified, reflecting the idea that geometrical structures can be transformed without losing
their essential properties.
4. Homotopy type theory has implications for foundational programs in mathematics, offering a new perspective on proof theory, category theory, and constructive mathematics.
5. This approach has gained traction in the development of proof assistants, allowing for rigorous formal verification of mathematical statements and enhancing our understanding of mathematical
Review Questions
• How does homotopy type theory integrate concepts from both homotopy theory and type theory to provide a new foundation for mathematics?
□ Homotopy type theory combines the principles of homotopy theory, which studies topological spaces and continuous mappings, with type theory, where types classify data and expressions. This
integration allows logical propositions to be interpreted as types, with proofs acting as concrete objects within those types. Thus, one can reason about both mathematical truths and their
topological implications, fostering a new understanding of foundational mathematics.
• Discuss the significance of the univalence axiom in homotopy type theory and its impact on mathematical reasoning.
□ The univalence axiom plays a critical role in homotopy type theory by asserting that equivalent types are interchangeable. This concept resonates with ideas in topology where two shapes that
can be continuously transformed into each other are considered the same. By introducing this principle into mathematical reasoning, it enhances the flexibility of how we understand
equivalence in various mathematical structures and supports the identification of different mathematical objects based on their properties rather than their specific forms.
• Evaluate the potential influence of homotopy type theory on future developments in proof assistants and foundational programs in mathematics.
□ Homotopy type theory presents a transformative influence on proof assistants by enabling more robust methods for formal verification of mathematical statements. Its integration of geometric
intuition into logical reasoning provides tools that enhance the expressiveness and capabilities of proof assistants. As this framework gains acceptance, it could reshape foundational
programs in mathematics by offering new ways to approach proofs, fostering connections between seemingly disparate areas such as algebraic topology and computational logic, ultimately leading
to innovative developments in mathematical theory.
"Homotopy type theory" also found in:
ยฉ 2024 Fiveable Inc. All rights reserved.
APยฎ and SATยฎ are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
|
{"url":"https://library.fiveable.me/key-terms/mathematical-logic/homotopy-type-theory","timestamp":"2024-11-07T12:17:01Z","content_type":"text/html","content_length":"157677","record_id":"<urn:uuid:034ec9bd-ddcf-4619-a0d5-1eb23c8d9147>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00620.warc.gz"}
|
Urgently Looking for CFD Computational Fluid Dynamics Training
Need a CFD Computational Fluid Dynamics Training professional guide in Kalpakkam, Chennai. The teacher should be able to travel to our location to teach. I need someone with experience. The CFD
Computational Fluid Dynamics Training should be punctual and be willing to work on weekdays.
22 Similar Jobs
Some of the CFD Computational Fluid Dynamics Tutor Jobs are given below:
|
{"url":"https://tutorjobs.co.in/cfd-computational-fluid-dynamics-training/urgently-looking-for-cfd-computational-fluid-dynamics-training/3258","timestamp":"2024-11-10T08:29:21Z","content_type":"text/html","content_length":"50635","record_id":"<urn:uuid:32c9a381-3136-4df7-8ce7-36cb157ce362>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00185.warc.gz"}
|
Unknown number - math word problem (6343)
Unknown number
Find a number that is by eight larger than its third.
Correct answer:
Did you find an error or inaccuracy? Feel free to
write us
. Thank you!
Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our
fraction calculator
Do you have a linear equation or system of equations and are looking for its
? Or do you have
a quadratic equation
You need to know the following knowledge to solve this word math problem:
Grade of the word problem:
Related math problems and questions:
|
{"url":"https://www.hackmath.net/en/math-problem/6343","timestamp":"2024-11-04T08:18:36Z","content_type":"text/html","content_length":"45312","record_id":"<urn:uuid:b4dc12b0-10d5-44bb-b477-3aa23af5055c>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00147.warc.gz"}
|
THE considerations of THE EQUALITY OF INERTIAL AND GRAVITATIONAL MASS AS AN ARGUMENT FOR THE GENERAL POSTULATE OF RELATIVITY show that the general theory of relativity puts us in a position to derive
properties of the gravitational field in a purely theoretical manner. Let us suppose, for instance, that we know the space-time “course” for any natural process whatsoever, as regards the manner in
which it takes place in the Galileian domain relative to a Galileian body of reference K. By means of purely theoretical operations (i.e. simply by calculation) we are then able to find how this
known natural process appears, as seen from a reference-body K' which is accelerated relatively to K. But since a gravitational field exists with respect to this new body of reference K', our
consideration also teaches us how the gravitational field influences the process studied.
For example, we learn that a body which is in a state of uniform rectilinear motion with respect to K (in accordance with the law of Galilei) is executing an accelerated and in general curvilinear
motion with respect to the accelerated reference-body K (chest). This acceleration or curvature corresponds to the influence on the moving body of the gravitational field prevailing relatively to
K'. It is known that a gravitational field influences the movement of bodies in this way, so that our consideration supplies us with nothing essentially new.
However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light. With respect to the Galileian reference-body K, such a ray of light is
transmitted rectilinearly with the velocity c. It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest
(reference-body K'). From this we conclude, that, in general, rays of light are propagated curvilinearly in gravitational fields. In two respects this result is of great importance.
In the first place, it can be compared with the reality. Although a detailed examination of the question shows that the curvature of light rays required by the general theory of relativity is only
exceedingly small for the gravitational fields at our disposal in practice, its estimated magnitude for light rays passing the sun at grazing incidence is nevertheless 1.7 seconds of arc. This ought
to manifest itself in the following way. As seen from the earth, certain fixed stars appear to be in the neighbourhood of the sun, and are thus capable of observation during a total eclipse of the
sun. At such times, these stars ought to appear to be displaced outwards from the sun by an amount indicated above, as compared with their apparent position in the sky when the sun is situated at
another part of the heavens. The examination of the correctness or otherwise of this deduction is a problem of the greatest importance, the early solution of which is to be expected of astronomers.
In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental
assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the
velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in
the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to
disregard the influences of gravitational fields on the phenomena (e.g. of light).
Since it has often been contended by opponents of the theory of relativity that the special theory of relativity is overthrown by the general theory of relativity, it is perhaps advisable to make the
facts of the case clearer by means of an appropriate comparison. Before the development of electrodynamics the laws of electrostatics were looked upon as the laws of electricity. At the present time
we know that electric fields can be derived correctly from electrostatic considerations only for the case, which is never strictly realised, in which the electrical masses are quite at rest
relatively to each other, and to the co-ordinate system. Should we be justified in saying that for this reason electrostatics is overthrown by the field-equations of Maxwell in electrodynamics? Not
in the least. Electrostatics is contained in electrodynamics as a limiting case; the laws of the latter lead directly to those of the former for the case in which the fields are invariable with
regard to time. No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as
a limiting case.
In the example of the transmission of light just dealt with, we have seen that the general theory of relativity enables us to derive theoretically the influence of a gravitational field on the course
of natural processes, the laws of which are already known when a gravitational field is absent. But the most attractive problem, to the solution of which the general theory of relativity supplies the
key, concerns the investigation of the laws satisfied by the gravitational field itself. Let us consider this for a moment.
We are acquainted with space-time domains which behave (approximately) in a “Galileian” fashion under suitable choice of reference-body, i.e. domains in which gravitational fields are absent. If we
now refer such a domain to a reference-body K' possessing any kind of motion, then relative to K' there exists a gravitational field which is variable with respect to space and time. 1 The character
of this field will of course depend on the motion chosen for K'. According to the general theory of relativity, the general law of the gravitational field must be satisfied for all gravitational
fields obtainable in this way. Even though by no means all gravitational fields can be produced in this way, yet we may entertain the hope that the general law of gravitation will be derivable from
such gravitational fields of a special kind. This hope has been realised in the most beautiful manner. But between the clear vision of this goal and its actual realisation it was necessary to
surmount a serious difficulty, and as this lies deep at the root of things, I dare not withhold it from the reader. We require to extend our ideas of the space-time continuum still farther.
Albert Enstein
No comments
|
{"url":"https://www.physicspace.com.ng/2018/09/a-few-inferences-from-general-principle.html","timestamp":"2024-11-09T17:19:52Z","content_type":"application/xhtml+xml","content_length":"158728","record_id":"<urn:uuid:31059c07-a9d8-4b95-b82d-2ea3ad4892ae>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00021.warc.gz"}
|
Finding Area Of Oblique Triangles Worksheet Answers - TraingleWorksheets.com
Calculating Area Of A Triangle Worksheet – Triangles are among the most fundamental designs in geometry. Understanding triangles is crucial to understanding more advanced geometric concepts. In this
blog post it will explain the various types of triangles, triangle angles, how to determine the dimensions and the perimeter of a triangle, and offer illustrations of all. Types of Triangles There
are three types that of triangles are equilateral, isoscelesand scalene. Equilateral triangles contain three equal sides and three … Read more
Area Of Oblique Triangle Worksheet Answers
Area Of Oblique Triangle Worksheet Answers – Triangles are one of the most fundamental shapes in geometry. Understanding triangles is crucial for studying more advanced geometric concepts. In this
blog we will discuss the different types of triangles with triangle angles. We will also discuss how to calculate the perimeter and area of a triangle, and present details of the various. Types of
Triangles There are three kinds from triangles: Equal, isosceles, as well as … Read more
Finding Area Of A Triangle Worksheet
Finding Area Of A Triangle Worksheet – Triangles are among the most fundamental forms in geometry. Understanding triangles is crucial to studying more advanced geometric concepts. In this
blog post this post, we’ll go over the various kinds of triangles that are triangle angles. We will also explain how to determine the dimensions and the perimeter of a triangle, as well as
provide the examples for each. Types of Triangles There are three kinds of … Read more
|
{"url":"https://www.traingleworksheets.com/tag/finding-area-of-oblique-triangles-worksheet-answers/","timestamp":"2024-11-10T18:42:38Z","content_type":"text/html","content_length":"61768","record_id":"<urn:uuid:def7c3c7-9995-4af7-a6a9-e0c1bc390e8e>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00614.warc.gz"}
|
Design speed
Cycle highway F173b (Batavierenpad Zuid), Netherlands.
Two different “speed” parameters are commonly used to describe how fast a cycle highway is:
• Design speed defines the geometric requirements for the route or its sections.
• Average speed (travel speed, route speed) takes into account stops and interruptions on the way.
|
{"url":"https://cyclehighways.eu/design-and-build/design-principles/design-speed.html","timestamp":"2024-11-13T03:18:18Z","content_type":"text/html","content_length":"47525","record_id":"<urn:uuid:6f43933c-841c-4fbd-9d8c-606aa237ebe0>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00843.warc.gz"}
|
Statistics – Page 4 – goji berries
Let’s say that we want to measure the effect of a phone call encouraging people to register to vote on voting. Let’s define compliance as a person taking the call (like they do in Gerber and Green,
2000, etc.). And let’s assume that the compliance rate is low. The traditional way to estimate the effect of the phone call is via an RCT: randomly split the sample into Treatment and Control, call
everyone in the Treatment Group, wait till after the election, and calculate the difference in the proportion who voted. Assuming that the treatment doesn’t affect non-compliers, etc., we can also
estimate the Complier Average Treatment Effect.
But one way to think about non-compliance in the example above is as follows: “Buddy, you need to reach these people using another way.” That is a useful thing to know, but it is an observational
point. You can fit a predictive model for who picks up phone calls and who doesn’t. The experiment is useful in answering how much can you persuade the people you reach on the phone. And you can
learn that by randomizing conditional on compliance.
For such cases, here’s what we can do:
1. Call a reasonably large random sample of people. Learn a model for who complies.
2. Use it to target people who are likelier to comply and randomize post a person picking up.
More generally, the Average Treatment Effect is useful for global rollouts of one policy. But when is that a good counterfactual to learn? Tautologically, when that is all you can do or when it is
the optimal thing to do. If we are not in that world, why not learn about—and I am using an example to be concrete—a) what is a good way to reach me? b) what message most persuades me? For instance,
for political campaigns, the optimal strategy is to estimate the cost of reaching people by phone, mail, f2f, etc., estimate the probability of reaching each using each of the media, estimate the
payoff for different messages for different kinds of people, and then target using the medium and the message that delivers the greatest benefit. (For a discussion about targeting, see here.)
Technically, a message could have the greatest payoff for the person who is least likely to comply. And the optimal strategy could still be to call everyone. To learn treatment effects among people
who are unlikely to comply (using a particular method), you will need to build experiments to increase compliance. More generally, if you are thinking about multi-arm bandits or some such dynamic
learning system, the insight is to have treatment arms around both compliance and message. The other general point, implicit in the essay, is that rather than be fixated on calculating ATE, we should
be fixated on an optimization objective, e.g., the additional number of people persuaded to turn out to vote per dollar.
It is useful to think about the cost and benefit of an incremental voter. Let’s say you are a strategist for party p given the task of turning out voters. Here’s one way to think about the problem:
1. The benefit of turning out a voter in an election is not limited to the election. It also increases the probability of them turning out in the next election. The benefit is pro-rated by the
voter’s probability of voting for party p.
2. The cost of turning out a voter is a sum of targeting costs and persuasion costs. The targeting costs could be the cost of identifying voters unlikely to vote unless contacted who would likely
vote for party p or you could also build a model for persuadability and target further based on that. The persuasion costs include the cost of contacting the voter and persuading the voter
3. The cost of turning out a voter is likely greater than the cost of voting. For instance, some campaigns spend $150, some others think it is useful to spend as much as $1000. If cash transfers
were allowed, we should be able to get people to vote at much lower prices. But given cash transfers aren’t allowed, the only option is persuasion and that is generally expensive.
Prediction Errors: Using ML For Measurement
1 Sep
Say you want to measure how often people visit pornographic domains over some period. To measure that, you build a model to predict whether or not a domain hosts pornography. And let’s assume that
for the chosen classification threshold, the False Positive rate (FP) is 10\% and the False Negative rate (FN) is 7\%. Here below, we discuss some of the concerns with using scores from such a model
and discuss ways to address the issues.
Let’s get some notation out of the way. Let’s say that we have $n$ users and that we can iterate over them using $i$. Let’s denote the total number of unique domains—domains visited by any of the $n$
users at least once during the observation window—by $k$. And let’s use $j$ to iterate over the domains. Let’s denote the number of visits to domain $j$ by user $i$ by $c_{ij} = {0, 1, 2, ....}$. And
let’s denote the total number of unique domains a person visits ($\sum (c_{ij} == 1)$) using $t_i$. Lastly, let’s denote predicted labels about whether or not each domain hosts pornography by $p$, so
we have $p_1, ..., p_j, ... , p_k$.
Let’s start with a simple point. Say there are 5 domains with $p$: ${1_1, 1_2, 1_3, 1_4, 1_5}$. Let’s say user one visits the first three sites once and let’s say that user two visits all five sites
once. Given 10\% of the predictions are false positives, the total measurement error in user one’s score $= 3 * .10$ and the total measurement error in user two’s score $= 5 * .10$. The general point
is that total false positives increase as a function of predicted $1s$. And the total number of false negatives increase as the number of predicted $0s$.
Read more here.
Comparing Ad Targeting Regimes
30 Aug
Ad targeting is often useful when you have multiple things to sell (opportunity cost) or when the cost of running an ad is non-trivial or when an irrelevant ad reduces your ability to reach the user
later or any combination of the above. (For a more formal treatment, see here.)
But say that you want proof—you want to estimate the benefit of targeting. How would you do it?
When there is one product to sell, some people have gone about it as follows: randomize to treatment and control, show the ad to a random subset of respondents in the control group and an equal
number of respondents picked by a model in the treatment group, and compare the outcomes of the two groups (it reduces to comparing subsets unless there are spillovers). This experiment can be
thought off as a way to estimate how to spend a fixed budget optimally. (In this case, the budget is the number of ads you can run.) But if you were interested in finding out whether a budget
allocated by a model would be more optimal than say random allocation, you don’t need an experiment (unless there are spillovers). All you need to do is show the ad to a random set of users. For each
user, you know whether or not they would have been selected to see an ad by the model. And you can use this information to calculate payoffs for the respondents chosen by the model, and for the
randomly selected group.
Let me expand for clarity. Say that you can measure profit from ads using CTR. Say that we have built two different models for selecting people to whom we should show ads—Model A and Model B. Now say
that we want to compare which model yields a higher CTR. We can have four potential scenarios for selection of respondents by the model:
model_a, model_b
0, 0
1, 0
0, 1
1, 1
For CTR, 0-0 doesn’t add any information. It is the conditional probability. To measure which of the models is better, draw a fixed size random sample of users picked by model_a and another random
sample of the same size from users picked by model_b and compare CTR. (The same user can be picked twice. It doesn’t matter.)
Now that we know what to do, let’s understand why experiments are wasteful. The heuristic account is as follows: experiments are there to compare ‘similar people.’ When estimating allocative
efficiency of picking different sets of people, we are tautologically comparing different people. That is the point of the comparison.
All this still leaves the question of how would we measure the benefit of targeting. If you had only one ad to run and wanted to choose between showing an advertisement to everyone versus fewer
people, then show the ad to everyone and estimate profits based on the rows selected in the model and profits from showing the ad to everyone. Generally, showing an ad to everyone will win.
If you had multiple ads, you would need to randomize. Assign each person in the treatment group to a targeted ad. In the control group, you could show an ad for a random product. Or you could show an
advertisement for any one product that yields the maximum revenue. Pick whichever number is higher as the one to compare against.
What’s Relevant? Learning from Organic Growth
26 Aug
Say that we want to find people to whom a product is relevant. One way to do that is to launch a small campaign advertising the product and learn from people who click on the ad, or better yet, learn
from people who not just click on the ad but go and try out the product and end up using it. But if you didn’t have the luxury of running a small campaign and waiting a while, you can learn from
organic growth.
Conventionally, people learn from organic growth by posing it as a supervised problem. And they generate the labels as follows: people who have ‘never’ (mostly: in the last 6–12 months) used the
product are labeled as 0 and people who “adopted” the product in the latest time period, e.g., over the last month, are labeled 1. People who have used the product in the last 6–12 months or so are
filtered out.
There are three problems with generating labels this way. First, not all the people who ‘adopt’ a product continue to use the product. Many of the people who try it find that it is not useful or find
the price too high and abandon it. This means that a lot of 1s are mislabeled. Second, the cleanest 1s are the people who ‘adopted’ the product some time ago and have continued to use it since.
Removing those is thus a bad idea. Third, the good 0s are those who tried the product but didn’t persist with it not those who never tried the product. Generating the labels in such a manner also
allows you to mitigate one of the significant problems with learning from organic growth: people who organically find a product are different from those who don’t. Here, you are subsetting on the
kinds of people who found the product, except that one found it useful and another did not. This empirical strategy has its problems, but it is distinctly better than the conventional approach.
Quality Data: Plumbing ML Data Pipelines
6 Aug
What’s the difference between a scientist and a data scientist? Scientists often collect their own data, and data scientists often use data collected by other people. That is part jest but speaks to
an important point. Good scientists know their data. Good data scientists must know their data too. To help data scientists learn about the data they use, we need to build systems that give them good
data about the data. But what is good data about the data? And how do we build systems that deliver that? Here’s some advice (tailored toward rectangular data for convenience):
• From Where, How Much, and Such
□ Provenance: how were each of the columns in the data created (obtained)? If the data are derivative, find out the provenance of the original data. Be as concrete as possible, linking to
scripts, related teams, and such.
□ How Frequently is it updated
□ Cost per unit of data, e.g., a cell in rectangular data.
Both, the frequency with which data are updated, and the cost per unit of data may change over time. Provenance may change as well: a new team (person) may start managing data. So the person who
‘owns’ the data must come back to these questions every so often. Come up with a plan.
• What? To know what the data mean, you need a data dictionary. A data dictionary explains the key characteristics of the data. It includes:
1. Information about each of the columns in plain language.
2. How were the data were collected? For instance, if you conducted a survey, you need the question text and the response options (if any) that were offered, along with the ‘mode’, and where in
a sequence of questions does this lie, was it alone on the screen, etc.
3. Data type
4. How (if at all) are missing values generated?
5. For integer columns, it gives the range, sd, mean, median, n_0s, and n_missing. For categorical, it gives the number of unique values, what each label means, and a frequency table that
includes n_missing (if missing can be of multiple types, show a row for each).
6. The number of duplicates in data and if they are allowed and a reason for why you would see them.
7. Number of rows and columns
8. Sampling
9. For supervised models, store correlation of y with key x_vars
• What If? What if you have a question? Who should you bug? Who ‘owns’ the ‘column’ of data?
Store these data in JSON so that you can use this information to validate against. Produce the JSON for each update. You can flag when data are some s.d. above below last ingest.
Store all this metadata with the data. For e.g., you can extend the dataframe class in Scala to make it so.
Auto-generate reports in markdown with each ingest.
In many ML applications, you are also ingesting data back from the user. So you need the same as above for the data you are getting from the user (and some of it at least needs to match the stored
For any derived data, you need the scripts and the logic, ideally in a notebook. This is your translation function.
Where possible, follow the third normal form of databases. Only store translations when translation is expensive. Even then, think twice.
Lastly, some quality control. Periodically sit down with your team to see if you should see what you are seeing. For instance, if you are in the survey business, do the completion times make sense?
If you are doing supervised learning, get a random sample of labels. Assess their quality. You can also assess the quality by looking at errors in classification that your supervised model makes. Are
the errors because the data are mislabeled? Keep iterating. Keep improving. And keep cataloging those improvements. You should be able to ‘diff’ data collection, not just numerical summaries of data.
And with what the method I highlight above, you should be.
Optimal Sequence in Which to Service Orders
27 Jul
What is the optimal order in which to service orders assuming a fixed budget?
Let’s assume that we have to service orders o_1,…,…o_n, with the n orders iterated by i. Let’s also assume that for each service order, we know how the costs change over time. For simplicity, let’s
assume that time is discrete and portioned in units of days. If we service order o_i at time t, we expect the cost to be c_it. Each service order also has an expiration time, j, after which the order
cannot be serviced. The cost at expiration time, j, is the cost of failure and denoted by c_ij.
The optimal sequence of servicing orders is determined by expected losses—service the order first where the expected loss is the greatest. This leaves us with the question of how to estimate expected
loss at time t. To come up with an expectation, we need to sum over some probability distribution. For o_it, we need the probability, p_it, that we would service o_i at t+1 till j. And then, we need
to multiply p_it with c_ij. So framed, the expected loss for order i at time t =
c_it – \Sigma_{t+1}_{j} p_it * c_it
However, determining p_it is not straightforward. New items are added to the queue at t+1. On the flip side, we also get to re-prioritize at t+1. The question is if we will get to the item o_i at
t+1? (It means p_it is 0 or 1.) For that, we need to forecast the kinds of items in the queue tomorrow. One simplification is to assume that items in the queue today are the same that will be in the
queue tomorrow. Then, it reduces to estimating the cost of punting each item again tomorrow, sorting based on the costs at t+1, and checking whether we will get to clear the item. (We can forgo the
simplification by forecasting our queue tomorrow, and each day after that till j for each item, and calculating the costs.)
If the data are available, we can tack on clearing time per order and get a better answer to whether we will clear o_it at time t or not.
Optimal Sequence in Which to Schedule Appointments
1 Jul
Say that you have a travel agency. Your job is to book rooms at hotels. Some hotels fill up more quickly than others, and you want to figure out which hotels to book at first so that your net booking
rate is as high as it could be the staff you have.
The logic of prioritization is simple: prioritize those hotels where the expected loss if you don’t book now is the largest. The only thing we need to do is find a way to formalize the losses. Going
straight to formalization is daunting. A toy example helps.
Imagine that there are two hotels Hotel A and Hotel B where if you call 2-days and 1-day in advance, the chances of successfully booking a room are .8 and .8, and .8 and .5 respectively. You can only
make one call a day. So it is Hotel A or Hotel B. Also, assume that failing to book a room at Hotel A and Hotel B costs the same.
If you were making a decision 1-day out on which hotel to call to book, the smart thing would be to choose Hotel A. The probability of making a booking is larger. But ‘larger’ can be formalized in
terms of losses. Day 0, the probability goes to 0. So you make .8 units of loss with Hotel A and .5 with Hotel B. So the potential loss from waiting is larger for Hotel A than Hotel B.
If you were asked to choose 2-days out, which one should you choose? In Hotel A, if you forgo 2-days out, your chances of successfully booking a room next day are .8. At Hotel B, the chances are .5.
Let’s play out the two scenarios. If we choose to book at Hotel A 2-days out and Hotel B 1-day out, our expected batting average is (.8 + .5)/2. If we choose the opposite, our batting average is (.8
+ .8)/2. It makes sense to choose the latter. Framed as expected losses, we go from .8 to .8 or 0 expected loss for Hotel A and .3 expected loss for Hotel B. So we should book Hotel B 2-days out.
Now that we have the intuition, let’s move to 3-days, 2-days, and 1-day out as that generalizes to k-days out nicely. To understand the logic, let’s first work out a 101 probability question. Say
that you have two fair coins that you toss independently. What is the chance of getting at least one head? The potential options are HH, HT, TH, and TT. The chance is 3/4. Or 1 minus the chance of
getting a TT (or two failures) or 1- .5*.5.
The 3-days out example is next. See below for the table. If you miss the chance of calling Hotel A 3-days out, the expected loss is the decline in success in booking 2-days or 1-day out. Assume that
the probabilities 2-days out and 1-day our are independent and it becomes something similar to the example about coins. The probability of successfully booking 2-days and 1-days out is thus 1 – the
probability of failure. Calculate expected losses for each and now you have a way to which Hotel to call on Day 3.
| | 3-day | 2-day | 1-day |
| Hotel A | .9 | .9 | .4 |
| Hotel B | .9 | .9 | .9 |
In our example, the number for Hotel A and Hotel B come to 1 – (1/10)*(6/10) and 1 – (1/10)*(1/10) respectively. Based on that, we should call Hotel A 3-days out before we call Hotel B.
Code 44: How to Read Ahler and Sood
27 Jun
This is a follow-up to the hilarious Twitter thread about the sequence of 44s. Numbers in Perry’s 538 piece come from this paper.
First, yes 44s are indeed correct. (Better yet, look for yourself.) But what do the 44s refer to? 44 is the average of all the responses. When Perry writes “Republicans estimated the share at 46
percent,” (we have similar language in the paper, which is regrettable as it can be easily misunderstood), it doesn’t mean that every Republican thinks so. It may not even mean that the median
Republican thinks so. See OA 1.7 for medians, OA 1.8 for distributions, but see also OA 2.8.1, Table OA 2.18, OA 2.8.2, OA 2.11 and Table OA 2.23.
Key points =
1. Large majorities overestimate the share of party-stereotypical groups in the party, except for Evangelicals and Southerners.
2. Compared to what people think is the share of a group in the population, people still think the share of the group in the stereotyped party is greater. (But how much more varies a fair bit.)
3. People also generally underestimate the share of counter-stereotypical groups in the party.
Automating Understanding, Not Just ML
27 Jun
Some of the most complex parts of Machine Learning are largely automated. The modal ML person types in simple commands for very complex operations and voila! Some companies, like Microsoft (Azure)
and DataRobot, also provide a UI for this. And this has generally not turned out well. Why? Because this kind of system does too little for the modal ML person and expects too much from the rest. So
the modal ML person doesn’t use it. And the people who do use it, generally use it badly. The black box remains the black box. But not much is needed to place a lamp in this black box. Really, just
two things are needed:
1. A data summarization and visualization engine, preferably with some chatbot feature that guides people smartly through the key points, including the problems. For instance, start with univariate
summaries, highlighting ranges, missing data, sparsity, and such. Then, if it is a supervised problem, give people a bunch of loess plots or explain the ‘best fitting’ parametric approximations with
y in plain English, such as, “people who eat 1 more cookie live 5 minutes shorter on average.”
2. An explanation engine, including what the explanations of observational predictions mean. We already have reasonable implementations of this.
When you have both, you have automated complexity thoughtfully, in a way that empowers people, rather than create a system that enables people to do fancy things badly.
Talking On a Tangent
22 Jun
What is the trend over the last X months? One estimate of the ‘trend’ over the last k time periods is what I call the ‘hold up the ends’ method. Look at t_k and t_0, get the difference between the
two, and divide by the number of time periods. If t_k > t_0, you say that things are going up. If t_k < t_0, you say things are going down. And if they are the same, then you say that things are
flat. But this method can elide over important non-linearity. For instance, say unemployment went down in the first 9 months and then went up over the last 3 but ended with t_k < t_0. What is the
trend? If by trend, we mean average slope over the last t time periods, and if there is no measurement error, then 'hold up the ends' method is reasonable. If there is measurement error, we would
want to smooth the time series first before we hold up the ends. Often people care about 'consistency' in the trend. One estimate of consistency is the following: the proportion of times we get a
number of the same sign when we do pairwise comparison of any two time consecutive time periods. Often people also care more about later time periods than earlier time periods. And one could build on
that intuition by weighting later changes more.
Targeting 101
22 Jun
Targeting Economics
Say that there is a company that makes more than one product. And users of any one of its products don’t use all of its products. In effect, the company has a \textit{captive} audience. The company
can run an ad in any of its products about the one or more other products that a user doesn’t use. Should it consider targeting—showing different (number of) ads to different users? There are five
things to consider:
• Opportunity Cost: If the opportunity is limited, could the company make more profit by showing an ad about something else?
• The Cost of Showing an Ad to an Additional User: The cost of serving an ad; it is close to zero in the digital economy.
• The Cost of a Worse Product: As a result of seeing an irrelevant ad in the product, the user likes the product less. (The magnitude of the reduction depends on how disruptive the ad is and how
irrelevant it is.) The company suffers in the end as its long-term profits are lower.
• Poisoning the Well: Showing an irrelevant ad means that people are more likely to skip whatever ad you present next. It reduces the company’s ability to pitch other products successfully.
• Profits: On the flip side of the ledger are expected profits. What are the expected profits from showing an ad? If you show a user an ad for a relevant product, they may not just buy and use the
other product, but may also become less likely to switch from your stack. Further, they may even proselytize your product, netting you more users.
I formalize the problem here (pdf).
Estimating Bias and Error in Perceptions of Group Composition
14 Nov
People’s reports of perceptions of the share of various groups in the population are typically biased. The bias is generally greater for smaller groups. The bias also appears to vary by how people
feel about the group—they are likelier to think that the groups they don’t like are bigger—and by stereotypes about the groups (see here and here).
A new paper makes a remarkable claim: “explicit estimates are not direct reflections of perceptions, but systematic transformations of those perceptions. As a result, surveys and polls that ask
participants to estimate demographic proportions cannot be interpreted as direct measures of participants’ (mis)information since a large portion of apparent error on any particular question will
likely reflect rescaling toward a more moderate expected value…”
The claim is supported by a figure that takes the form of plotting a curve over averages. (It also reports results from other papers that base their inferences on similar figures.)
The evidence doesn’t seem right for the claim. Ideally, we want to plot curves within people and show that the curves are roughly the same. (I doubt it to be the case.)
Second, it is one thing to claim that the reports of perceptions follow a particular rescaling formula and another to claim that people are aware of what they are doing. I doubt that people are.
Third, if the claim that ‘a large portion of apparent error on any particular question will likely reflect rescaling toward a more moderate expected value’ is true, then presenting people with
correct information ought not to change how people think about groups, for e.g., perceived threat from immigrants. The calibrated error should be a much better moderator than the raw error. Again, I
doubt it.
But I could be proven wrong about each. And I am ok with that. The goal is to learn the right thing, not to be proven right.
Measuring Segregation
31 Aug
Dissimilarity index is a measure of segregation. It runs as follows:
$\frac{1}{2} \sum\limits_{i=1}^{n} \frac{g_{i1}}{G_1} - \frac{g_{i2}}{G_2}$
$g_{i1}$ is population of $g_1$ in the ith area
$G_{i1}$ is population of $g_1$ in the larger area
from which dissimilarity is being measured against
The measure suffers from a couple of issues:
1. Concerns about lumpiness. Even in a small area, are black people at one end, white people at another?
2. Choice of baseline. If the larger area (say a state) is 95\% white (Iowa is 91.3% White), dissimilarity is naturally likely to be small.
One way to address the concern about lumpiness is to provide an estimate of the spatial variance of the quantity of interest. But to measure variance, you need local measures of the quantity of
interest. One way to arrive at local measures is as follows:
1. Create a distance matrix across all addresses. Get latitude and longitude. And start with Euclidean distances, though smart measures that take account of physical features are a natural next
step. (For those worried about computing super huge matrices, the good news is that computation can be parallelized.)
2. For each address, find n closest addresses and estimate the quantity of interest. Where multiple houses are similar distance apart, sample randomly or include all. One advantage of n closest
rather than addresses in a particular area is that it naturally accounts for variations in density.
But once you have arrived at the local measure, why just report variance? Why not report means of compelling common-sense metrics, like the proportion of addresses (people) for whom the closest house
has people of another race?
As for baseline numbers (generally just a couple of numbers): they are there to help you interpret. They can be brought in later.
Sample This: Sampling Randomly from the Streets
23 Jun
Say you want to learn about the average number of potholes per unit paved street in a city. To estimate that quantity, the following sampling plan can be employed:
1. Get all the streets in a city from Google Maps or OSM
2. Starting from one end of the street, split each street into .5 km segments till you reach the end of the street. The last segment, or if the street is shorter than .5km, the only segment, can be
shorter than .5 km.
3. Get the lat/long of start/end of the segments.
4. Create a database of all the segments: segment_id, street_name, start_lat, start_long, end_lat, end_long
5. Sample from rows of the database
6. Produce a CSV of the sampled segments (subset of step 4)
7. Plot the lat/long on Google Map — filling all the area within the segment.
8. Collect data on the highlighted segments.
For Python package that implements this, see https://github.com/soodoku/geo_sampling.
Clustering and then Classifying: Improving Prediction for Crudely-labeled and Mislabeled Data
8 Jun
Mislabeled and crudely labeled data are common problems in data science. Supervised prediction of such data expectedly yields poor results—coefficients are biased, and accuracy with regards to the
true label is poor. One solution to the problem is to hand code labels of an `adequate’ sample and infer true labels based on a model trained on that data.
Another solution relies on the intuition (assumption) that the distance between rows (covariates) of a label will be lower than the distance between rows of different labels. One way to leverage that
intuition is to cluster the data within each label, infer true labels from erroneous labels, and then predict inferred true labels. For a class of problems, the method can be shown to always improve
accuracy. (You can also predict just the cluster labels.)
Here’s one potential solution for a scenario where we have a binary dependent variable:
Assume a mis_labeled vector called mis_label that codes some true 0s as 1 and some true 1s as 0s.
1. For each mis_label (1 and 0), use k-means with k = 2 to get 2 clusters within each label for a total of 4 labels
2. Assuming mislabeling rate < 50%, create a new col. = est_true_label, which takes: 1 when mis_label = 1 and cluster label is of the majority class (that is cluster label class is more than 50% of
the mis_label = 1), otherwise 0. 0 when mis_label = 0 and cluster label is of the majority class (that is cluster label class is more than 50% of the mis_label = 0), otherwise 1.
3. Predict est_true_label using logistic regression and produce accuracy estimates based on true_labels and bias estimates in coefficient estimates (compared to coefficients from logistic regression
coefficients from true labels)
The Missing Plot
27 May
Datasets often contain missing values. And often enough—at least in social science data—values are missing systematically. So how do we visualize missing values? After all, they are missing.
Some analysts simply list-wise delete points with missing values. Others impute, replacing missing values with mean or median. Yet others use sophisticated methods to impute missing values. None of
the methods, however, automatically acknowledge that any of the data are missing in the visualizations.
It is important to acknowledge missing data.
One can do it is by providing a tally of how much data are missing on each of the variables in a small table in the graph. Another, perhaps better, method is to plot the missing values as a function
of a covariate. For bivariate graphs, the solution is pretty simple. Create a dummy vector that tallies missing values. And plot the dummy vector in addition to the data. For instance, see:
(The script to produce the graph can be downloaded from the following GitHub Gist.)
In cases, where missing values are imputed, the dummy vector can also be used to ‘color’ the points that were imputed.
About 85% Problematic: The Trouble With Human-In-The-Loop ML Systems
26 Apr
MIT researchers recently unveiled a system that combines machine learning with input from users to ‘predict 85% of the attacks.’ Each day, the system winnows down millions of rows to a few hundred
atypical data points and passes these points on to ‘human experts’ who then label the few hundred data points. The system then uses the labels to refine the algorithm.
At the first blush, using data from users in such a way to refine the algorithm seems like the right thing to do, even the obvious thing to do. And there exist a variety of systems that do precisely
this. In the context of cyber data (and a broad category of similar such data), however, it may not be the right thing to do. There are two big reasons for that. A low false positive rate can be much
more easily achieved if we do not care about the false negative rate. And there are good reasons to worry a lot about false negative rates in cyber data. And second, and perhaps more importantly,
incorporating user input on complex tasks (or where data is insufficiently rich) reduces to the following: given a complex task with inadequate time, the users use cheap heuristics to label the data,
and supervised aspect of the algorithm reduces to learning cheap heuristics that humans use.
Interpeting Clusters and ‘Outliers’ from Clustering Algorithms
19 Feb
Assume that the data from the dominant data generating process are structured so that they occupy a few small portions of a high-dimensional space. Say we use a hard partition clustering algorithm to
learn the structure of the data. And say that it does—learn the structure. Anything that lies outside the few narrow pockets of high-dimensional space is an ‘outlier,’ improbable (even impossible)
given the dominant data generating process. (These ‘outliers’ may be generated by a small malicious data generating processes.) Even points on the fringes of the narrow pockets are suspicious. If so,
one reasonable measure of suspiciousness of a point is its distance from the centroid of the cluster to which it is assigned; the further the point from the centroid, the more suspicious it is.
(Distance can be some multivariate distance metric, or proportion of points assigned to the cluster that are further away from the cluster centroid than the point whose score we are tallying.)
How can we interpret an outlier (score)? Tautological explanations—it is improbable given the dominant data generating process—aside.
Simply providing distance to the centroid doesn’t give enough context. And for obvious reasons, for high-dimensional vectors, providing distance on each feature isn’t reasonable either. A better
approach involves some feature selection. This can be done in various ways, all of which take the same general form. Find distance to the centroid on features on which the points assigned to the
cluster have the least variation. Or, on features that discriminate the cluster from other clusters the best. Or, on features that predict distance from the cluster centroid the best. Limit the
features arbitrarily to a small set. On this limited feature set, calculate cluster means and standard deviations, and give standardized distance (for categorical variable, just provide ) to the
Sampling With Coprimes
1 Jan
Say you want to sample from a sequence of length n. Multiples of a number that is relatively prime to the length of the sequence (n) cover the entire sequence and have the property that the entire
sequence is covered before any number is repeated. This is a known result from number theory. We could use the result to (sequentially) (see below for what I mean) sample from a series.
For instance, if the sequence is 1, 2, 3,…, 9, the number 5 is one such number (5 and 9 are coprime). Using multiples of 5, we get:
X X
X X
X X
X X
If the length of the sequence is odd, then we all know that 2 will do. But not all even numbers will do. For instance, for the same length of 9, if you were to choose 6, it would result in 6, 3, 9,
and 6 again.
Some R code:
seq_length = 6
rel_prime = 5
multiples = rel_prime*(1:seq_length)
multiples = ifelse(multiples > seq_length, multiples %% seq_length, multiples)
multiples = ifelse(multiples ==0, seq_length, multiples)
Where can we use this? It makes passes over an address space less discoverable.
Beyond Anomaly Detection: Supervised Learning from `Bad’ Transactions
20 Sep
Nearly every time you connect to the Internet, multiple servers log a bunch of details about the request. For instance, details about the connecting IPs, the protocol being used, etc. (One popular
software for collecting such data is Cisco’s Netflow.) Lots of companies analyze this data in an attempt to flag `anomalous’ transactions. Given the data are low quality—IPs do not uniquely map to
people, information per transaction is vanishingly small—the chances of building a useful anomaly detection algorithm using conventional unsupervised methods are extremely low.
One way to solve the problem is to re-express it as a supervised problem. Google, various security firms, security researchers, etc. everyday flag a bunch of IPs for various nefarious activities,
including hosting malware (passive DNS), scanning, or actively . Check to see if these IPs are in the database, and learn from the transactions that include the blacklisted IPs. Using the model, flag
transactions that look most similar to the transactions with blacklisted IPs. And validate the worthiness of flagged transactions with the highest probability of being with a malicious IP by checking
to see if the IPs are blacklisted at a future date or by using a subject matter expert.
|
{"url":"http://gojiberries.io/category/statistics/page/4/","timestamp":"2024-11-06T16:45:57Z","content_type":"text/html","content_length":"112326","record_id":"<urn:uuid:47a9fbaf-5b41-4b8e-9ef1-fbe62c29aa15>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00725.warc.gz"}
|
Chapter 288: Modelling Of Investment Attractiveness And Economic Stability Of Region
A systematic study of the modeling investment attractiveness and economic stability of region has been carried out. A priori, current and a posteriori investment objective are picked out. A general
description of investment attractiveness of the Kabardino-Balkarian Republic, one of the subjects of the North Caucasus Federal District, is given. One of the conditions for attracting a potential
investor is a reliable assessment of the investment territory attractiveness. For these purposes, the authors, using the information-entropy approach, developed a model for assessing the investment
attractiveness and region economic stability, which was based on the passive investment strategy and the generalized Cobb-Douglas production function. In the process of developing the model, basic
investment parameters were considered of the Kabardino-Balkarian Republic. Twenty variables (the volume of attracted domestic and foreign investments, the number of the working-age population) are
used. The proposed integral model can be used both to assess the investment attractiveness of a region, as well as for taxonomy and ranking organizations, regions by level of investment activity. The
quantitative and qualitative levels of the classification of state investment attractiveness of an economic object are determined. The application fields of the research results are programs and
strategies for regional development, sectoral planning, forecasting the dynamics of gross regional product based on investment growth.
Keywords: InvestmentmodellingCobb-Douglas functionregion
Nowadays economic growth, an increase in investment activity and a buildup of innovative resources are observed in certain supporting regions only, whereas in the so-called depressed regions only the
subsequent, residual spread of investment and innovation activity continues. The polarization principle of the Russian economy development as the strategy basis of innovative modernization of the
regional economy is unacceptable. At the same time, both old and new institutions, investment activity tools do not ensure the realization of the innovation scenario of various types of Russian
regions, especially problematic ones. The study of the scientific research results shows that the state largely declares the country’s movement along the formation path of an innovation economy. In
fact, it is forced to carry out this movement in conditions when the regions differ not only in the volume of the gross product or in separate generalized macroeconomic indicators, but also in
different steps of the economic development “quality”, which is now objectively observed.
The investment management system at the regional level duplicates the investment project management system of a single business unit. It aims to achieve several goals: a priori, current and
posteriori. A priori goals are related to investment planning. They mean a justification of investment strategies and policies, an assessment of acceptable risk levels and a profitability of
investment instruments, a determination of optimal sources of financing investment activities. Current goals are directly related to the implementation of investments. They mean a determination of
the optimal structure of investment portfolio, an organization of regular monitoring of external and internal factors of the investment environment, an adoption of corrective investment decisions. A
posteriori goals are associated with the results of investment activities. In other words, they mean development of accounting indicators system, control and effectiveness evaluation of investment
activities. An achievement of a priori, current and a posteriori goals is possible using various techniques and approaches that can be classified according to the investment object as active and
Active methods are used to manage investment assets, which are highly profitable, high-risk and at the same time short-term financial instruments. These methods are based on the systematic monitoring
of the financial market, the search for irrelevant priced securities, forecasting (modeling), expert evaluation of changes in their value and profitability in the future. Passive methods are used to
manage investment assets that have the following characteristics: a low level of profitability, riskiness, and usually a long circulation period. An investor using passive methods is guided when
making management decisions on the market index profitability indicators, and the structure of the formed investment portfolio is permanent and changes only to adaptively approach the chosen yield
trajectory (Rossokhin, 2012).
An attraction, a placement, a diversification of investments and a management of the region’s investment portfolio are a multidimensional process that requires relevant methods, narrowing the
“underinvestment - reinvestment” strip. It is important to have appropriate resources to predict and adapt to changes in investment conditions. Here, passive investing has an advantage in order to
effectively manage risks, diversify, minimize deviations from the target yield curve and maximize the evolutionary potential of the investment portfolio.
Problem Statement
A. Al’bekov, V. An’shin, YU. Bogatin, A. Bystryakova, G. Kleyner, E. Velichko, V. Zolotogorov, N. Igoshina, E. Bukhval’d, A. Amosova, V. Denisova, B. Koltynyuk, V. Kosov, L. Kruvshits, I. Lipsits, A.
Margolin, YA. Melkumova, S. Prilipko, R. Samuseva, A. Smolyak, V. Savchuk studied the conceptual and methodological issues of managing regions in the conditions of differentiation and asymmetry of
the development of their economies, investment design and evaluation of the effectiveness of regional investments.
Various aspects of assessing the investment attractiveness of economic entities are reflected in the studies of L. Beklaryan, V. Vlasovoy, M. Egorovoy, A. Ivanova, E. Krylova, A. Nedosekina, I.
Sakharova, V. Sobolevoy, E. Khrustaleva. Among other researchers it should be noted the works of G. Aleksander, G. Arnol’d, V. Berens, R. Breyli, G.V. Beyli, E. Granta, D. Dina, Ch. Kanta, Kh. Levi,
S. Mayyersa, R. Payka, S. Rossa, P. Khavraneka (Endovitskiy, 2017).
It can be stated that in recent years works on the development of management tools have appeared in Russian science, the use of which gives a synergistic effect, for example: engineering, business
process reengineering; derivatives and others. At the same time, issues relating to the information support of the management mechanism of the territory’s investment strategy have not been fully
Сurrently there is no single, universal method of analyzing the investment attractiveness of the territory. Most of the techniques are based on mathematical, expert or scoring estimates. At the same
time, the set of indicators characterizing the region investment attractiveness does not coincide in various methods. In foreign practice, a wide range of indicators is used to form the ratings of
the most investment-attractive countries (regions), in particular: factors of instability (volatility of real GDP growth, inflation), financial development of countries, government efficiency,
business environment, access to potential sales markets, human potential, tax regime, transport infrastructure, the presence of transnational corporations, innovative, scientific and educational
For example, according to the assessment of the Expert RA rating agency, the Kabardino-Balkarian Republic in 2017 was attributed to the regions of the penultimate 3C2 group, which are characterized
by “insignificant potential - high risk”. The investment climate in the region cannot be called favorable. There is a tendency to increase investment risks (especially criminal and social) while
reducing financial, production and institutional capacities.
Analyzing the investment potential, it should be noted that it increased by 3 positions - from 65 to 68 and amounted to 0.489 points in the all-Russian potential, which is less by 0.026 points in
2016. Among the components of the investment potential, infrastructure, natural resource and labor potentials have a positive effect; and the production, financial and institutional potentials have a
negative effect. The rank of the investment potential of the Kabardino-Balkarian Republic has remained steadily low over the past five years.
The investment risk increased from 77 to 79 and amounted to 0.402 points in the all-Russian risk, which is less by 0.013 points in 2016. Among the components of investment risk, a low level of
environmental risk had a positive effect, while criminal, social and financial risks were consistently high.
In these conditions, it is required to develop a model for assessing the investment attractiveness and economic stability of the region and, further, based on the obtained estimates, the formation of
a set of measures to improve the investment climate, which will attract the interest of Russian and foreign investors.
Research Questions
The subject of study is the problem of developing a model that allows assessing the investment attractiveness and economic stability of a region based on a passive investment strategy. In the process
of developing a model, there is the task of considering key factors of sustainable development for all territories (general economic, institutional, political risks, the state of the financial and
credit and tax system, demographic potential, purchasing power of the population, etc.) and specific factors (tourist flows, leading sectors of the regional economy, transport and social
infrastructure, budget subsidies, etc.).
To solve this problem, it is necessary to form a system of the most informative, quantitatively measured indicators, with the help of which it is possible to describe the investment potential of the
problem regional economy. Examples of indicators describing financial and economic criteria are expenses in R & D, investments in fixed assets, the cost of financial leasing contracts, etc. Social
investments characterize such indicators as the number of computers per 1000 inhabitants, the number of students, the number of Internet users, etc. Demographic parameters of investment activity can
be estimated using indicators of fertility and mortality, life expectancy, survival age, migration flow, etc. It should be considered that there are investment factors that are difficult to quantify.
In this case expert assessment methods, surveys, linguistic and fuzzy systems for their actualization should be applied (Jennings, Greenwood, Lounsbury, & Suddaby, 2013).
Purpose of the Study
In an information intensive society, the innovation and investment potential of economic development is largely determined by ideas, knowledge, technologies, competencies, information resources that
ensure the achievement of investors’ goals quickly and reliably, with minimal risks. In these conditions, the categories of “potential”, “risk”, “knowledge”, “innovation”, “investment”, and “goals”
are systemic, emergent in nature (Rakhimov, 2008). They are difficult to formalize and to estimate, and if they are to be estimated, then often with a “superposition of noise”.
The solution to this problem can be the development of infological, mathematical models with the identification of integral indicators (indicators of investment attractiveness) and their subsequent
use in the forecast of passive investment indices. Such parameters implicitly reflect both risks and investment potential (Smirnova & Zhukov, 2010), but, most importantly, help to implement the
taxonomy of investment objects according to their investment potential. Investment potential determines needs and opportunities of potential investors. The ratio of investment potential and
investment capacity determines the “coverability” of investment needs. For example, if an object has insufficient investment attractiveness, then it will most likely not attract enough investment
volume for its potential or it will lose on commission, attracting high-cost funds.
Any investment process considers the time lag. The specific value of this lag is identified expertly, analytically, or heuristically, considering the intensity of external factors. There is a need
for a systematic analysis of the region activities with changes in the environment, taxonomy, classification of environmental factors, identification of the relevant system of indicators, and their
The task is difficult, mainly due to the lack of representative official statistics. There is no set monitoring system for the investment environment, as well as relevant analysis tools, for example,
cognitive, allowing to determine the type of investment situation (stable, poorly stable, unstable, crisis, etc.).
Research Methods
To model a system, systems analysis methods are used, for example, decomposing it into subsystems, identifying a control subsystem that provides not only solutions, but also structural activity, the
growing role of passive control mechanisms. Simulation procedures should consider the integral links of the system structures and its subsystems. In the study of the system, it is analyzed using the
methods of evolutionary economics, mathematical methods (least squares, taxonomy, optimization, etc.), and investment analysis.
Consider the i- subsystem of the system S , the vector $x ( i ) = x 1 ( i ) , x 2 ( i ) , … , x n i ( i )$of basic factors (relevantly describing, affecting the functioning of the subsystem) and the
functional $f ( i ) = f x ( i )$ of subsystem activity (passivity). For system S , we similarly introduce the vector of its state $x$, the system activity $f x$ and the potential $P$.
If we consider the control subsystem, then, as in technical systems, it makes sense to speak not about the activity of the system, but about its “fatigue”, emphasizing that this is only a figurative
comparison, since the investment processes are more complex. It is important to identify the activity functional, its parameters (for example, the integral parameter of self-regulation).
In the one-dimensional case $( n = 1 , x = x ( t ) , 0 < t < T , 0 < x < X )$ it is demonstrated how to determine the evolutionary potential of investment activity in the context of a problematic
regional economy.
If we assume the renewability of the investment flow in the environment with the pace according to the law $v = v ( τ )$, and the coefficient of investment attractiveness (activity) equal $p = p ( τ
)$, then the evolutionary potential can be determined (Kaziev, Kazieva, & Kaziev, 2016) in the form:
$P = ∫ 0 T v ( τ ) e x p ∫ 0 τ ρ ( ω ) d ω d τ$. (1)
In this case, the higher the rate of renewal, the higher the evolutionary potential, and vice versa. If the evolutionary potential is less than one, then regardless of the investment at the initial
moment, the value of the investment will decrease.
It is important to identify quantitatively the factors of increasing investment attractiveness, their permissible boundary and optimal values. Especially in a “problem” region, where setting
priorities, developing and implementing anti-crisis programs strongly influences the evolutionary investment potential. Investors do not want to go to problem regions (Anokhin & Schulze, 2008).
The following system of basic parameters is proposed for situational modeling of the evolutionary investment potential of the regional economy. We classify them as follows:
natural (volume, ratio and efficiency of investments in land, water, raw materials, recreational and other resources of the region);
financial and economic (dynamics and efficiency of investments in the industrial and non-industrial sectors of the economy, investments in the region’s infrastructure provision, etc.);
demographic (dynamics, structure and efficiency of investments aimed at improving the demographic situation - an increase in birth rates and a decrease in mortality rates, an increase in the duration
and quality of life, optimization of pension load indicators, etc.);
production (volume and efficiency of investments in the main and working capital, in the upgrading of skills and productivity of industrial personnel, in the automation and rationalization of
production processes, etc.);
social (size and dynamics of investments associated with the intellectualization of labor, approaching individual and social welfare installations, information and public openness, reducing
unemployment, poverty and uncontrolled migration, efficiency of social services, improving the crime situation in the region, etc.);
educational (volume, structure and effectiveness of investments related to the modernization of the educational system, expanding the range of educational services and improving their quality,
developing and introducing modern systems and methods of teaching, etc.);
scientific and technical (volume, structure and efficiency of investments related to the implementation of the achievements of scientific and technological progress in the region, support of
innovation-active organizations, commercialization of scientific, technical and innovative developments, etc.);
environmental (volume, dynamics and structure of investments in projects aimed at reducing environmental threats, risks of pollution, increasing the efficiency of environmental measures, etc.
(Galindo & Méndez, 2014).
After the formation of a system of indicators, the evolutionary modeling of the investment potential is carried out, its integral assessment is given, and the elasticity of investment activity
indicators is determined. For example, in the way, as it was done in the works (Kaziyev, Kaziyeva, & Kaziyev, 2016).
A model for assessing the investment attractiveness and sustainability of the regional economy is proposed. It is based on a generalized Cobb-Douglas production function (Hutchinson & MacArthur, 1959
$F = F 0 ∏ i = 1 n x i ( t ) - x i m a x x i o p t - x i m i n β i ( t ) x i m a x - x i ( t ) x i m a x - x i o p t β i ( t ) x i m a x - x i o p t x i o p t - x i m i n$
, (2)
where $F 0$ – initial level of investment attractiveness, $n$ – number of model main factors, $x i ( t )$$x i m a x , x i m i n , x i o p t$– i -factor and its maximum, minimum and optimal values for
investment stability, t – time (calculating period), $β i ( t )$ – importance of i -factor, a parameter that determines its contribution to ensuring investment attractiveness and economic stability.
The parameter identified by statistical and expert data $β i ( t )$ reflects the self-regulation capabilities by the i -factor.
The model can emphasize the type of region by basic investment parameters. For example, for the economy of Kabardino-Balkaria, we offer the following system of variables $x i ( i = 1,2 , … , 20 )$:
volume of attracted domestic investments (million rubles);
volume of foreign investments (million rubles);
number of able-bodied population (thousand people);
average annual growth rate of GRP (%);
retail sales per capita (million rubles);
rate of fixed assets renewal (%);
volume of commissioned construction objects (thousand buildings);
growth rate of population real incomes (%);
energy intensity of GRP (kg of coal equivalent / 10 thousand rubles);
crime rate (crimes / thousand people);
growth rate of number of high-performance jobs (%);
population with income below the subsistence level (thousand people);
migration of able-bodied population (thousand people);
education expenses (million rubles);
health care expenditures (million rubles);
volume of information services provided to the society (million rubles);
gross value added of the tourist industry (million rubles);
expenses for environmental protection, ecology (million rubles);
regional budget subsidies (%);
volume of innovative goods, works, services (million rubles).
In the model for each factor the coefficient (pace) $β i ( t )$ is usually unknown and should be identified either by the totality of the selected factors or by their clusters (by considering
sub-models, for example, a general economic or tourist cluster). In the short-term forecasting of investment potential, all the parameters $β i ( t )$can be considered constant. Then, using the least
squares functional
$Φ β 1 , β 2 , β m = ∑ i = 1 m l n F t i - f i 2 ⇒ m i n$ (3)
where $m$ – number of considered factors, (above $m = 21$), $f i$ –data, as well as a sufficient criterion for the optimum of this quadratic form, the values of the parameters $β i$can be identified
by the following system of equations:
$∂ Φ ∂ β i = 0 , i = 1,2 , … , m$
After identifying the model, it is suitable for preparing a short-term (if the conditions are stable - and for the medium-term) forecast of the region investment potential, based on a solution (for
example, using the square root method modified by the Gauss method) of the normal system of least squares equations:
$F ( t ) = F 0 e x p ∑ i = 1 m β i l n A i ( t )$ (5)
Where $A i ( t )$ – input form (Shirshova & Dement’yeva, 2015).
The proposed integral model can be used to assess the region investment, taxonomy and ranking of regions according to the level of investment activity. In addition, it considers that a consistent
increase in the amount of investment is not sufficiently inefficient, and the factors (sub-models) are limited in scope. Efficiency is determined by the interaction and interconnectedness of factors;
the model should consider the synergistic effect of such interaction and the self-regulation of investment processes.
The distribution of points is set expertly, for example, by the Delphi method (brainstorming, commission, court). It is not informative enough, and it does not fully classify the group. Therefore, e
the concept of amplitude and importance is introduced (Hallward-Driemeier & Smith, 2005).
Amplitude is a measure of the investment readiness of a system for a given factor. Importance is a measure of each factor significance in a model. It is required to separate the actual data
(amplitudes) from the subjective assessments (importance) in order to obtain the most objective assessment (relatively independent of experts). The dimension problem (more precisely, measurements) is
resolved by normalization and scaling.
Simplified classes can be considered: absolute unattractiveness (crisis), relative attractiveness (for individual main factors), attractiveness (for all key factors), full attractiveness (for all
factors). In the work, a system of “positive - negative indicators” and weights of investment attractiveness was applied for the Krasnoyarsk Territory, for example, for GRP per capita - weight 0.4,
for paid services per capita - 0.6, for the share of economically active population - 0.3, for the share of pensioners - 0.05, for average per capita incomes - 0.4.
For the proposed model, the quantitative and qualitative levels of classification is determined. Rating marks are given in brackets using a nine-point system (Jones, Coviello, & Tang, 2011):
complete (unconditional, absolute) unattractiveness (0);
strongly pronounced unattractiveness for all factors (1);
pronounced unattractiveness for all key factors (2);
unattractiveness for some key factors (3);
poorly expressed unattractiveness for non-key factors (4);
poorly pronounced attractiveness for non-key factors (5);
attractiveness for some key factors (6);
pronounced attractiveness for all key factors (7);
strongly pronounced attractiveness for all factors (8);
full attractiveness (9).
Thus, the investment potential is determined by a small number of factors for which grouping can be performed according to the criteria of investment activity (passivity) and attractiveness,
investment risks, investment efficiency (ratio of activity to potential) and use (ratio of activity to attractiveness).
The only possibility of integral accounting of all these diverse criteria is through self-regulation measures $β i t , i = 1,2 , … , m$ and investment potential modeling.
It should be borne in mind that the risks that always reduce the dynamism of capital are considered when passively investing. Characterized by maximum risks with low commission, profitability, low
dynamics, infrequent changes in the formed investment portfolio and frequent tracking of the dynamics of market indices.
The integral weighted average risk of investment can be defined as:
$R = ∑ i = 1 n ∑ j = 1 m z j R i j n m$ (6)
where $z j$ – importance j -investment process (stage) in a risk situation, $R i j$ – risk of the j -event of the i -class (taxon) (Modigliani, Miller, 1958).
In the dynamic case, it is possible to conduct a factor analysis of the dynamics, determining the multiplicative relation (analogous to the Cobb-Douglas type utility function), with the
differentiation of investments by time series $y i ( t ) , t = 1,2 , … , T$ (for example, by year):
$y i ( t ) = δ i y i m a x I i q ( t ) I i p ( t )$
where $y i ( t )$ – investment volume, $I i q t , I i p ( t )$– volume and investment indices, $δ i$– importance parameter (scaling).
It is important to use diversification in the interests of effective risk management, reducing their likelihood, mathematical and statistical predictability of strategy results, adaptability based on
the results of predictive estimates of deviations from the target trajectory (yield curve).
A correlation and regression analysis of the impact of the of passive investments share and an identification of a parametric dependence, for example, a quadratic one can be conducted:
$f = a 2 m 2 + a 1 m + a 0$ (8)
Where $f$ – increase in passive investments, $m$ – their share in the portfolio, $a 0 , a 1 , a 2$ – identifiable parameters
The category of “diversity” determines the development of portfolio investment and the resulting investment risks (credit, market, currency, operational, liquidity losses, legal, inflation, etc.).
The selection of a relevant instrument is based the principle “from simple instruments to complex ones”, for example, “deposit - government bonds - UIF - ETF” (Murphy, 2012).
It is important to have relevant measures (criteria) of diversity. In this case, we will adhere to the information-entropy approach, because information is the very reflection of diversity, and the
amount of information is a measure of the diversity of the situation outcome. In the information-entropy approach, diversity is an attribute of information transfer, and the information obtained is
considered a measure of removing uncertainty in the system when choosing a controlling influence (for example, when diversifying an investment portfolio). As a result of the decision, there should be
only one choice. Each stage of the analysis of investment attractiveness should introduce certainty and reduce information noise.
The developed model makes it possible to adequately assess the change in the complex of factors influencing the investment attractiveness and region economic stability. The performed system analysis,
the proposed model and the algorithm for its identification can be used in situational modeling of investment management, their diversification, forecasting the profitability of the investment
portfolio, both at the level of a single region, and for taxonomy and ranking of organizations and regions by level of investment activity. The quantitative and qualitative levels of the state
investment attractiveness of an economic object are determined.
The conclusions and generalizations can serve as source material for further scientific research on an investment strategy at the national and regional levels, sectoral planning, and forecasting the
dynamics of the gross regional product based on investment growth.
However, it is necessary to consider the complexity. Situational investment analysis in the regions is complicated by the lack of an effective investment policy, effective legal measures that promote
the growth of responsibility not only for tax, but investment offenses that increase the investment activity of economic entities. There is no systematic approach to making investment decisions by
regional authorities, assessing inflation expectations and mismatch risks, etc.
The competitiveness of a region is determined not only by the level of its technological development, but also by its penetration into the business processes of innovative mechanisms. For an
innovative project and product to be profitable, an IT-supported regional policy and infrastructure are needed, which provide complete information about the prospects for the implementation of
innovations. Such information in the Russian Federation is presented as statistical indicators of innovative activities of industrial organizations in the context of regions, industries, types of
ownership, etc. One of the approaches to solving this problem is to use controlling as the basis of information technology management in the region.
For example, if the functional F(s,u), where s(t) is a region’s investment activity, u(t) is admissible controls, $u o p t$ is the optimal one of admissible, then the success of the region’s
investment development is estimated by the formula
$H = F m a x - F m i n / F m a x - F m i n$, (9)
$F m a x = m a x F u o p t , s m a x$, (10)
$F m i n = m i n F u o p t , s m i n$, (11)
$t ∈ [ 0 ; T ] , s ∈ s m i n ; s m a x$. (12)
To develop a relevant procedure, a methodology for developing investment-oriented conclusions on the sustainability of a region’s state, evaluating ratings, it is necessary to use unconventional, but
already popular methods, tools: odd sets (logic), catastrophe, situational modeling, neural networks, etc. The authors attempted to build such a technique.
The article is published in the framework of research under the grant of the Russian Foundation for Basic Research, project No. 17-02-00467-OGN.
1. Anokhin, S., Schulze, W. (2008). Entrepreneurship, innovation, and corruption. Journal of Business Venturing, 5(24), 465-476.
2. Endovitskiy, D.A. (2017). Analysis of the enterprise investment attractiveness. Moscow: KNORUS.
3. Galindo, M., Mйndez, M. (2014). Entrepreneurship, economic growth, and innovation: Are feedback effects at work? Journal of Business Research, 5(67), pp. 825-829.
4. Hallward-Driemeier, M., Smith, W. (2005). Understanding the Investment Climate. Finance and Development, 42. 1, 40–43.
5. Hutchinson, G.E., MacArthur, Rh. A. (1959). Theoretical Ecological Model of Size Distribution among Species of Animal. American Nature, 93, 117-125.
6. Jennings, P., Greenwood, R., Lounsbury, M., Suddaby, R. (2013). Institutions, entrepreneurs, and communities: A special issue on entrepreneurship. Journal of Business Venturing, 1(28), 1-9.
7. Jones, M., Coviello, N., Tang, Y. (2011). International Entrepreneurship research (1989–2009): A domain ontology and thematic analysis. Journal of Business Venturing, 6(26), 632-659.
8. Kaziyev, V.M., Kaziyeva, B.V., Kaziyev, K.V. (2016). Evolutionary modelling and sustainable development’s basic factors of the region. Informatsionnyye tekhnologii v nauke, obrazovanii i biznese
- Information technology in science, education and business. рр. 255-260.
9. Modigliani, F., Miller, M. (1958). The cost of capital, corporation finance and the theory of investment. American Economic Review, 48(3), 261-297.
10. Murphy, J. (2012). Intermarket analysis: Interaction principles of financial markets. Moscow: Al’pina Pablisher.
11. Rakhimov, T.R. (2008). Classification of methods for assessing the investment climate and its use for regional development. Retrieved from: http://region.mcnip.ru
12. Rossokhin, V.V. (2012). Risk assessment of active and passive investment strategies. Finansy i kredit - Finance and credit, 2, pp. 19-27.
13. Smirnova, E.V, Zhukov, M.Yu. (2010). Method of assessing a region investment attractiveness. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. M.F. Reshetneva - Bulletin of
the Siberian State Aerospace University named after M. F. Reshetnev, 2(28), 146-150.
14. Shirshova, L.A., Dement’yeva, M.V. (2015). Analysis of strategies for managing a portfolio of financial assets. Retrieved from: http://naukovedenie.ru/PDF/29EVN515.pdf
About this article
Publication Date
29 March 2019
Article Doi
eBook ISBN
Edition Number
1st Edition
Sociolinguistics, linguistics, semantics, discourse analysis, science, technology, society
Cite this article as:
Kaziyev, V. M., Kaziyeva, B. V., & Gedgafova, I. Y. (2019). Modelling Of Investment Attractiveness And Economic Stability Of Region. In D. K. Bataev (Ed.), Social and Cultural Transformations in the
Context of Modern Globalism, vol 58. European Proceedings of Social and Behavioural Sciences (pp. 2499-2509). Future Academy. https://doi.org/10.15405/epsbs.2019.03.02.288
|
{"url":"https://www.europeanproceedings.com/article/10.15405/epsbs.2019.03.02.288","timestamp":"2024-11-09T21:06:10Z","content_type":"text/html","content_length":"99835","record_id":"<urn:uuid:836eb422-2a8c-49dc-a594-fefd924ea5fd>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00343.warc.gz"}
|
CSU Math 126 Videos - Private Tutoring for Colorado State University
CSU Math 126 Videos
Get the same quality tutoring in video format.
You can purchase access to the videos by scrolling through the list of videos below and finding the video for your specific math problem, then just click on the image and you will be provided three
options to purchase in order to gain access to the video. Or you can click on one of the links below.
Try for Free!
Check Out My Skills Review Exam Videos for Free to See if You Like My Style!
If you are looking for some better videos to help you get through CSU's Math 126 course, then take a look through my videos below.
I know that you might have a bad taste in your mouth based upon your experience with the PACe videos, but I assure you that you will find these videos far more helpful.
I have used my experience tutoring Math 126 students to put together the easiest to understand, simplest solutions for all the Math 126 questions you will face.
Skills Review Exam
Need help passing the Math 125 Skills Review Exam? Check out my videos!
Math 126 Unit 1 Collection
Check out my complete collection of Math 126 Unit 1 video solutions. The collection includes every problem I have ever seen in my 20+ years of tutoring PACe courses at CSU.
Math 126 Unit 2 Collection
Check out my complete collection of Math 126 Unit 2 video solutions. The collection includes every problem I have ever seen in my 20+ years of tutoring PACe courses at CSU.
Math 126 Unit 3 Collection
Check out my complete collection of Math 126 Unit 3 video solutions. The collection includes every problem I have ever seen in my 20+ years of tutoring PACe courses at CSU.
Math 126 Unit 4 Collection
Check out my complete collection of Math 126 Unit 4 video solutions. The collection includes every problem I have ever seen in my 20+ years of tutoring PACe courses at CSU.
If you do not find what you are looking for please Contact Me and let me know what you need. I have made many videos for high school, middle school, and colleges other than Colorado State University.
|
{"url":"https://csumathtutor.com/csu-math-tutor/tutoring-videos/csu-pace-course-videos/csu-math-126-videos/","timestamp":"2024-11-09T19:51:38Z","content_type":"text/html","content_length":"102118","record_id":"<urn:uuid:67498024-7675-47cf-a90d-e59a97bd6c3b>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00104.warc.gz"}
|
Efficient Math problem solving
Submitted by Atanu Chaudhuri on Tue, 09/05/2017 - 16:01
The chosen problem this time is not so difficult, and on most occasions it will be solved conventionally. But driven by the general objective of equalizing the denominators, if the lightly hidden key
pattern is discovered, everything becomes easy and straightforward with solution only a few light steps away...
|
{"url":"https://mail.suresolv.com/efficient-math-problem-solving?page=2","timestamp":"2024-11-06T05:48:43Z","content_type":"text/html","content_length":"53042","record_id":"<urn:uuid:de0917b1-866f-4f27-9793-0a94119b2406>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00504.warc.gz"}
|
Sum of Interior & Exterior Angles (Video) Polygons, Pentagon & More
Sum of Interior & Exterior Angles
Fact-checked by
Paul Mazzola
Finding the sum of interior & exterior angles
Polygons are like the little houses of two-dimensional geometry world. They create insides, called the interior, and outsides, called the exterior. You can measure interior angles and exterior
angles. You can also add up the sums of all interior angles, and the sums of all exterior angles, of regular polygons.
Our formula works on triangles, squares, pentagons, hexagons, quadrilaterals, octagons and more.
What is a regular polygon?
For a polygon to be a regular polygon, it must fulfill these four requirements:
• Be two-dimensional
• Enclose a space, creating an interior and exterior
• Use only line segments for sides
• Have all sides equal in length to one another, and all interior angles equal in measure to one another
Interior Angles of a Polygon
Get free estimates from geometry tutors near you.
Sum of interior angles of a polygon
Regular polygons exist without limit (theoretically), but as you get more and more sides, the polygon looks more and more like a circle. The regular polygon with the fewest sides – three – is the
equilateral triangle.
The regular polygon with the most sides commonly used in geometry classes is probably the dodecagon, or 12-gon, with 12 sides and 12 interior angles:
Sum of Interior Angles of a Polygon
Pretty fancy, isn't it? But just because it has all those sides and interior angles, do not think you cannot figure out a lot about our dodecagon. Suppose, for instance, you want to know what all
those interior angles add up to, in degrees?
Sum of interior angles
Triangles are easy. Their interior angles add to 180°. Likewise, a square (a regular quadrilateral) adds to 360° because a square can be divided into two triangles.
The word "polygon" means "many angles," though most people seem to notice the sides more than they notice the angles, so they created words like "quadrilateral," which means "four sides."
Regular polygons have as many interior angles as they have sides, so the triangle has three sides and three interior angles. Square? Four of each. Pentagon? Five, and so on.
Our dodecagon has 12 sides and 12 interior angles.
Sum of interior angles formula
The formula for the sum of that polygon's interior angles is refreshingly simple. Let n equal the number of sides of whatever regular polygon you are studying. Here is the formula:
Sum of Interior Angles Formula
Sum of interior angles $=(n-2)\times 180°$
Sum of angles in a triangle
You can do this. Try it first with our equilateral triangle:
Sum of Angles in a Triangle
Sum of interior angles = 180°
Sum of angles of a square
And again, try it for the square:
Sum of Angles in a Square
Sum of interior angles = 360°
How to find one interior angle
To find the measure of a single interior angle, then, you simply take that total for all the angles and divide it by n, the number of sides or angles in the regular polygon.
The new formula looks very much like the old formula:
Formula to find the measure of one interior angle
$=\frac{(n-2)\times 180°}{n}$
Again, test it for the equilateral triangle:
$\frac{(3-2)\times 180°}{3}$
And for the square:
$\frac{(4-2)\times 180°}{4}$
Hey! It works! And it works every time. Let's tackle that dodecagon now.
Interior angles examples
Remember what the 12-sided dodecagon looks like? Let's find the sum of the interior angles, as well as one interior angle:
Interior angles examples
Find the sum of interior angles of a dodecagon
Sum of interior angles = 1,800°
Now, let's find one interior angle
$\frac{(n-2)\times 180°}{n}$
$\frac{(12-2)\times 180°}{12}$
$\frac{10\times 180°}{12}$
One interior angle = 150°
Sum of exterior angles
Every regular polygon has exterior angles. These are not the reflex angle (greater than 180°) created by rotating from the exterior of one side to the next. That is a common misunderstanding.
For instance, in an equilateral triangle, the exterior angle is not 360° - 60° = 300°, as if we were rotating from one side all the way around the vertex to the other side.
Sum of exterior angles
Exterior angles are created by extending one side of the regular polygon past the shape, and then measuring in degrees from that extended line back to the next side of the polygon.
Since you are extending a side of the polygon, that exterior angle must necessarily be supplementary to the polygon's interior angle. Together, the adjacent interior and exterior angles will add to
For our equilateral triangle, the exterior angle of any vertex is 120°. For a square, the exterior angle is 90°.
Exterior angle formula
If you prefer a formula, subtract the interior angle from 180°:
Exterior angle = 180° − interior angle
Exterior angles examples
What do we have left in our collection of regular polygons? That dodecagon! We know any interior angle is 150°, so the exterior angle is:
Sum of exterior angles formula and examples
Checking your work
Look carefully at the three exterior angles we used in our examples:
Prepare to be amazed. Multiply each of those measurements times the number of sides of the regular polygon:
• Triangle = 120°×3=360°
• Square = 90°×4=360°
• Dodecagon = 30°×12 =360°
Every time you add up (or multiply, which is fast addition) the sums of exterior angles of any regular polygon, you always get 360°.
It looks like magic, but the geometric reason for this is actually simple: to move around these shapes, you are making one complete rotation, or turn, of 360°.
Get free estimates from geometry tutors near you.
Still, this is an easy idea to remember: no matter how fussy and multi-sided the regular polygon gets, the sum of its exterior angles is always 360°.
Lesson summary
After working through all that, now you are able to define a regular polygon, measure one interior angle of any polygon, and identify and apply the formula used to find the sum of interior angles of
a regular polygon.
You also can explain to someone else how to find the measure of the exterior angles of a regular polygon, and you know the sum of exterior angles of every regular polygon.
What you learned:
After working your way through this lesson and the video, you learned to:
• Define a regular polygon
• Identify and apply the formula used to find the sum of interior angles of a regular polygon
• Measure one interior angle of a polygon using that same formula
• Explain how you find the measure of any exterior angle of a regular polygon
• Know the sum of the exterior angles of every regular polygon
|
{"url":"https://tutors.com/lesson/sum-of-exterior-interior-angles","timestamp":"2024-11-08T23:46:46Z","content_type":"text/html","content_length":"291578","record_id":"<urn:uuid:b3b75a62-4992-4639-8436-365893b0f2d7>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00646.warc.gz"}
|
TWO TYPES OF FUNCTION GRAPHS IN EXCEL - icplpa
We will assume that the functions whose graphs we need to build are always located in columns. Moreover, in column a, let there be the values of the variable x, and in columns B, C … the values of
the functions f1.f2,… respectively.
Excel has a special chart type called “graph”. With it, you can plot the dependence of data in a column (for example, In) on the line number. Regardless of which category axis labels we set. (Even if
the values from column A are signed on the X-axis, the graph will not express the dependence f1(x) in the general case). It is built like a very ordinary diagram. You can plot multiple function
graphs on a single diagram. If column A contains an arithmetic progression, then we can assume that the graph of the constructed function expresses the dependence f1(x). This method of plotting a
function is convenient if the function is given a tabulated function. In step 2, you need to specify the corresponding cells of column B as a range, and on the “Row” tab, in the “X-axis Signatures”
line, specify the corresponding cells of column A.
The second method of constructing a dependency graph “is more universal.
It is necessary to build a diagram of the “Dot” type. (If you choose the third type, it will be completely similar to the graph). In the second step, we specify column B as the range. And on the row
tab, we specify column A as the “X Value”. If we want to build several graphs (for example, graphs of functions f1 and f2) on one diagram, we need to click the “Add” button, and for the added series,
specify column C in the column “Y Values”, column A in the column “X Values”. Similarly, using a “Dot” type diagram, you can draw a graph of some non-trivial dependence. For example, f1(f2).
|
{"url":"https://icplpa.org/website-hosting/two-types-of-function-graphs-in-excel/","timestamp":"2024-11-07T22:24:43Z","content_type":"text/html","content_length":"64242","record_id":"<urn:uuid:14d4c71f-d51f-4793-8a14-0940de452357>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00209.warc.gz"}
|
Mathematics Notes for 9th Class Exercise 4 Rev - eStudent.pk
Mathematics Notes for 9th Class Exercise 4 Rev
0 Comments
Mathematics Notes for 9th Class Exercise 4 Rev
“Math” a compulsory subject for 9th class Science students. and Mathematics Notes for 9th Class Exercise 4 Rev or Math Notes Class 9 English Medium (Science Group) included in this book. Lets take a
visit on English Medium also Urdu Medium version and enjoy your study also share with your friends for the easiness of other classmates and colleagues.
Note: If you find any error, then just inform us in comments or email address admin@eStudent.pk
Time is over
Thanks for taking Quiz, Click Finish Button to see your Result
Math Ch#4, 09th Class
Here MCQs for your Revision
For Good Revision & Grip on Concept, You Should take the MCQs and Revise it again and again
Good Luck. . . . (:
You Should Enter your Name
1 / 15
• $x^{2}+\frac{1}{x^{2}}+2$
• $x^{2}-\frac{1}{x^{2}}+2$
• $x^{2}+\frac{1}{x^{2}}-2$
(Select Correct Option)
3 / 15
$x^{3}+\frac{1}{x^{3}}&space;=&space;\left&space;(&space;x+\frac{1}{x}&space;\right&space;)$ (_____________)
• $x^{2}-1+\frac{1}{x^{2}}$
• $x^{2}+1+\frac{1}{x^{2}}$
• $x^{2}-1-\frac{1}{x^{2}}$
• $x^{2}+1-\frac{1}{x^{2}}$
(Select Correct Option)
4 / 15
Conjugate of surd $a&space;+&space;\sqrt{b}$ is _________
• $-a&space;+&space;\sqrt{b}$
• $a&space;-&space;\sqrt{b}$
• $\sqrt{a}&space;+&space;\sqrt{b}$
• $\sqrt{a}&space;-&space;\sqrt{b}$
(Select Correct Option)
5 / 15
The degree of polynomial $4x^{4}+&space;2x^{2}y$ is ___________
6 / 15
$\frac{1}{a-b}-\frac{1}{a+b}$ is equal to ______
• $\frac{2a}{a^{2}-b^{2}}$
• $\frac{2b}{a^{2}-b^{2}}$
• $\frac{-2a}{a^{2}-b^{2}}$
• $\frac{-2b}{a^{2}-b^{2}}$
(Select Correct Option)
7 / 15
$(3&space;+&space;\sqrt{2})&space;(3&space;-&space;\sqrt{2})$ is equal to __________
8 / 15
"4x +3y -2" is an algebraic _____________
9 / 15
The Degree of polynomial $x^{2}y^{2}&space;+&space;3&space;x&space;y&space;+y^{3}$ is _________
10 / 15
$(\sqrt{a}+\sqrt{b})&space;(\sqrt{a}-\sqrt{b})$ is equal to __________
• $a^{2}+b^{2}$
• $a^{2}-b^{2}$
(Select Correct Option)
11 / 15
Order of Surd $\sqrt[3]{x}$ is ________
12 / 15
• $2&space;-&space;\sqrt{3}$
• $2&space;+&space;\sqrt{3}$
• $-2&space;-&space;\sqrt{3}$
• $-2&space;+&space;\sqrt{3}$
(Select Correct Option)
13 / 15
14 / 15
$\frac{a^{^{2}}-b^{2}}{a+b}$ is equal to __________
15 / 15
$a^{3}&space;+&space;b^{3}$ is equal to ____________
Your score is
Can u write your Feelings
How You Feel this
If you find any mistake in MCQs, please inform us by Commenting or by Contact us menu to improve the Quality of this free content.
Let’s see, How Students Solve this . . . . . . . Results . . .
Math Solution 9th Class (Science Group)
9th Class Math Solution:
There are Seventeen chapters in Mathematics 9th Class for Punjab Textbook Board, Lahore. Solutions of all the chapters are given below. Anyone can download the PDF file of the notes. Note that, you
can view these notes only if you have PDF reader software/ App on your device. However online view of the notes is also available on eStudent.pk . You can find all solution along with 9th Class Math
Notes in Urdu (Science Group), Math MCQs Class 9. if you are searching the topics like class 9th maths notes pdf, 9th class math notes chapter 3, mathematics class 9 pdf, class 9 maths notes chapter
Math Notes Class 9:
class 9th maths notes pdf, 9th class math notes chapter 1, mathematics class 9 pdf, 9th class math notes chapter 2, 9th class math solution chapter 1 pdf, 9th class math book solution, 9^th class
math notes, Math notes for class 9, math notes class 9 pdf, class 9 math notes pdf, math class 9 notes Punjab board, 9^th class math solution pdf free download, key book of mathematics 9^th class
Punjab text book board, maths class 9 notes kpk board pdf, class 9 maths notes pdf, maths class 9 notes punjab board, key book of mathematics 9th class punjab text book pdf, 9^th class math notes
chapter 4, 9^th class math solution chapter 4 pdf, math notes class 9 chapter 4, Math Notes Class 9 Exercise 4 Rev, exercise 4 Rev class 9, exercise 4 Rev class 9 then this post is specially for you
and your future. All Boards of Intermediate & Secondary Educations in Punjab, Federal Board of Intermediate and Secondary Education, kpd board, Sindh board, Agha Khan Board and also Allama Iqbal Open
University are taking examination according to Mathematics 9th Class. 9th Class Math key book pdf in English, Notes of 9th Class Math
9th Math Solution:
here is also related keywords to search the topic as class 9th maths notes pdf, 9th class math notes chapter 4, mathematics class 9 pdf, 9th class math solution chapter 4 pdf, 9th class math notes
chapter 2, maths class 9 notes punjab board, 9th class math book solution, maths class 9 notes sindh board.
some other keywords are also as math notes class 9 pdf, math notes class 9 kpk board, math notes class 9 urdu medium, math notes class 9 chapter 4, fbise math notes class 9, general math notes class
9, adamjee math notes class 9, ncert math notes class 9, math notes class 9th,
One thought on “Mathematics Notes for 9th Class Exercise 4 Rev”
1. You need to be a part of a contest for one of the best blogs on the net. I will highly recommend this blog!
|
{"url":"https://estudent.pk/mathematics-notes-for-9th-class-exercise-4-rev/","timestamp":"2024-11-09T16:24:59Z","content_type":"text/html","content_length":"367981","record_id":"<urn:uuid:6938e716-f4a9-4f6c-874d-5d2213a1c9ea>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00846.warc.gz"}
|
How Many Decimeters Is 4.1 Kilometers?
4.1 kilometers in decimeters
How many decimeters in 4.1 kilometers?
4.1 kilometers equals 41000 decimeters
Unit Converter
Conversion formula
The conversion factor from kilometers to decimeters is 10000, which means that 1 kilometer is equal to 10000 decimeters:
1 km = 10000 dm
To convert 4.1 kilometers into decimeters we have to multiply 4.1 by the conversion factor in order to get the length amount from kilometers to decimeters. We can also form a simple proportion to
calculate the result:
1 km → 10000 dm
4.1 km → L[(dm)]
Solve the above proportion to obtain the length L in decimeters:
L[(dm)] = 4.1 km × 10000 dm
L[(dm)] = 41000 dm
The final result is:
4.1 km → 41000 dm
We conclude that 4.1 kilometers is equivalent to 41000 decimeters:
4.1 kilometers = 41000 decimeters
Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 decimeter is equal to 2.4390243902439E-5 × 4.1 kilometers.
Another way is saying that 4.1 kilometers is equal to 1 ÷ 2.4390243902439E-5 decimeters.
Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that four point one kilometers is approximately forty-one thousand decimeters:
4.1 km ≅ 41000 dm
An alternative is also that one decimeter is approximately zero times four point one kilometers.
Conversion table
kilometers to decimeters chart
For quick reference purposes, below is the conversion table you can use to convert from kilometers to decimeters
|
{"url":"https://convertoctopus.com/4-1-kilometers-to-decimeters","timestamp":"2024-11-05T00:36:21Z","content_type":"text/html","content_length":"33330","record_id":"<urn:uuid:82499b72-d27b-4e52-ae99-370528f9dece>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00274.warc.gz"}
|
-semigroups of operators by a chronological integral.
Representation of ${c}_{0}$-semigroups of operators by a chronological integral.
Gogodze, Ioseb K., and Gelashvili, Koba N.. "Representation of -semigroups of operators by a chronological integral.." Memoirs on Differential Equations and Mathematical Physics 11 (1997): 47-66.
author = {Gogodze, Ioseb K., Gelashvili, Koba N.},
journal = {Memoirs on Differential Equations and Mathematical Physics},
keywords = {monoid; arrow inversion; integration by parts; -semigroup of operators; right and left chronological integrals; exponential function; chronological exponent; -semigroup of operators},
language = {eng},
pages = {47-66},
publisher = {A. Razmadze Mathematical Institute of the Georgian Academy of Sciences},
title = {Representation of -semigroups of operators by a chronological integral.},
url = {http://eudml.org/doc/222612},
volume = {11},
year = {1997},
TY - JOUR
AU - Gogodze, Ioseb K.
AU - Gelashvili, Koba N.
TI - Representation of -semigroups of operators by a chronological integral.
JO - Memoirs on Differential Equations and Mathematical Physics
PY - 1997
PB - A. Razmadze Mathematical Institute of the Georgian Academy of Sciences
VL - 11
SP - 47
EP - 66
LA - eng
KW - monoid; arrow inversion; integration by parts; -semigroup of operators; right and left chronological integrals; exponential function; chronological exponent; -semigroup of operators
UR - http://eudml.org/doc/222612
ER -
You must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.
|
{"url":"https://eudml.org/doc/222612","timestamp":"2024-11-13T16:11:13Z","content_type":"application/xhtml+xml","content_length":"36001","record_id":"<urn:uuid:983088bc-aa85-41bf-80de-06d60be815a9>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00626.warc.gz"}
|
The full order Model to reduce.
The basis of the reduced space onto which to project. If None an empty basis is used.
Inner product Operator w.r.t. which RB is orthonormalized. If None, the the Euclidean inner product is used.
Inner product Operator w.r.t. which the initial_data of fom is orthogonally projected. If None, the Euclidean inner product is used.
If True, no mass matrix for the reduced Model is assembled. Set to True if RB is orthonormal w.r.t. the mass matrix of fom.
See ProjectionBasedReductor.
See ProjectionBasedReductor.
|
{"url":"https://docs.pymor.org/2024-1-0/autoapi/pymor/reductors/basic/index.html","timestamp":"2024-11-06T17:28:24Z","content_type":"text/html","content_length":"79452","record_id":"<urn:uuid:1fad8879-d513-4204-b22e-f3d88f97dcd5>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00003.warc.gz"}
|
Free Calculator For Cantilever Beam Upto 3 Point Load
Calculator For Cantilever Beam Upto 3 Point Load ,This free calculator is designed for civil engineers to quickly and accurately calculate the shear force (SF) and bending moment (BM) for cantilever
beams with up to 3 point loads.
In just two simple steps, users will be able to input the total span of the beam in meters and the Point Loads in kN to quickly obtain values for shear force (SF) and bending moment (BM).It
eliminates the need for manual calculations, saving time and reducing the chance of errors.
Input the total span (in meters).
Input Span 1(in meters).
Input Span 2(in meters).
Input Span 3(in meters).
Enter the Point Load W 1 (in kN).
Enter the Point Load W 2 (in kN).
Enter the Point Load W 3 (in kN).
Please Refer SFD,BMD Diagram for more clarity.
Why This Tool Is Valuable
Point loads are common in real-world construction scenarios, and correctly calculating the resulting forces is critical for safe design. This calculator makes it easy to handle complex loading
situations, ensuring that engineers can focus on optimizing designs while meeting safety standards. It’s a must-have tool for those involved in structural analysis and construction planning.
2 thoughts on “Free Calculator For Cantilever Beam Upto 3 Point Load”
Leave a Comment
|
{"url":"https://engineers.digitalshare.in/free-calculator-for-cantilever-beam-2/","timestamp":"2024-11-07T18:51:14Z","content_type":"text/html","content_length":"172590","record_id":"<urn:uuid:24f84c0b-aaf8-4d04-978f-f5406e21bc64>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00350.warc.gz"}
|
Indicated Airspeed Calculator - AviationHunt
Indicated Airspeed Calculator
Calculate Indicated Airspeed (IAS) from True Airspeed (TAS)
Indicated Airspeed (IAS) Calculator
Note: This calculator is not suitable for supersonic speeds.
Simply enter the true airspeed, pressure altitude, and outside air temperature, and the calculator will instantly compute the indicated airspeed using the ISA model, accounting for altitude and
temperature effects.
To compute Indicated Airspeed (IAS) from True Airspeed (TAS), the process involves correcting for air density, which is affected by Pressure Altitude, and for temperature using the ISA 1976
atmospheric model. First, the TAS is adjusted based on the air density at the given altitude by calculating the ratio between the current air density and standard sea-level density. Then, a
correction is applied for temperature by considering the difference between the Outside Air Temperature (OAT) and the standard ISA temperature at that altitude. This method provides an accurate
conversion from TAS to IAS, accounting for altitude and temperature effects.
What is Indicated Airspeed (IAS)?
Indicated Airspeed (IAS) is the airspeed read directly from an aircraft's pitot-static system, without any correction for altitude or temperature. It's the speed displayed on the airspeed indicator
in the cockpit. IAS is crucial because it reflects the dynamic pressure experienced by the aircraft, which is directly related to the forces acting on the airframe, such as lift and drag.
Key Characteristics
• Depends on Air Density: IAS is influenced by the density of the air, which changes with altitude and temperature. As altitude increases, air density decreases, so IAS will read lower at high
altitudes compared to the actual speed through the air (True Airspeed or TAS).
• Primary for Piloting: Pilots rely on IAS for maintaining safe flight operations, as it indicates aerodynamic performance. Critical speeds like stall speed, takeoff speed, and approach speeds are
often given in IAS, since it reflects how the aircraft "feels" in the air.
• Not Corrected for Environmental Factors: IAS does not account for changes in pressure altitude, temperature, or compressibility effects at high speeds. To get an accurate measure of speed through
the air, corrections need to be made, which result in True Airspeed (TAS).
How to Calculate Indicated Airspeed (IAS)?
To calculate Indicated Airspeed (IAS) from True Airspeed (TAS), Pressure Altitude, and Outside Air Temperature (OAT), you must adjust for the differences in air density and temperature at various
altitudes using the International Standard Atmosphere (ISA) model. First, determine the atmospheric pressure and temperature at the given altitude, which decreases with height according to the ISA
model. Next, compute the air density based on the calculated pressure and temperature. Finally, adjust the TAS using the ratio of the standard sea-level air density to the air density at the current
altitude. This correction accounts for the thinner air at higher altitudes, which affects how the aircraft’s speed is measured by onboard instruments. Indicated Airspeed will always be lower than TAS
in thinner air, reflecting the reduced aerodynamic force on the aircraft.
Step 1: Calculate Pressure (P)
• For altitudes below 11,000 meters:
□ P = 101325 × (1 - 0.0000225577 × h)^5.25588
• For altitudes between 11,000 and 20,000 meters:
□ P = 22632.1 × e^(-0.0001577 × (h - 11000))
• Where:
□ h = Altitude in meters
□ 101325 Pa is the standard atmospheric pressure at sea level
□ 22632.1 Pa is the standard atmospheric pressure at 11,000 meters
Step 2: Calculate Temperature (T)
• For altitudes below 11,000 meters:
• For altitudes above 11,000 meters:
• Where:
□ 288.15 K is the standard temperature at sea level
□ 0.00649 is the temperature lapse rate in the troposphere
Step 3: Calculate Air Density (ρ)
ρ = (P / (R × T_K)) × 1000
• Where:
□ ρ = Air density (kg/m³)
□ R = Specific gas constant for air (287.05 J/kg·K)
□ T_K = T + 273.15 (temperature in Kelvin)
Step 4: Calculate IAS from TAS
IAS = TAS × √(ρ / ρ₀)
• Where:
□ IAS = Indicated Airspeed
□ TAS = True Airspeed
□ ρ₀ = Sea level air density (1.225 kg/m³)
□ ρ = Air density at altitude (calculated in Step 3)
Limitations: The calculator is designed to work for altitudes up to 20,000 meters and is restricted to subsonic speeds, as it does not account for compressibility effects at supersonic speeds.
|
{"url":"https://www.aviationhunt.com/indicated-airspeed-calculator/","timestamp":"2024-11-11T16:03:25Z","content_type":"text/html","content_length":"109583","record_id":"<urn:uuid:cd2e3ea4-0ba9-4398-b274-6d94f5615808>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00232.warc.gz"}
|
The support vector machine (SVM) and other reproducing kernel Hilbert space
The support vector machine (SVM) and other reproducing kernel Hilbert space (RKHS) based classifier systems are drawing much attention recently due to its robustness and generalization capability.
vectors. We pose the same problem if we exchange the role played by and in IVM. Hence the idea is to create Dauricine a dimension/feature screening/selection methodology via a sequential search
strategy over the original feature space. Our proposal has following features: It uses kernel machine for classifier construction It produces a nonlinear classification boundary in the original Mouse
monoclonal to KLHL25 input space The feature selection is done in the original input space not in the kernel transformed feature space Unlike SVM (both = (x≤ ∈ = {?1 1 or ∈ and x= (> 0 is the
smoothing or regularization parameter and ? is a space of functions on which is called reproducing kernel Hilbert space (RKHS). In this article we will employ radial basis function (RBF) as kernel
which is given by on a positive definite reproducing kernel to achieve this seemingly impossible computation. The optimal solution of the (3.1) is given by equation (2.2). It turns out that for most
cases a sizeable number of = 1|= x) giving classification probability is often of interest by itself. Noting the similarity of the hinge loss of SVM and that of the NLL of the binomial distribution
(plotted in Figure 1) Zhu and Hastie (2005) proposed to replace the hinge loss in equation 3.1. This essentially produces kernel logistic regression (KLR) given by: Figure 1 Hinge loss of SVM and NLL
of binomial distribution for two class classification ∈ {?1 1 and input xto select a Dauricine subset of to approximate the full model. However for feature selection we face a problem of different
kind where selection of dimension (small domain reduction of dimension (and is another possibility in the recently popular context. However in this paper our focus is exclusively on dimension/feature
selection. In the variable selection context Lasso proposed Dauricine by Tibshirani (1996) is a very successful method for automatic feature selection. In penalized regression context small domain (?
dimensions only. Also in situations where two (or more) dimensions have high correlation Lasso tends to select only one dimension from the group. Park and Hastie (2008) considered NLL of the binomial
distribution with introduced latter) as many/few dimensions can be selected as desired. 4 Feature Selection in KLR Framework Let us denote the index set ? = {1 2 … = ( ) ≤ denotes the dimension of
the transformed feature space. The classification boundary which is a hyperplane in the transformed feature space is given by coordinates are true features (or signals) and x* = (< is the shortest
distance from the training data to the separating hyperplane in ??. A KLR problem in ? can be equivalently stated as obtaining coordinates of x and its last ? coordinates are noises we can partition
coordinates of solution by → ∞ coordinates of with respect to a equals to zero and use the Newton-Raphson method to iteratively solve the score equation. With a little bit of algebra it can be shown
that Newton-Raphson step is a weighted least square method and = 1. For each ∈ ? \ let {= = + 1. Repeat Dauricine Steps 2 and 3 until convergence criteria are satisfied. The dimensions in are called
imported features. 4.3 Convergence Criteria In their original IVM algorithm Zhu and Hastie (2005) compared the quantity in different iterations. At step they compare with is a pre chosen small
integer say Δ= 1. If the ratio is less than a pre chosen small number = 0.001 the algorithm stops adding new observations. This convergence criterion is fine in IVM context as their algorithm
compares individual observations without altering dimensions. For FIVM in a specific iteration different we compute ? defined as the proportion of correctly classified training observations with
imported features. If the ratio is less than a pre chosen small number = 0.001 the algorithm stops adding new features. Though it was not discussed in their original paper we would like to mention
that the convergence criterion described in Zhu and Hastie (2005) has a mild assumption of no repetition of observations to be successfully applicable. In case there are two (or more) identical data
points and Δ= 1 is chosen and if it turns out that in one of those identical points is also an imported observation in any step of the iteration then the algorithm will stop there as it will produce
could be an unstable quantity. While this is true the way we define relative ratio of and (to compare with we closely follow the computational consideration of Zhu and Hastie (2005)..
|
{"url":"http://www.techblessing.com/2016/09/the-support-vector-machine-svm-and-other-reproducing-kernel-hilbert-space/","timestamp":"2024-11-04T04:48:24Z","content_type":"text/html","content_length":"35023","record_id":"<urn:uuid:1f00bd20-6970-45b8-9e4a-4a972c8ba945>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00516.warc.gz"}
|
Help electric charge Coulomb's law two charges?
• Thread starter asdf12312
• Start date
In summary, the problem involves two identical conducting balls suspended in equilibrium and making the same angle with the vertical axis. The magnitude of the Coulomb force between the balls and the
amount of charge on each ball need to be determined. The first problem involves using the small angle approximation to calculate the Coulomb force, while the second problem involves finding the
distance between the balls using the small angle approximation and the equation F=q1*q2*k/(r^2). In both problems, the angles are very small and the size of the balls can be ignored.
Homework Statement
Two identical conducting balls, A and B, of identical masses m = 10 kg, are suspended in equilibrium by insulating massless strings in length L = 3 m. Both balls make the same angle θ = 30° with the
vertical axis. Both masses have equal charge. You can ignore the size of the balls.
What is the magnitude of the Coulomb force, i.e. electric force, exerted on A from B due to the charges? (From free body diagram analysis)
What is the amount of charges (do not worry it is positive charge or negative charge) on each ball? Problem#2:
Two identical conducting balls, A and B, of identical masses m = 40 kg, are suspended in equilibrium by insulating massless strings in length L = 2 m. Both balls make the same angle θ with the
vertical axis. The angles are very small such that small angle approximation applies (i.e. tan θ = sin θ). Both masses have equal charge Q= 3e-06 C. You can ignore the size of the balls.
What is the distance r between the two balls?
Homework Equations
where k=9*10^9
The Attempt at a Solution
the only part i figured out (sadly) is the 1st part to find the Coulomb force. and that was only because the teacher gave us the equation :(
((40kg*10)/cos(30))*sin(30)=i got 57.7N for coulomb force
still don't no why that's the answer, but at least i no how to get it.
but i don't know what to do from here. i don't know how to find r so i assume it is L given (=3m). so i don't know how to find q (amt of charges).
for problem#2 i am stumped. i don't understand angle approximation and i can't use the cos/sin method that our teacher gave us. so wat do i do??
The problem gave you one small-angle approximation. Another is [itex]\sin\theta \approx \theta[/itex].
The first step to solve the problem is to draw a diagram showing the forces on each ball. From that calculate the horizontal forces. That equation will include [itex]r[/itex], which you can then
solve for.
Last edited by a moderator:
do i need sin in one of the equations?? wat am i doing wrong. also i don't understand small angle approximation so how to find the angle if i know sin=tan?
For problem #1, you can calculate r by recognising that the triangle made from the 2 strings and a line connecting the 2 charges is equilateral.
asdf12312 said:
What are these supposed to be?
do i need sin in one of the equations?? wat am i doing wrong.
For one thing, you are not using conventional orthography; ignoring the conventions hinders communication.
also i don't understand small angle approximation so how to find the angle if i know sin=tan?
What don't you understand about the approximations? Look at their series expansions, and think about what happens to the sine and cosine when the angle is very small.
tms said:
What are these supposed to be?
For one thing, you are not using conventional orthography; ignoring the conventions hinders communication.
What don't you understand about the approximations? Look at their series expansions, and think about what happens to the sine and cosine when the angle is very small.
ohhh i see..yeah so now i kinda understand. cos approaches 1 at small angles, but i still don't know how to use the sin one.
so the F(t) tension force would be (40*10)/cos(0)=400N
but that means the total electric force is 0? because i multiply this by sin(0) and get 400*0=0.
i'm just approaching this like i got the answer to the 1st part on problem#1, coz the two seem very similar. but i have a feeling I am doing something wrong.
asdf12312 said:
ohhh i see..yeah so now i kinda understand. cos approaches 1 at small angles, but i still don't know how to use the sin one.
Again, look at the series expansion of sine (remembering that the expansions use radians, not degrees). I don't know how to make it clearer.
so the F(t) tension force would be (40*10)/cos(0)=400N
That is the horizontal component of the tension. Except that the angle is not zero; it is small, but not zero. You will also need the vertical component,.
but that means the total electric force is 0? because i multiply this by sin(0) and get 400*0=0.
Not at all. Again, the angle is small, but not zero.
i'm just approaching this like i got the answer to the 1st part on problem#1, coz the two seem very similar. but i have a feeling I am doing something wrong.
You will communicate better if you use conventional orthography and spelling. Things like 'kinda' and 'coz' are okay in casual speech, but writing is more formal, and such spellings and lack of
capitals and so forth are at best distractions.
series expansion?? all i know is that sin is like the inverse of cos, so sin(90) is same as cos(0). but i don't see how that helps me because i planned to use cos/tan like in the last one.
for the vertical component in my FBD i got mass*gravity=400N. is that right?
i still don't know how to find the very small angle so if i have to use cos(0.01) instead of cos(0).
tms said:
Again, look at the series expansion of sine (remembering that the expansions use radians, not degrees). I don't know how to make it clearer.
That is the horizontal component of the tension. Except that the angle is not zero; it is small, but not zero. You will also need the vertical component,.
Not at all. Again, the angle is small, but not zero.
You will communicate better if you use conventional orthography and spelling. Things like 'kinda' and 'coz' are okay in casual speech, but writing is more formal, and such spellings and lack of
capitals and so forth are at best distractions.
The series expansion for sine is
\sin x &= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} \,x^{2n+1} \\
&= x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots.
The other circular functions have similar expansions. In this case, you want to eliminate all terms in x to a higher power than 1.
The only vertical force is gravity. The tension has a vertical component, which must offset gravity. Since the angle is small ...
As for the angle, that is what you are solving for. isn't it?
i plugged in 1 into the first 3 terms of the sine expansion and got 0.842. this is angle right, not radians?
for the coulomb force i got mass*gravity=(400N/cos(0.842))*sin(0.842)=5.88N
but I'm still gettin the wrong answer. what did i do wrong?
asdf12312 said:
i plugged in 1 into the first 3 terms of the sine expansion and got 0.842. this is angle right, not radians?
Just use the first term of the expansion. That leads to the approximation [itex]\sin x = x[/itex], as I said above.
still getting the wrong answer..don't know what I'm doing wrong.
Q=3e-06 C
First, you can't just assume a particular value for theta. Use the approximations to find a relation between r and theta.
did i do this right?
asdf12312 said:
What are O and H?
Why are you squaring k?
sorry O/H is opposite/hypotenuse. in the right triangle i got r/2 for the opposite (since r is line from A to B) and L=2m for hypotenuse. and no sorry i wasn't squaring k that was a typo.
can you please just tell me how to get the answer? i have tried but i just don't understand it o.o
No; it is against the rules here to do that.
Let's start over from the beginning. Draw the diagram showing all the forces. Each ball is acted on by the tension in the string, gravity, and the electrostatic force. Since the system in in
equilibrium, all the forces on each ball will add up to zero. You want to break the forces into their vertical and horizontal components (since the setup is symmetric, you only have to do this for
one side.
So what are the components of the forces on the ball? You'll get two equations in two unknowns: [itex]T[/itex] and [itex]\theta[/itex]. Don't worry about the small-angle approximation yet.
Use symbols everywhere, not numbers, so you can see more easily what is going on. Let [itex]\theta[/itex] be the angle between the string and the vertically down direction.
all i know is electrostatic/coulomb force=mass*gravity*tan(θ). and since the problem says tan(θ)=sin(θ), force=mass*gravity*sin(θ)
for the FBD..don't really know how to draw it. in the negative Y direction i get mass*gravity. don't know how to calculate string tension, i am assuming it is just L given.
Last edited:
There are three forces on each charged body: gravity, tension, and electrostatic. Gravity is down, electrostatic is horizontal, tension is at an angle [itex]\theta[/itex] to the vertical. Since the
bodies are at rest, the forces must cancel. That is, the vertical component of the tension must be equal and opposite to gravity, and the horizontal component of the tension must be equal and
opposite to the electrostatic force.
ok, so the vertical tension is mass*gravity=400N
the horizontal electrostatic force = KQ^2/R^2 = (9x10^9)(3e-06 C)^2/R^2 = 0.081/R^2
asdf12312 said:
ok, so the vertical tension is mass*gravity=400N
That is the vertical component of the tension.
the horizontal electrostatic force = KQ^2/R^2 = (9x10^9)(3e-06 C)^2/R^2 = 0.081/R^2
You need to express the distance in terms of the angle and the length of the string.
It would be helpful to use symbols in your calculations until the very end. That way you can see what is going on better, and might find some simplifications that are hidden by the numbers.
ok, so i have to find equation for R. length of string=2m.
how about R/2=sin(θ)*L
i am using pythagorean theorem. cut the triangle into two right traingles.
Okay. Now set up the two equations for the horizontal and vertical forces. After you do that, use the small-angle approximations to eliminate [itex]theta[/itex].
FAQ: Help electric charge Coulomb's law two charges?
1. What is electric charge?
Electric charge is a fundamental property of matter that causes it to experience electromagnetic interactions. It can be either positive or negative, and like charges repel each other while opposite
charges attract.
2. What is Coulomb's law?
Coulomb's law is a fundamental law of electrostatics that describes the force between two charged particles. It states that the force is directly proportional to the product of the two charges and
inversely proportional to the square of the distance between them.
3. How does Coulomb's law apply to two charges?
Coulomb's law applies to two charges by calculating the force between them based on their individual charges and the distance between them. The force will be attractive if the charges are of opposite
signs and repulsive if they are of the same sign.
4. What is the unit of electric charge used in Coulomb's law?
The unit of electric charge used in Coulomb's law is the Coulomb (C). It is a derived unit in the SI system and is defined as the amount of charge that passes through a conductor in one second when
there is a constant current of one ampere.
5. How is Coulomb's law related to electric fields?
Coulomb's law is related to electric fields because it describes the force between two charged particles in terms of the strength of the electric field produced by each particle. The electric field
is a measure of the force per unit charge, and Coulomb's law relates this force to the distance between the charges.
|
{"url":"https://www.physicsforums.com/threads/help-electric-charge-coulombs-law-two-charges.670979/","timestamp":"2024-11-09T15:42:00Z","content_type":"text/html","content_length":"186252","record_id":"<urn:uuid:71cd2679-c101-47b1-87ce-28d1b6143aa9>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00666.warc.gz"}
|
Learn Theory of Computation MCQ Questions with answers and solutions. Share Theory of Computation MCQ Questions with answers and solutions with others.
Home / Engineering / Theory of Computation MCQs / Page 13
Theory of Computation MCQs | Page - 13
Dear candidates you will find MCQ questions of Theory of Computation here. Learn these questions and prepare yourself for coming examinations and interviews. You can check the right answer of any
question by clicking on any option or by clicking view answer button.
Q. 121) Which statement is true?
Q. 122) TM is more powerful than FSM because
Q. 123) The symbols that can’t be replaced by anything are called -----------------
Q. 124) Left hand side of a production in CFG consists of:
Q. 125) Choose the incorrect statement:
Q. 126) Choose the incorrect statement.
Q. 127) In FA, if one enters in a specific state but there is no way to leave it, then that specific state is called
Q. 128) Which statement is true?
Q. 129) If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by Select correct option:
Q. 130) Which of the following will be used for text searching application-?
|
{"url":"https://www.mcqbuddy.com/engineering/mcqs/theory-of-computation/13","timestamp":"2024-11-02T06:24:22Z","content_type":"text/html","content_length":"81308","record_id":"<urn:uuid:39630dd8-4821-47c3-9ab6-6322b8db3e1b>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00061.warc.gz"}
|
How to Help Your Child Tackle 5th-Grade Math Word Problems | Brighterly
How to Help Your Child Tackle 5th-Grade Math Word Problems
Updated on April 22, 2024
If math is similar to a skyscraper, then word problems are the elevators; the higher you go, the broader your exposure and understanding of its concepts.
On the 5th floor of this building, the children are expected to understand how to interpret and solve word problems, think logically and creatively, as well as apply several math concepts
Utilizing math word problems 5th grade in your daily learning routine is a great way to help young learners build confidence, and hone their critical thinking and reading skills. It also helps tutors
gauge their students’ actual understanding of math concepts and provide instruction and support where necessary.
5th-grade math word problems are a bit more complex than early-grade math problems because it combines math concepts learnt at the elementary level. They might be complex, but not impossible to
tackle with the right tutor, routine, and mindset.
The Right Tutor
Getting the right tutor to help your child excel at 5th-grade math common core word problems can be daunting, but not if you know how and where to look.
The internet is the ideal place to start when looking for competent tutors for your child. Various websites offer math lessons online, but Brighterly happens to be one of the best.
Brighterly is a math learning website that infuses gameplay into the learning process to teach math concepts to your child effectively. It offers live one-on-one classes with professional tutors that
teach 5th-grade math word problems online.
You can rest assured that your child is in good hands as Brighterly tutors use innovative teaching techniques and worksheets tailored to your child’s needs.
Homeschoolers aren’t left behind as this platform also allows you to download 5th-grade math word problems pdf worksheets to practice with your child at your leisure!
The Right Mindset
One of the essential ingredients to tackling word problems is patience. Word problems may seem overwhelming at first glance as you may not have all the information you need, but with gradual steps
and logical thinking, you will uncover the solution.
A positive outlook is the best mindset to have when dealing with word problems. We have all battled math anxiety at least once in our lives, so it is crucial to avoid passing this fear on to your
child. The best way to foster positive thinking in your child is to motivate them. Using phrases like “You did great”. “We can solve this” helps build confidence in their ability to solve the
The Right Routine
Children are creatures of habit and like adults, benefit from routines they are familiar with. According to Vince Lombardi, a famous American football coach, Only perfect practice makes perfect.
Having a fixed daily routine for practising 5th-grade common core math word problems boosts their efficiency and confidence in problem-solving.
To make the practice perfect, it is crucial to arrange and design your child’s routine when your kids are well-rested and alert to aid knowledge assimilation.
Examples of Popular 5th-grade common core math word problems
Common core math word problems 5th grade are multi-layered and require children to think outside the box to arrive at the answer. It is advisable for children to express their ideas and thoughts with
pictures to map out their plans and solve each problem.
Word problems in 5th grade typically cover common core math concepts like addition, subtraction, division, multiplication, time, money, place value, and fractions.
Here are a few word problems you can practice with your youngster at home or during lessons.
Mixed Four Operations
These problems involve the basic four operations of addition, subtraction, multiplication and division. The aim of this set of problems is to improve the mastery of the child’s knowledge of basic
math concepts.
1. On a normal day, there are 300 planes taking off from the airport but the airport is a lot rowdier during Christmas. During the Christmas holidays, about 400 planes take off every day from the
1. The airport opens for 12 hours each day during the Christmas holidays; how many planes take off per hour?
2. On average, each plane takes 200 passengers and 5 tons of cargo. How many passengers depart from the airport every day during the Christmas holidays?
3. Compared to a normal day, how many more passengers depart the airport during the Christmas holidays?
4. There are 60 kittens for sale at a pet shop. 12 are black and 28 are orange. How many kittens are striped?
Estimating and Rounding Word Problems
These problems encourage children to use rounding and estimating to arrive at approximate answers to questions. It utilizes basic operations like addition, subtraction, multiplication, and division.
1. There are about 650 houses in the area. The average family size is 5 people. Estimate the number of people living in the area.
2. In a village, there are 500 families. If there are an average of two children attending elementary school from each family and each school accommodates 100 children. What is the minimum number
of elementary schools needed in the region?
Fractions and Decimal Word Problems
These problems are an interesting mix as they involve the addition, subtraction, division and multiplication of fractions, mixed numbers, and decimals. Children would learn
1. It is harvest season at Patty’s farm. She has two corn fields and the total area of the two fields is 5 ½ acres. The big field yields 3 ⅖ corn while the small field yields 2 ⅓ corn. What is the
total yield of corn?
2. Mary took out 5 glasses and poured juice from the pitcher. The capacity of each glass is 5/20 liter. If there is enough juice for 6 glasses, how much juice was there?
3. Judy is baking croissants. She has 15 pounds of dough. If each croissant requires ⅛ pounds of dough, how many croissants can she make?
Volume Word Problems
5th grade math volume word problems focus on measurements of volume and capacity and are typically in customary units such as pints, cups, milliters, liters, etc.
1. Before a party, Emily bought a tray of 12 bottles, each having a capacity of 12 oz. There are 15 guests. If each guest had 1 cup of water, would there be enough water for all the guests?
2. Amy made a pot of chili sauce for Thanksgiving dinner. She used 6 cups of water to make the soup. She poured the soup into 10 small soup bowls. How much water (in oz) is used for each small soup
3. Jodie mixed 2 cartons of orange juice,5 cans of cocktail fruits and 4 bottles of soda water to make a fruit punch for his housewarming party. The can of cocktail fruits are 2 pints each. Each
carton of orange juice is 1 gallon and 2 quartz. Each soda bottle is 5 pints each. How much (in gallons) fruit punch did Jodie make?
Probability word problems
5th grade math probability word problems provide children with the understanding of probability. The students are expected to calculate simple probability by expressing them as fractions or decimals.
Probability is usually expressed as likely, unlikely, and certain.
1. A glass jar contains a total of 20 marbles. The jar has red marbles and blue marbles. There are 16 red marbles in the jar. What is the probability of picking a blue marble?
2. A number cube has 6 sides. The sides are numbered 1 to 6. If the cube is thrown once, what is the probability of getting the number 6?
If you want to increase your child’s ability to solve 5th grade word problems quickly, enrolling them at Brighterly is the right call to make. Register now to kickstart their math learning journey.
We hope these tips help. Good luck!
|
{"url":"https://brighterly.com/blog/5th-grade-math-word-problems/","timestamp":"2024-11-02T18:32:14Z","content_type":"text/html","content_length":"96294","record_id":"<urn:uuid:763916b7-c722-4656-a360-ef90e2893167>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00378.warc.gz"}
|
Invnorm Calculator – Easy To Use Calculator (FREE)
Welcome to the Invnorm Calculator – an easy-to-use calculator that allows you to quickly and conveniently calculate the inverse normal probability distribution. With this free calculator, you can
quickly and accurately compute the inverse normal probability distribution for a specified probability, mean and standard deviation, with the efficiency and accuracy of a professional mathematician.
What is Invnorm?
Inverse normal (invnorm) is a mathematical computation that allows you to find the inverse probability distribution of a given probability, mean and standard deviation. This is usually used in
probability and statistics applications, where it is necessary to determine the probability of an event occurring in a certain range of values.
How Does the Invnorm Calculator Work?
Using the Invnorm Calculator is easy and straightforward. All you have to do is enter the probability (p), mean (m) and standard deviation (sd) – all of which you can find using the resources
provided – and the calculator will generate the inverse normal probability distribution.
The Invnorm Calculator is a great tool for quickly and accurately computing the inverse normal probability distribution of a given probability, mean and standard deviation. This calculator is easy to
use and provides users with a reliable and efficient way to calculate the inverse normal probability distribution.
Leave a Comment
|
{"url":"https://slickspring.com/answer-calculator-tutorials-and-reviews/invnorm-calculator-easy-to-use-calculator-free/","timestamp":"2024-11-05T15:47:15Z","content_type":"text/html","content_length":"140799","record_id":"<urn:uuid:0af5a37e-83db-41f6-b5b1-7e77936b52ff>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00703.warc.gz"}
|
Cite as
Roberto Grossi, Costas S. Iliopoulos, Chang Liu, Nadia Pisanti, Solon P. Pissis, Ahmad Retha, Giovanna Rosone, Fatima Vayani, and Luca Versari. On-Line Pattern Matching on Similar Texts. In 28th
Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Copy BibTex To Clipboard
author = {Grossi, Roberto and Iliopoulos, Costas S. and Liu, Chang and Pisanti, Nadia and Pissis, Solon P. and Retha, Ahmad and Rosone, Giovanna and Vayani, Fatima and Versari, Luca},
title = {{On-Line Pattern Matching on Similar Texts}},
booktitle = {28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
pages = {9:1--9:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-039-2},
ISSN = {1868-8969},
year = {2017},
volume = {78},
editor = {K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.9},
URN = {urn:nbn:de:0030-drops-73379},
doi = {10.4230/LIPIcs.CPM.2017.9},
annote = {Keywords: string algorithms, pattern matching, degenerate strings, elastic-degenerate strings, on-line algorithms}
|
{"url":"https://drops.dagstuhl.de/search/documents?author=Rosone,%20Giovanna","timestamp":"2024-11-04T14:23:25Z","content_type":"text/html","content_length":"105486","record_id":"<urn:uuid:4fc5b1f2-b27d-4f55-a166-f83709b3a4ab>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00512.warc.gz"}
|
Breaking Down Deductive Reasoning Errors in LLMs | HackerNoon
(1) Zhan Ling, UC San Diego and equal contribution;
(2) Yunhao Fang, UC San Diego and equal contribution;
(3) Xuanlin Li, UC San Diego;
(4) Zhiao Huang, UC San Diego;
(5) Mingu Lee, Qualcomm AI Research and Qualcomm AI Research
(6) Roland Memisevic, Qualcomm AI Research;
(7) Hao Su, UC San Diego.
Table of Links
Motivation and Problem Formulation
Deductively Verifiable Chain-of-Thought Reasoning
Conclusion, Acknowledgements and References
A Deductive Verification with Vicuna Models
B More Discussion on Improvements of Deductive Verification Accuracy Versus Improvements on Final Answer Correctness
C More Details on Answer Extraction
E More Deductive Verification Examples
3 Motivation and Problem Formulation
We observe that for all cases where LLMs produce erroneous final answers, there exists at least one mistake among the intermediate reasoning steps S. Moreover, even when the final answer is correct,
there might still exist some mistakes among S. This phenomenon, as illustrated in Tab. 1, occurs for all LLMs we tested, including state-of-the-art models such as ChatGPT and GPT-4 [32]. Since later
reasoning steps are conditioned on prior reasoning steps, these mistakes often initiate a snowball effect, causing subsequent mistakes to compound. This significantly diminishes the likelihood of
correct problem-solving and impedes the progress towards achieving human-level complex reasoning.
Therefore, in this work, we place significant emphasis on ensuring the validity of every reasoning step, not just the correctness of the final answer. In particular, we focus on the validity of
deductive reasoning, an essential component of a logical reasoning process. In deductive reasoning, we are
given a (premise, conclusion) pair, and we are interested in determining whether the conclusion follows from the premises. In the context of reasoning-based QA tasks, for each reasoning step si , we
define its deductive validity V (si) as a binary variable. A reasoning step is deductively valid (V (si) = 1) if and only if si can be logically deduced from its corresponding premises pi , which
consist of the context C, the question Q, and all the previous reasoning steps sj (j < i). Then, we can also define the deductive validity for the entire reasoning chain S as V (S) = ∧M i=1V (si).
Compared to evaluating answer correctness, which can be accomplished by simple functions such as exact string match, evaluating deductive validity is a lot more challenging. Thanks to the recent
progress on LLMs, which demonstrate impressive in-context learning capabilities across diverse scenarios, we propose to use LLMs to examine reasoning chains and predict the deductive reasoning
|
{"url":"https://hackernoon.com/breaking-down-deductive-reasoning-errors-in-llms","timestamp":"2024-11-11T08:46:15Z","content_type":"text/html","content_length":"223097","record_id":"<urn:uuid:968ef254-4df9-4b1d-82bf-3f6321123c84>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00046.warc.gz"}
|
NCERT Books for Class 7 Maths PDF Download
NCERT Books Class 7 Maths: The National Council of Educational Research and Training (NCERT) publishes Maths textbooks for Class 7. The NCERT Class 7th Maths textbooks are well known for it’s updated
and thoroughly revised syllabus. The NCERT Maths Books are based on the latest exam pattern and CBSE syllabus.
NCERT keeps on updating the Maths books with the help of the latest question papers of each year. The Class 7 Maths books of NCERT are very well known for its presentation. The use of NCERT Books
Class 7 Maths is not only suitable for studying the regular syllabus of various boards but it can also be useful for the candidates appearing for various competitive exams, Engineering Entrance
Exams, and Olympiads.
NCERT Class 7 Maths Books in English PDF Download
NCERT Class 7 Maths Books are provided in PDF form so that students can access it at any time anywhere. Class 7 NCERT Maths Books are created by the best professors who are experts in Maths and have
good knowledge in the subject.
NCERT Books for Class 7 Maths – English Medium
NCERT Solutions for class 7 Maths
NCERT Books for Class 7 Maths – Hindi Medium
The NCERT syllabus mainly focuses on this book to make it student-friendly to make it useful for both the students and the competitive exam aspirants. The book covers a detailed Maths based on the
syllabuses of various boards. NCERT Maths Books for Class 7 is perfectly compatible with almost every Indian education state and central boards.
We hope that this detailed article on NCERT Books Class 7 Maths helps you in your preparation and you crack the Class 7 exams or competitive exams with excellent scores.
|
{"url":"https://www.ncertbooks.guru/ncert-books-class-7-maths/","timestamp":"2024-11-06T21:31:42Z","content_type":"text/html","content_length":"80312","record_id":"<urn:uuid:55290bdd-8128-4891-83ce-b9782ba553a0>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00588.warc.gz"}
|
Jeremy Côté
July 15, 2016
Ask any scientist or mathematician, and this is the quality that they would love their solution to have. They want the result to be elegant, simple, and intuitive.
To give you an example, I remember doing a problem in my calculus class which involved using a bunch of trigonometric functions. Naturally, the integral kind of exploded as I worked on it, and the
result was super-complicated. However, after applying a bunch of different identities and swapping sines and cosines, the answer came back as simply tangent of theta.
When I got this result, I immediately knew I was right. The result was just too perfect after all that work for it not to be true (of course, this is a bias). Additionally, the answer made me feel
good. It was a nice answer to look at, particularly after all the work required to get there.
This underscores our tendency in science and mathematics to revere simple answer. Consequently, we tend to “dress up” our equations and concepts in order to make them much more compact than they are
in reality. I have two examples to illustrate the point.
First, in physics (particularly, wave motion), there’s the notion of forced oscillations for a spring or other kind of object feeling some sort of oscillation. The illusion of “dressing up” the
equation was so strong in this sense that I felt moved enough to create a small comic of it:
Even as my teacher talked about this equation, she looked sheepish. As soon as we saw the whole equation, we could see why (and this was only the steady state solution).
The second example comes from the recent World Science Festival, where I watched the panel on gravitational waves. During this panel at around the thirty minute mark, the moderator (Brian Greene)
walked through some of the equations of general relativity, and showed just how complicated these equations can be. Despite looking relatively (sorry!) simple, the equations are just being dressed up
to cover their complexities. There’s nothing necessarily wrong about this, but it does illustrate how equations in science and mathematics can be a bit more challenging than they appear. This is all
done in the name of elegance. If we can make an equation more compact, we will do it.
Often, we seek the elegant answer, wanting to have something simple after working through a bunch of mathematics. This leads us to covering up the complexities of many equations, which make them
difficult to understand while looking in from the outside.
Perhaps we should embrace a little more complexity?
|
{"url":"https://jeremycote.net/2016/07/15/elegance/","timestamp":"2024-11-08T18:55:57Z","content_type":"text/html","content_length":"6385","record_id":"<urn:uuid:0bdf17a4-62b7-4d80-b2d4-902d77cc0774>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00065.warc.gz"}
|
Tellusant’s Universal Profit Equation (TUPE)
• 2024-03-21
• 11:55 am
• Posted By: Tellusant
Pricing optimization is the fastest way to increase profits. Here we describe methods for how companies can achieve this.
These methods are universal. We here go into depth describing pricing within consumer goods.
In the following we discuss:
• The Tellusant universal profit equation
• Pricing approach in consumer goods
• Conclusions
Every company follows the basic equation: profit = revenue − cost. Tellusant has extended it to be more actionable, what we call the Tellusant Universal Profit Equation (TUPE).
It uses one revenue component and three cost components as shown in the equation below.
Executives are used to thinking about variable and fixed costs. Here we explicitly break out discretionary costs that are neither variable nor fixed but chosen at the discretion of management.
The beauty of TUPE is that:
• It is parsimonious (exactly what is required — nothing more, nothing less) and applies to all industries
• It breaks out discretionary costs that a company can choose to incur, or not
• It lends itself to more detailed expansions with elasticities and other commonly used concepts
With this as the starting point, we now turn to pricing in consumer goods. We leverage a brilliant paper by Sethuraman and Tellis throughout.¹
TUPE adapted to consumer goods is shown below. It includes advertising/promotion and assumes that R&D and other discretionary costs are low.
To make the equation come alive, we introduce three ratios:
ₚ is familiar to any reader.² The contribution-price ratio k is intuitive (note that the correct formula is more complex, but this is a good approximation). The pass-through ratio may be less
commonly known.
The pass-through ratio is the percentage of a price discount by a manufacturer that is passed on to consumers by retailers. It is by no means a given that if a manufacturer offers a 10% price
discount, the retailer also reduces price by 10%.
In affluent countries, modern trade pass through may be 80%. In traditional trade in emerging countries, it may be 40% and in some cases zero.
We also need the fraction of sales that is sold at a discount (f).
With this, the extended equation below is derived. We do not give the proof¹ since our focus is on the implications.
kϵₚ and a profit loss proportional to f/g since the original price is not realized, and the retailer pass through is less than 1.
There is a breakeven price elasticity. A company takes different actions depending on whether the actual price elasticity is above or below this breakeven.
This breakeven elasticity is derived by setting the term in parenthesis to zero. This gives:
If ϵₚ > f/(gk) then the company should reduce price.
We find that it is of critical importance to continuously track four factors:
• Price elasticity ϵₚ. The higher the price elasticity, the more it pays off to discount (if above the breakeven)
• Pass through g. The higher the pass through, the more discounting is suitable.
• Fraction of sales sold at discount f. The less consumers switch to the discounted price away from the original price, the better the discount works.
• Contribution-price ratio k. If contribution is high, companies should be willing to reduce price.³
In inflationary times, these four factors tend to change significantly.
With less detail, we derive equations for advertising/promo. The advertising/promo elasticity is given by:
The profit formula (here without proof¹) becomes:
For an advertising/promo change ΔA/A there is a profit gain proportional to kϵₐ and a profit loss proportional to the advertising/promo share of sales.
As with price, we find a breakeven elasticity for advertising/promo:
If ϵₐ > (A/S)/k then then the company should increase advertising/promo expenses. If ϵₐ < (A/S)/k then those expenses should be reduced.
The ratios to track for advertising/promo are simpler than for price:
• Advertising/promo elasticity ϵₐ. The higher the elasticity is, the more the company should spend on advertising/promo (if above the breakeven).
• Contribution-price ratio k. If this ratio is high, then the company should spend more on advertising/promo.
• Advertising share of sales A/S. If this ratio is high, the required actual elasticity is high.
Pricing and advertising/promotion together
Finally, we combine the two profit drivers with a realistic example.
• Contribution-price ratio k = 0.5
• Fraction of sales sold at discount f = 0.6
• Pass through g = 0.8
• Advertising share of sales A/S = 0.05
This gives a breakeven price elasticity price of 1.5 and a breakeven advertising/promo elasticity of 0.1. Across hundreds of studies, the average price elasticity is around −1.5 and the average
advertising elasticity is +0.09 to +0.12 both with large variations around the means.
The graph below summarizes optimal strategies for the example.
1. In the lower left quadrant consumers know what they get and are not swayed by price or advertising/promo. These are typically highly mature niche products.
2. The lower right quadrant is typically populated with well-established mass market brands. Consumers know what they get, and advertising does not play a significant role; consumers look for the
best deal.
3. Upper left quadrant holds luxury goods and new products that require image or informational marketing.
4. Differentiated brands are often found in the upper right quadrant, as are seasonal products.
Each quadrant requires its own distinct strategy. For a large consumer goods companies, brands can typically be found in at least three of the quadrants.
Updating established beliefs is crucial to any consumer goods company. What used to be in one quadrant may have moved to an entirely new position over the last year.
Beyond this, systematically analyzing the market conditions as described above makes sense any time. The urgency prompted by inflation makes now the time to start.
Many companies have implemented elements of this generalized framework. They may know their elasticities, sometimes they have the contribution figured out.
The goal should be to have all elements implemented in a structured and repeatable fashion across geographies and business units. Few, if any, companies have this.
• • •
To learn more, contact us by filling out this online form.
• • •
¹ R. Sethuraman and G. Tellis: An Analysis of the Tradeoff between Advertising and Price Discounting. Journal of Marketing Research. Vol. 28, №2 (May, 1991), pp. 160–174
² The elasticity symbol ϵ is a lunate epsilon and should be called epsilon. Other ways to denote elasticity are ey/ex (with y and x substituted with variables used), E, el., and possibly more.
³ Note that this is not the EBITDA metric which has nothing to do with contribution (or for that matter, profitability). EBITDA combines some variable and fixed costs and omits many costs. It is
perhaps useful in investor presentations as a proxy for cash flow. True variable and fixed costs are best quantified with a regression analysis.
|
{"url":"https://tellusant.com/tupe/","timestamp":"2024-11-07T06:34:04Z","content_type":"text/html","content_length":"100911","record_id":"<urn:uuid:a9aaf22d-6947-4e83-a212-3e4d04dd0f53>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00781.warc.gz"}
|
Free the Turkey! Multiplication Game
Free the Turkey! Multiplication Game
Price: 200 points or $2 USD
Subjects: math,mathElementary,operationsAndAlgebraicThinking,multiplicationAndDivision,holiday,firstDayOfAutumn,thanksgivingUS
Grades: 3
Description: The Key Idea behind this game is that students will practice their multiplication fact fluency with an emphasis on 2's, 3's, 4's, 5's, and 10's facts. The turkeys are behind a wall of
answers. One section of the wall disappears as students correctly solve the problems. The turkey is freed when the wall is completely broken down. There are three different turkeys to break free for
a total of 27 multiplication problems. Standard address in this game: CCSS: 3.OA.C.7
|
{"url":"https://wow.boomlearning.com/deck/BC5JdxmhcjtNhDJ3p","timestamp":"2024-11-12T13:37:27Z","content_type":"text/html","content_length":"2407","record_id":"<urn:uuid:545aa06a-48f5-4fdb-8a49-d60eec10c21b>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00715.warc.gz"}
|
Vertex Cover | Brilliant Math & Science Wiki
A vertex cover of a graph \(G\) is a set of vertices, \(V_c\), such that every edge in \(G\) has at least one of vertex in \(V_c\) as an endpoint. This means that every vertex in the graph is
touching at least one edge. Vertex cover is a topic in graph theory that has applications in matching problems and optimization problems. A vertex cover might be a good approach to a problem where
all of the edges in a graph need to be included in the solution.
Say you have an art gallery with many hallways and turns. Your gallery is displaying very valuable paintings, and you want to keep them secure. You are planning to install security cameras in
each hallway so that the cameras have every painting in view. If there is a security camera in a hallway, it can see every painting in the hallway. If there is a camera in the corner where two
hallways meet (the turn), it can view paintings in both hallways. We can model this system as a graph where the nodes represent the places where the hallways meet or when a hallway becomes a dead
end, and the edges are the hallways.
In this graph, show where you would place the cameras such that all paintings are covered — this is a vertex cover! (There are many solutions).
There are many possible solutions — here are a few.
The first is a trivial solution — have cameras at all of the nodes. By definition, this is a vertex cover since all of the edges in graph must be connected to at least one of the vertices in
the cover.
A vertex cover of a graph \(G\) is a set, \(V_c\), of vertices in \(G\) such that every edge of \(G\) has at least one of vertex in \(V_c\) as an endpoint. This means that every vertex in the graph
is touching at least one edge. Vertex cover is an NP problem because any solution can be verified in polytime with \(n^2\) examinations of all the edges to see if their endpoints are included in the
proposed vertex cover.
Here are images showing vertex cover. Each of the red vertices in the graphs make up the graph's vertex cover. The set of all red nodes in each graph touch every edge in the graph.
Which of the following graphs do not show a vertex cover? (The vertices in the vertex cover are red).
It can be shown that vertex cover is NP-complete by showing that 3SAT is reducible to vertex cover (and by the Cook-Levin Theorem, this proves NP-completeness). In bipartite graphs, however, a vertex
cover may be found in polynomial time.
The vertex covering number also called the minimum vertex covering number is the size of the smallest vertex cover of \(G\) and is denoted \(\tau(G)\).
Here are some examples of minimum vertex covers where the nodes in the minimum vertex cover are red.
Finding a smallest vertex cover is classical optimization problem and is an NP-hard problem. In fact, the vertex cover problem was one of Karp's 21 NP-complete problems and is therefore a classical
NP-complete problem in complexity theory.
For instance, in the example in the introduction with the security cameras, perhaps the gallery owner wants to minimize the cost of installing the camera and therefore wants to buy as few as
possible, while still covering all of the paintings. In this case, a minimum vertex cover would be needed.
What is the least number of nodes you can have to make a minimum vertex cover of this graph?
Calculating a Vertex Cover
There are several algorithms for determining a vertex cover. Here's a psuedocode description of an algorithm that gives an approximate vertex cover using ideas from matching and greedy algorithms.
Because the vertex cover problem is NP-complete finding an exact answer is very difficult and time consuming. Many times, approximation algorithms are useful. These run much faster than exact
algorithms, but may produce a suboptimal solution. Here is an approximation algorithm for vertex cover.
1 def greedy(E, V)
2 C = {}
3 while E not empty:
4 select any edge with endpoints (u,v) from E
5 add (u,v) to C
6 remove all edges incident to u or v from E
7 return C
Basically, the algorithm works by finding a maximal matching in \(G\) and adding at least one endpoint of each edge to the covering set of vertices \(C\). The optimal answer will contain one vertex
from each edge in the matching, but a suboptimal covering could contain both endpoints from each edge, so the covering set \(C\) could be as much as two times as big as the optimal answer. This
algorithm can be adapted to handle weighted graphs.
This is a polynomial time approximation algorithm (since it isn't guaranteed to return the optimal vertex cover) that runs in \(O(V + E)\) time.
Some problems that use ideas of vertex cover have additional and/or modified constraints compared to vertex cover. Below is a problem that uses a fairly straight-forward vertex cover approach.
The Traveling Salesperson Problem
The traveling salesperson problem is a classic computer science problem discussed in graph theory and complexity theory — especially when talking about NP-complete problems. The traveling salesperson
problem goes like this:
A salesperson needs to visit a set of cities to sell their goods. They know how many cities they need to go to and the distances between each city. In what order should the salesperson visit each
city exactly once so that they minimize their travel time and so that they end their journey in their city of origin?
Here's an example of the traveling salesperson problem where the salesperson needs to travel from the origin city to three other cities and then back to the origin. The salesperson must take roads
that have fees associated with them, and they want to minimize the cost of their journey — so they need to find the path with the least edge weight.
|
{"url":"https://brilliant.org/wiki/vertex-cover/","timestamp":"2024-11-05T15:54:10Z","content_type":"text/html","content_length":"62458","record_id":"<urn:uuid:57203ca8-7a76-4143-9575-052f23ab5347>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00568.warc.gz"}
|
ence of artifacts is eliminated. Fig.7 demonstrates the
time-frequency representation obtained by the algo-
rithm based on the expression (28) in the case, where
the number of analysis frequencies are varied accord-
ing to the sampling density. The chirp can be tracked
without any presence of artifacts.
The processing of non-stationary signal using level-
crossing sampling approach has been investigated.
On the one hand, such a sampling strategy provides
several interesting properties - signal to quantization
noise ratio does not depend on the number of quan-
tization bits, local sampling density reflects the in-
stantaneous bandwidth of signal, etc. On the other
hand, the captured samples are placed non-uniformly
and that requires rethinking of the processing method-
ology. The classical approaches of time-frequency
analysis have been discussed. Time-frequency repre-
sentations have been obtained using general forms of
them, which are suitable also for processing of non-
uniformly sampled signals. The simulation shows
that the main drawback of STFT is the appearance of
spurious components, while wavelet transform gives
low spectral resolution at high frequencies and low
temporal resolution at low frequencies.
Several enhancements have been proposed, which
are based on the idea of minimizing the error be-
tween the original signal and that reconstructed by
the Fourier series, not only at sampling time instants,
but also between them with the same accuracy. The
problem lies in the fact that the original signal values
are known only at sampling instants. One solution is
based on the consideration, that the continuous time
signal is constructed by interpolation of known sig-
nal samples. The expressions for zero-order and first
order polynomial interpolation as well as for band-
limited interpolation with sinc functions have been
established. The other approach is to interpolate the
error samples in the same manner.
Simulation results show the improvement of TFRs
if enhanced algorithms are used instead of classical
ones. Additional benefits can be gained if the band-
width of analysis is varied along the time axis accord-
ing to changes in local sampling density: the artifacts
are removed, the complexity of calculations can be
decreased. The common drawback of STFT based
methods is restrictions on the resolution. Extension of
the windows w(t) length improves the frequency res-
olution but at the same time degrades the temporal se-
lectivity. To overcome this rule, the signal-dependent
transformation described in (Greitans, 2005) can be
used. Due to the limited size of the paper, this method
is not discussed above, however the TFR obtained by
Figure 8: TFR of test-signal if signal-dependent transfor-
mation is used.
signal-dependent algorithm is shown in the Fig.8 for
the illustration. The increased resolution is achieved
by adapting the transformation functions to the local
spectral characteristics of the signal. As it is being
done in an iterative way, the mathematical complex-
ity is higher than for STFT based algorithms.
The proposed approach of processing non-
stationary signals using level-crossing sampling is
attractive for clock-less designs, which are now re-
ceiving increasing interest. Their advantages can play
a significant role in future electronics’ development.
Akay, M., editor (1998). Time frequency and wavelets in
biomedical signal processing. IEEE Press.
Baraniuk, R. G. and Jones, D. L. (1993). A signal-
dependent time-frequency representation: Optimal
kernel design. IEEE Trans. Signal Proc., 41(4):1589–
Chui, C. K. (1992). Wavelet Analysis and its Applications.
Academic Press, Boston, MA.
Cohen, L. (1995). Time-frequency analysis. Prentice-Hall.
E. Allier, G. Sicard, L. F. and Renaudin, M. (2003). A new
class of asynchronous a/d converters based on time
quantization. In Proc. of International Symposium on
Asynchronous Circuits and Systems ASYNC’03, pages
196–205, Vancouver, Canada.
Ellis, P. H. (1959). Extension of phase plane analysis to
quantized systems. IRE Transactions on Automatic
Control, AC(4):43–59.
Gabor, D. (1946). Theory of communication. Journal of
the IEE, 93(3):429–457.
Greitans, M. (2005). Spectral analysis based on signal de-
pendent transformation. In Proc. of the International
Workshop on Spectral methods and multirate signal
processing, pages 179–184, Riga, Latvia.
Hauck, S. (1995). Asynchronous design methodologies: An
overview. Proc. of the IEEE, 83(1):69–93.
Mark, J. W. and Todd, T. D. (1981). A nonuniform sam-
pling approach to data compression. IEEE Trans. on
Comm., 29(1):24–32.
|
{"url":"http://www.scitepress.net/PublishedPapers/2006/15690/pdf/index.html","timestamp":"2024-11-05T19:08:58Z","content_type":"application/xhtml+xml","content_length":"227564","record_id":"<urn:uuid:d1af4142-7b1d-46e0-ae76-3d2f35babc60>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00744.warc.gz"}
|
measures of central tendency
A measure of central tendency is a value that indicates the central or average value of a set of data. The most commonly used measures of central tendency are the arithmetic mean, the mode, and the
median, and which of these gives the best measure depends on the data.
For numerical data that is symmetric in its distribution, i.e., not skewed and not having large outliers, the arithmetic-mean gives a good measure. However, for datasets that are skewed or have large
outliers, the mean can be a misleading measure, and in such cases the median is a better measure.
The mode, which is simply the frequency of the most frequently occurring value, is typically used for non-numerical data since the mean and median cannot be used.
Less common measures of central tendency include the midrange, the harmonic mean, and the geometric mean.
|
{"url":"https://platonicrealms.com/encyclopedia/measures-of-central-tendency","timestamp":"2024-11-13T11:30:59Z","content_type":"text/html","content_length":"78374","record_id":"<urn:uuid:62385923-8e7c-404e-a858-21f1d8f964bf>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00311.warc.gz"}
|
Analog To Digital Conversion – Performance Criteria - Electronics-Lab.com
Analog To Digital Conversion – Performance Criteria
• Kamran Jalilinia
• 15 min
• 406 Views
• 0 Comments
In this series of articles, we considered PCM (Pulse Code Modulation) as a method of digital representation of an analog signal. In the PCM method, the samples of the continuous wave are allowed to
take only certain discrete values. These amplitudes are then assigned a code, where each code uniquely represents the magnitude of the sample. These code words as digital data find application in
various contexts.
Analog-to-digital converters (ADCs) are devices or circuits that practically transform analog signals into digital ones using the PCM concept. They have many applications in the industry. For
example, many modern microcontrollers are equipped with built-in ADC converters. This allowed designers to interface easily with analog sensors, convert analog signals from the environment into
digital data, and process it within the microcontroller for various applications.
The process of analog-to-digital conversion can be executed through various architectures, such as successive approximation register (SAR), parallel (flash) conversion, sigma-delta conversion, and
The task of the digital-to-analog converter (DAC) is the inverse of the ADC: it converts numerical digital values back into continuous analog signals. DACs are employed to translate the outcomes of
digital processing into real-world variables for control, information display, or other forms of analog processing. Figure 1 illustrates a general block diagram of a digital processing system.
Figure 1: Interfacing digital processing system with the analog world using n-bit ADC and DAC
Analog quantities are often representative of real-world phenomena. In this configuration, the primary variable typically relates to a physical parameter like temperature, light, etc., which is
transduced into electric voltages or currents by a transducer.
Here, analog filters are used to comply with the sampling theorem. The first filter placed before the ADC is an LPF called an anti-alias filter. This filter, placed prior to the ADC, eliminates
frequency components above half of the sampling rate (fs/2) that could lead to aliasing during sampling. The filtered analog signal is then transformed into digital codes by the ADC block and
directed into the digital processing system, which could be a microcontroller or other forms of data processing and manipulation.
After that, the processed digital signal is fed to the DAC stage to convert it back into an analog signal. The second filter placed after the DAC block is also an LPF and is called a reconstruction
filter. It also removes frequencies above the Nyquist rate (f[s]/2). Finally, the analog output signal is transduced back to the physical world by an actuator stage for any further physical
As an example, in an audio signal processing configuration, an ADC converts the analog audio signal captured by a microphone, into a digital signal for computer-based sound effects processing. The
DAC then converts the processed digital signal back into analog form, which can be played through a loudspeaker.
In contemporary electronics, instrumentation, information technology, data acquisition and transmission, control systems, medical imaging, professional and consumer audio/video, and computer
graphics, converting analog signals to digital has become a fundamental process.
In this article, we explore the key performance criteria that define the effectiveness of ADCs in their applications.
Quantization Errors
There are various sources of errors in conversion circuits. Among them, quantization error (Q[e]) or quantization uncertainty stands out as one of the most critical factors that significantly impact
the performance of A/D or D/A converters.
Quantization errors occur in analog-to-digital conversion when the continuous analog signal is approximated by discrete digital values. In a PCM encoder, every voltage sample is already rounded off
(quantized) to the nearest available level and then translated into its corresponding binary code. When the code is converted back to analog at the decoder, any round-off errors are reproduced.
Theoretically, the conversion will never be 100% accurate; that is, a finite amount of information will be lost forever during the conversion process. It means when the digital representation is
converted back to analog, the result will not be identical to the original waveform.
Let’s refer to Figure 2 as the block diagram of a 3-bit A/D converter.
Figure 2: Block diagram of a 3-bit ADC
Obviously, a 3-bit ADC has 8 digital (quantum) levels. The output digital results of this system in comparison to the analog input, are represented in Figure 3 and a typical sample of Q[e] is
indicated on the graph.
Figure 3: Digital representation of the analog waveform by a 3-bit ADC
Now, we may look at the effects of quantization. Figure 4 shows the transfer characteristics for a 3-bit unipolar ADC with a full-scale voltage of 1 volt.
Figure 4: The characteristic diagram of the 3-bit ADC with a full-scale voltage of 1 volt
Figure 4 represents a 3-bit quantizer, which maps a range of analog input values to only eight (2^3) possible output digital values. If the maximum peak-to-peak value of the input signal is 1 V, each
step in the staircase has (ideally) the same size along the y-axis, which is defined as 1 LSB (the least significant bit) in terms of voltage. In this case, 1 LSB is equal to 1/8 V (or 125 mV).
Under these conditions, as an example, it would be impossible to perfectly encode a value of 300 mV. The nearest value available would be binary 010, which yields 250 mV. Obviously, the resulting
round-off creates some error in the digital representation.
In an ideal assumption, the characteristic of the conversion system could be a straight diagonal line with no steps at all. But in reality, an ADC quantizes a sampled signal by selecting a single
discrete value from a pre-established finite list of such values to represent each analog input sample. This rule gives the transfer function of analog input to digital output a uniform ‘staircase’
The vertical difference between the actual analog value and the quantized digital value at each sample point defines the quantization error (Q[e]). The graph of quantization errors in Figure 5 is
resulted from the subtraction of ideal values of the linear function from the actual values of the staircase function. The maximum magnitude of the quantization error equals half of a quantum level
(q/2) where q is the width of an individual step. Then, Q[e] can fluctuate within the range of ± (1/2) LSB or ± (q/2) as illustrated in Figure 5.
Figure 5: The characteristic diagram of the quantization error
The result is a sawtooth-pattern error voltage that manifests itself as white noise added to the analog input signal. The quantization error is an actual voltage, as it alters the signal amplitude.
Consequently, the quantization error is also referred to as the quantization noise (Q[n]).
The quantization error is generally larger when the number of bits used for conversion (n) is small, as there are fewer quantization levels to represent the continuous signal accurately. As the
number of bits increases, the quantization error becomes smaller, resulting in a more accurate representation of the original analog signal. In practical terms, it is possible to reduce the error to
such small values that it may be ignored in many applications.
The Signal-to-Quantization Noise Ratio (SQNR) is a measure of the ratio between the power of the original analog signal (P[s]) and the power of the quantization noise (P[qn]) introduced during the
analog-to-digital conversion. However, it is assumed that the ADC is relatively free of random noise and that the transitions can be easily measured.
Then, the Signal-to-Quantization Noise Ratio (SQNR) can be generally calculated in terms of dB using Equation 1.
Equation 1: Calculating Signal-to-Quantization Noise Ratio
In an ideal n-bit converter scenario where the input signal is a full-amplitude sine wave, the corresponding SQNR can be determined using Equation 2.
Equation 2: Calculating SQNR for an n-bit ADC
This gives the ideal value for an n-bit converter and shows that each extra 1 bit of resolution provides approximately 6 dB improvement in the SQNR.
SQNR is a valuable metric for assessing the quality of the analog-to-digital conversion in contrast to the quantization error. A higher SQNR value indicates better accuracy and a smaller impact of
quantization noise on digital representation.
A/D And D/A Conversion Performance Criteria
The specifications which impact the performance of an ADC are similar to those for a DAC. In addition to SQNR, some other major factors that determine the performance of D/A and A/D converters are
resolution, sampling rate, speed, accuracy and dynamic range. They are explained below.
Resolution: In an A/D system, the resolution is the smallest change in voltage at the input that the system can detect and convert into a corresponding change in the digital code at the output.
Similarly, for a D/A circuit, resolution refers to the smallest change in the output analog signal that the circuit can produce.
D/A or A/D IC manufacturers usually specify the resolution in terms of the number of bits in the digital code (n) or voltage corresponding to the least significant bit (LSB) of the system.
Another approach to expressing resolution is by indicating the voltage step magnitude between quantization levels, also termed the quantization width (q). For an n-bit DAC, the LSB carries a weight
of 2^-n. For instance, an 8-bit DAC can resolve 1 part in 2^8 or 0.39% of the full-scale output voltage when the binary input code is incremented by one LSB. Then, for full-scale voltage (V[FS] = V
[max] – V[min]) equals 10 volts, the resolution of the 8-bit system is 0.039 (= 10/2^8) volts.
Generally, it can be calculated in terms of voltage by Equation 3.
Equation 3: Calculating resolution for an n-bit ADC
Sampling Rate: The sampling rate denotes the frequency at which the analog signal can be sampled and translated into a digital code per unit of time. For proper A/D conversion, the minimum sampling
rate must be at least two times the highest frequency of the analog signal being sampled to satisfy the Nyquist sampling criterion. The more samples taken in a given unit of time, the more accurately
the analog signal is represented in digital form.
Speed: For A/D converters, the speed is specified as the conversion time, which represents the time taken to complete a single conversion process, including sampling the analog signal, processing,
and generating the digital output. In A/D converters, conversion speed, along with other timing factors, must be considered to determine the maximum sampling rate of the converter.
For D/A converters, the speed is specified as the settling time, which is the delay between the binary data appearing at the input and the output voltage reaching a stable value. This sets the
maximum data rate that the converter can handle.
Accuracy: Accuracy is the degree of conformity between the converter’s output and the actual analog signal value. The resulting round-off error occurs due to the quantization process, leading to some
deviation from the actual analog value.
As the number of bits increases, the step size between quantization levels decreases, leading to higher accuracy when converting between analog and digital signals. For example, an eight-bit word (n
= 8) provides 256 distinct values (2^8) for representation, offering a more precise conversion of the analog signal than using a four-bit word with 16 distinct values (= 2^4).
Dynamic Range: Dynamic Range refers to the range of signal amplitudes that an ADC can accurately represent in its digital output without significant loss of accuracy. In other words, the dynamic
range is the difference between the maximum and minimum input signal levels that the ADC can handle effectively.
Dynamic range is expressed as the ratio of the maximum input voltage to the minimum detectable voltage and, it is subsequently transformed into decibels. Calculation of the Dynamic Range (DR) is
defined in Equation 4, combining logarithmic (dB) and linear (voltage) aspects.
Equation 4: Calculating dynamic range for an n-bit ADC
The full-scale voltage (V[FS] = V[max] – V[min]) is the voltage range that the ADC uses to represent the analog input signal.
For example, if the ADC uses a reference voltage of V[ref] = 5 volts, the input voltage should fall within this range for accurate conversion. For a 12-bit ADC (n = 12) and the reference voltage of 5
volts, the dynamic range can be assessed as follows:
Dynamic Range (in dB) = 20 log (2^12) = 20 log (4096) ≈ 72 dB
Dynamic Range (in volts) = 5 .2^12 = 5 (4096) = 20480 volts
It is essential to remember that all performance parameters of electronic components, including converters, can be influenced by variations in supply voltage and temperature. Datasheets commonly
specify these parameters under specific temperatures and supply voltage conditions to offer standardized information. However, in practical systems, operating conditions may deviate significantly
from the specified figures. As a result, actual performance can differ from what is outlined in the datasheet.
• The real-world analog input to an ADC is a continuous signal with an infinite number of possible states, whereas the digital output is, by its nature, a discrete function with a finite number of
different states.
• An ADC is a device that performs PCM. It samples and translates an analog signal into a digital format, where each sample is represented by a binary code.
• A digital binary code is converted to an analog output (current or voltage) by a DAC.
• Quantization Error (Q[e]), also known as quantization noise, is the error introduced during the process of converting a continuous analog signal into a discrete digital representation. It is
essentially the error caused by approximating the continuous signal with discrete digital values. Obviously, the resulting round-off creates some errors in the digital representation. It results
in a deviation between the actual analog value and its digital representation.
• There may be a difference of up to ½ LSB between the actual input and its digital form.
• This error can be reduced by increasing resolution so that finer steps may be detected.
• For A/D circuits, the resolution is the smallest input voltage that is detected by the system. Resolution is the smallest standard incremental change in the output voltage of a DAC. The number of
discrete steps or bits that an ADC/DAC can represent, determines its precision in converting analog signals to digital data or vice versa. Typically, the resolution is specified using a number of
bits in digital codes (n), although a voltage specification (LSB) is also possible.
• The sampling rate is the frequency at which the ADC samples the analog input signal to convert it into discrete digital data points.
• For A/D converters, the speed is specified as the conversion time i.e., the time to perform a single conversion process. For D/A converters, the speed is specified as the settling time e., the
delay between the binary data appearing at the input and a stable voltage being obtained at the output.
• As the number of bits increases, the step size between quantization levels decreases. Therefore, the accuracy of the system is increased when a conversion is made between an analog and digital
• The dynamic range (DR) of an ADC is the ratio of the largest to the smallest signals the converter can represent. It measures the range of signal amplitudes that an ADC can accurately represent
in its digital output without significant distortion.
Inline Feedbacks
View all comments
|
{"url":"https://www.electronics-lab.com/article/analog-to-digital-conversion-performance-criteria/","timestamp":"2024-11-05T13:53:12Z","content_type":"text/html","content_length":"223442","record_id":"<urn:uuid:7c591ee5-ccd8-4c9b-93e1-3cd28252343c>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00707.warc.gz"}
|
What is the solution set for 4x-5=5x-10? | HIX Tutor
What is the solution set for #4x-5=5x-10#?
Answer 1
Sign up to view the whole answer
By signing up, you agree to our Terms of Service and Privacy Policy
Answer 2
To find the solution set for the equation 4x - 5 = 5x - 10, we need to isolate the variable x.
First, we can simplify the equation by moving all the terms containing x to one side and constants to the other side.
Adding 10 to both sides, we get: 4x - 5 + 10 = 5x - 10 + 10 4x + 5 = 5x
Now, subtracting 4x from both sides, we get: 4x - 4x + 5 = 5x - 4x 5 = x
So, the solution set for the equation is {5}.
Sign up to view the whole answer
By signing up, you agree to our Terms of Service and Privacy Policy
Answer from HIX Tutor
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
Not the question you need?
HIX Tutor
Solve ANY homework problem with a smart AI
• 98% accuracy study help
• Covers math, physics, chemistry, biology, and more
• Step-by-step, in-depth guides
• Readily available 24/7
|
{"url":"https://tutor.hix.ai/question/what-is-the-solution-set-for-4x-5-5x-10-8f9af8f8f7","timestamp":"2024-11-01T23:34:17Z","content_type":"text/html","content_length":"566834","record_id":"<urn:uuid:e249fc5a-3725-4a19-82c4-c33e66b1677c>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00180.warc.gz"}
|
Thread about an unsolvable riddle?
Thread about an unsolvable riddle? August 20, 2014 10:29 AM Subscribe
I can't seem to locate a thread I read here once about an impossible riddle or logic puzzle. I don't recall the riddle itself except that it was math-related, and the answers were multiple choice
series of percentages: 50%, 25%, 10%, etc. The ensuing metafilter meltdown over the answer was highly entertaining, but I foolishly didn't mark it as a favorite, and now my searches are coming up
empty. Can anyone help?
I don't know if this is the one you're thinking of specifically, but there've been a couple threads talking about the infamously counter-intuitive Monty Hall problem, including
this one
from several years ago and a more recent related one about
opportunity cost and concert tickets
posted by cortex (staff) at 10:31 AM on August 20, 2014 [2 favorites]
If it's the one I remember, the question was something like "What is the probability of answering this question correctly?". It creates a feedback between what you choose and what the right answer
is. I'll look around for it.
posted by benito.strauss at 10:40 AM on August 20, 2014 [2 favorites]
Benito.strauss and zamboni have it! And thanks to Cortex, I have two other new threads for lunch break reading. Thanks so much!
posted by backwards compatible at 10:44 AM on August 20, 2014 [1 favorite]
5 minutes ago I would have said the chance of me taking some ibuprofen was 50%. Now it's definitely 100%.
posted by Marie Mon Dieu at 11:15 AM on August 20, 2014 [3 favorites]
If enough people think about this we end up destroying the Matrix so keep circulating those tapes!
posted by Potomac Avenue at 12:51 PM on August 20, 2014 [2 favorites]
I love this problem, because the answer is so obviously "those were the times that I carried you."
posted by gauche at 12:58 PM on August 20, 2014 [17 favorites]
The ultimate answer to any and every question is
it depends on what you mean by [question]
For example, the idea that we should rely on the lettered options provided is not indicated by the question itself. In their absence, our answer must be...
The abyss just gazed into me, and now
have a headache.
posted by The Confessor at 1:24 PM on August 20, 2014 [4 favorites]
I think the question is improved if c) 60 is deleted and d) none of the above is added, making the choices a) 25 b) 50 c) 25 d) none of the above.
As originally posed, I can buy into the "0% theory", since whichever of the enumerated answers you choose leads to an inconsistent situation. But with "none of the above" as an alternative, even the
"0% theory" doesn't liberate you from choosing an answer which isn't present to give some claim of a consistent system.
posted by jepler at 2:45 PM on August 20, 2014 [2 favorites]
> I love this problem, because the answer is so obviously "those were the times that I carried you."
Well, it's a math problem, so it's more likely the answer is "those were the time I carried two".
posted by benito.strauss at 3:30 PM on August 20, 2014 [14 favorites]
I think the question is improved if c) 60 is deleted and d) none of the above is added, making the choices a) 25 b) 50 c) 25 d) none of the above.
But if you mean that "none of the above" would be right, then the answer is 25%. But then A and C are also right, so the answer is 75%. But if the answer is 75%, then A, B, and C are wrong, so the
answer is "none of the above." But then the answer is 25% ...
posted by John Cohen at 7:35 PM on August 20, 2014 [1 favorite]
If you pick 50% or 60% then the answer is 25%. If you pick 25% then the answer is 50%.
So it's impossible to pick a right answer.
posted by Chocolate Pickle at 7:40 PM on August 20, 2014
Jepler is saying that "none of the above" itself includes "0%", which would make it the correct answer, except then if 1/4 of the answers is correct then 25% of random guesses will get it, et cetera.
posted by teremala at 8:05 PM on August 20, 2014
Jepler is saying that "none of the above" itself includes "0%", which would make it the correct answer, except then if 1/4 of the answers is correct then 25% of random guesses will get it, et cetera.
That's why I'm saying that changing "60%" to "none of the above" makes it no less paradoxical.
posted by John Cohen at 9:55 PM on August 20, 2014
That's why I'm saying that changing "60%" to "none of the above" makes it no less paradoxical.
The point is that it currently isn't paradoxical, the answer simply isn't a-d, it's secret option e, 0%. If 60% is replaced with 0% then there is now no correct answer.
posted by Cannon Fodder at 12:25 AM on August 21, 2014 [1 favorite]
I'm not quite convinced, jepler. Once you answer "none of the above", you're home free. You've answered the question "what is the chance you will be correct?" And you close the book.
"But if the answer is D, then the answer is really 25%, and that leads to an inconsistency!"
Nope, you don't have to go there. Once you've answered "none of the above", you're done. It's not an affirmative chance statement that affects the other answers.
posted by naju at 1:30 AM on August 21, 2014
(To be clear, I think it ultimately changes the question into a philosophical one on language and logic, i.e. "can something be an answer, a non-answer and a denial of the possibility of an answer at
the same time?" It can. It's just not satisfying, but we don't need satisfying. Talk to me further and I'll explain why the impossibility of God is actually proof of God, in between massive bong
posted by naju at 1:53 AM on August 21, 2014
The World Famous
: "
The abyss just gazed into me, and now I have a headache.
I haven't given a moment's thought to The Simpsons in longer than I can recall, but that's got to be a Ralph Wiggum quote, right?
I couldn't tell if
was making another referential joke that I'm not familiar with, or if he actually thought the "that's where I'm a viking!" thing originated on mefi...
posted by Grither at 4:27 AM on August 21, 2014
I love this problem, because the answer is so obviously "those were the times that I carried you."
Friend of mine had the "Footprints" poster on his way, but he'd used Photoshop wizardry to change it, so his read,
"But Lord, at my worst times I looked down and there were only one set of footprints in the sand,"
and the Lord said,
"Yeah, those were the times when you were a real downer to be around and an asshole and I can't abide assholes."
He had it on his wall for years and says I was the only one to ever notice. Everyone else just read the first line and knew what it was and moved on.
posted by cjorgensen at 6:26 AM on August 21, 2014 [6 favorites]
The point is that it currently isn't paradoxical, the answer simply isn't a-d, it's secret option e, 0%. If 60% is replaced with 0% then there is now no correct answer.
Sure it's paradoxical. The implication is that there's a right answer. I know: there just is no right answer. But if you don't think that's a paradox, I'd suggest looking into the meaning of the word
"paradox." It might be subtler than you think.
posted by John Cohen at 6:30 AM on August 21, 2014
(If you interpret the word "paradox" narrowly and strictly enough — two things that are true but mutually incompatible — there's no such thing as a paradox!)
posted by John Cohen at 6:31 AM on August 21, 2014
Nope, just a reference to Nietzsche, and a rephrase of
Marie Mon Dieu
's ibuprofen comment.
posted by The Confessor at 7:30 AM on August 21, 2014
Well, it's a math problem, so it's more likely the answer is "those were the time I carried two".
I wish I could favorite that twice, benito.strauss. That is the best pun I have heard in an indeterminate period of time.
posted by maryr at 8:03 AM on August 21, 2014 [2 favorites]
We've quips and quibbles heard in flocks, but none to beat this paradox!
posted by Kabanos at 9:28 AM on August 21, 2014
cjorgensen, the best
of the Footprints poster I've even seen has Christ respond "Oh, that's when I was surfing."
If your friend's poster looks something like
, they could also photoshop in a small image on the distant waves, long hair an robe flapping in the wind.
posted by benito.strauss at 10:19 AM on August 21, 2014 [2 favorites]
If you interpret the word "paradox" narrowly and strictly enough — two things that are true but mutually incompatible — there's no such thing as a paradox!
Israel has a right to defend itself.
Palestine has a right to exist free of occupation by a foreign power.
posted by flabdablet at 10:22 AM on August 21, 2014
Chocolate Pickle
: "
If you pick 50% or 60% then the answer is 25%. If you pick 25% then the answer is 50%.
So it's impossible to pick a right answer.
You're not picking 25 percent, though. You're picking A or C. Don't confuse the key for the value.
posted by boo_radley at 10:58 AM on August 21, 2014 [3 favorites]
The thing you have to remember about "Footprints" is that
are not the intended audience. It was written for the sort of Christian so married to their faith that they cannot even conceive of the reality that the circumstances of our lives are the result of
human action or inaction upon an environment that is essentially random for its complexity.
I was on the verge of calling it a "new parable" when it hit me: most of the parables of Jesus have a moral lesson that applies even beyond the context of Christian faith.
The sole purpose of "Footprints" is to say "Hey, you! Struggling with your faith? Had a few recent setbacks? Here's a facile fantasy to help you square your unfortunate experiences with the existence
of a God worthy of worship."
posted by The Confessor at 10:58 AM on August 21, 2014 [2 favorites]
oh god its happening again
posted by Hoopo at 1:48 PM on August 21, 2014
(At least nobody's claiming every true or false statement has, by definition, a 50/50 chance of being one or the other. I skimmed through the original thread, started getting...agitated when that
theme showed up, and then -- finally -- remembered I'd commented in that thread however many years ago, and that I was maybe a bit of a jerk about it.)
posted by nobody at 5:31 PM on August 21, 2014
So did the person who created it say there was an answer and if so what is it?
posted by Carillon at 6:01 PM on August 21, 2014
Here's a paradox for the Monty Hall problem, which I've been thinking about since cortex mentioned it.
You have a 2/3 chance of being right if you switch, and a 1/3 chance of being right if you stay.
What if you obliterate this information? Either pick a door based on the flip of a coin, or have someone who doesn't know which door you picked, pick one of the remaining doors? Is the chance 50/50,
or does it remain 2/3 to 1/3?
posted by graymouser at 7:57 AM on August 22, 2014
What's important is that Monty Hall has two doors (2/3 chance of the car) and always narrows it down to one door by showing you a goat. Thus you only get the better odds if you know which door Monty
Hall has left unopened. If you don't know which door is Monty Hall's remainder and which was the original choice, your odds are 1/2, the same as if you begin the game with just two doors.
posted by Thing at 9:23 AM on August 22, 2014
The key factor is whether the door the person who chooses a door to open is based on knowledge of what's behind the doors; the thing Monty will never, ever do is pick a door with the prize behind it
to open, because he'd be losing the game for you. So any replacement system has to either (a) maintain that function of avoiding-the-winning-door or (b) fundamentally changes the setup.
Both your proposed mechanics break the game's assumptions taken at face value:
- Flip a coin when the player's chosen a non-winner and you'll reveal a winner half the time. As the player will initially choose a non-winner in two thirds of all cases, that means .666 * .5 = .333
of all games will end with a coin flip opening the winning door and you're presumably not allowed to switch to the winning door once it's revealed, so you've lost. The remaining two thirds of cases
are split evenly between the other two doors, which each have equal chances of being the winner, so your chances of winning by either sticking or switching are even at .5 vs .5. That's .5 chance of
being correct to stick or switch * .666 of games = .333 chance of winning all in all. One third of the time you second-guess right and win, one third of the time you second-guess wrong and lose, and
one third of the time you don't a chance to second guess because the coinflip opens the winner door and loses the game out from under you. p = .333 and the game develops a new weird instant-loser
- Have hapless, inattentive Milton Hall, who was distracted by a bright light on the wall and so doesn't know what door you chose, pick at random a door to choose and one third of the time he'll
choose the same door you chose. Given that it was your first choice, let's suppose that if it opens on a prize that means you win immediately because you'd be an idiot to switch to another door; if
it does not open on a prize, it's a useful hint and you get to make your second guess with the knowledge that you should definitely switch away from that door. So: in one third of cases, Milton picks
the same as you; in two thirds he picks other doors. In the case where he picks the same as you, one third of
will be winners, so that's .333 * .333 = .111 total wins. In two thirds of cases, Milton chooses differently from you; one third of
will be Milton choosing the the winning door by chance, losing you the game, so that's .666 * .333 = .222 total losses. The remaining cases, Milton chooses the same non-winner door as you and Milton
chooses a non-winning different door than you, all reduce to a .5 vs .5 guess as to whether your original or the remaining door is correct. So that's the remaining .666 of cases with .5 chance of
winning, .666 * .5 = .333 winning on second guess results. Add to that the .111 of same-guess instant win results and you've got a .444 chance or four ninths odds of winning. And, again, a somewhat
weirder flow of the game.
Both of those depend on some just-so handwaving on my part about how to deal with the hint revealing a winner or loser; you could tweak them so that e.g. the hint door revealing a chosen loser or
revealing an unchosen is not an instant loss but instead a really great hint and that would up the odds of winning in both cases significantly. But would
be weird.
Not that the aesthetics of the game show should matter for a probability story problem, but, hey, there's a certain elegance all else aside to the Monty Hall proposition.
posted by cortex (staff) at 9:30 AM on August 22, 2014
Leonard Mlodinow's
The Drunkard's Walk
explains the Monty Hall Problem very thoroughly...
I first saw this puzzle on Reddit and copied what I took to be the most thorough analysis
None of the choices are self-consistent.
If A or D is correct, that means that the probability of getting the correct answer is both 25% (because that's what A and D say) and 50% (because you have a 50% chance of choosing A or D. That's a
contradiction. It can't be both at once, so A and D are both wrong.
If B is correct, then the correct answer is both 50% (what it says) and 25% (the odds of choosing B). Same deal. B is self-contradictory, therefore wrong.
Likewise, if C is correct, then the answer is both 60% and 25%.
So none of the choices are right, and the actual probability of getting the right answer by choosing among them (by any means) is 0%. No paradox, no ambiguity, just a multiple-choice question that
doesn't give any right answers, like "What is the longest river in Europe? A) The Nile B) The Mississippi C) CowboyNeal"
The tricky part is that if you did include 0% among the answers -- replacing C, let's say -- it would stop being right. It would become subject to the same problem as the current C does: it would
imply both a 0% and a 25% chance of getting the correct answer. In that case, you wouldn't just have a multiple-choice question that omits the correct answer, but one that doesn't have a correct
answer, like "Is the correct answer to this question 'no'?" But paradoxes of this sort are well-understood and don't faze logicians.
The variant I find more interesting is when there's more than one self-consistent answer. Like, what if the choices were: A) 50% B) 25% C) 60% D) 50%? You could answer A/D without contradiction, but
you could also answer B without contradiction. You could even say "None of the answers are correct; the probability is 0%" without contradiction. But questions of the form "What is the probability of
event X?" aren't the sort of thing that can have more than one correct answer. You just have no basis for choosing one answer over another. Well, that's not unusual: it's easy to come up with
probability questions where you just don't have enough information to answer. (For example: "I have ten marbles in a bag. Some are black, some are white. If I draw one out, what is the probability
that it is black?") But this variant isn't quite like that: it's impossible that more information will allow us to choose one answer over another. It's as unanswerable as the paradoxical variant, but
without the paradox.
posted by lazycomputerkids at 10:10 AM on August 22, 2014 [1 favorite]
What if you obliterate this information? Either pick a door based on the flip of a coin, or have someone who doesn't know which door you picked, pick one of the remaining doors? Is the chance 50/50,
or does it remain 2/3 to 1/3?
I take it that by "remaining doors" you mean "doors Monty didn't open", and you're proposing to alter the game as follows:
1. Contestant nominates a door.
2. Monty chooses a different door that has a goat behind it, and opens it.
3. Contestant flips a coin. If the coin turns up heads the contestant opens the originally nominated door. If it turns up tails the contestant opens the other unopened door.
After the completion of step 2, it is certain that the car is behind either the originally chosen door or the the other unopened door. Picking one of those on a coin flip gives you a winning
probability of 1/2.
However, after step 2 it is also the case that the probability of the car being behind the originally nominated door is 1/3; behind the other unopened door, 2/3.
So picking your final door on a coin flip is a better idea than always staying with the original door, but a worse idea than always switching to the other unopened door.
If you want to break it down into cases, here are the cases:
1. Coin turns up heads (p = 1/2) and car is behind original door (p = 1/3); win (p = 1/6).
2. Coin turns up heads (p = 1/2) and car is behind other door (p = 2/3); lose (p = 1/3).
3. Coin turns up tails (p = 1/2) and car is behind original door (p = 1/3); lose (p = 1/6).
4. Coin turns up tails (p = 1/2) and car is behind other door (p = 2/3); win (p = 1/3).
The win and loss probabilities add up to 1/2 each.
posted by flabdablet at 12:05 PM on August 22, 2014
I love this problem, because the answer is so obviously "those were the times that I carried you."
The Onion is on it.
Sure, the sandal footprints came back when I got that big job promotion, but right at the point where my son Tommy died, they veer off again. Actually, now that I look again, it seems like
there's an unusually large distance between each of the sandal-wearer's footprints around the time of my son's death, as if the person were actually running away.
posted by el io at 2:23 PM on August 22, 2014 [3 favorites]
The only way to answer correctly is not to answer.
posted by dg at 5:35 PM on August 22, 2014
A rabbi, a priest, and a guru walk into a bar. The conditional probabilities of each one having a drink are 50%, 25%, and 10%. What is the probability all of them will get drunk?
Voted Second Prize for "Worst Joke" at the International Festival of Bad Humor.
posted by twoleftfeet at 7:09 PM on August 22, 2014
Right, but who cares about friggin probability.
DOES THE @#%#$ PLANE TAKE OFF OR NOT ?
posted by k5.user at 10:46 AM on August 25, 2014
Here's an insoluble logic puzzle for you: Does the set of all possible sets contain itself?
posted by clarknova at 5:45 PM on August 25, 2014
Look, Kurt, I told you to stay out of this tavern when I threw you out last time for making Bertrand cry.
posted by cortex (staff) at 6:04 PM on August 25, 2014 [1 favorite]
Does the set of all possible sets contain itself?
If you say so.
posted by flabdablet at 8:51 PM on August 25, 2014
Yes, like all of us, it tries to be inclusive.
posted by maryr at 9:42 PM on August 25, 2014
The complex number that electrical engineers conventionally refer to as j has long been
to be the same one that mathematicians conventionally refer to as i. But what if that's not true? What if j is actually -i? Is there any way to be sure?
posted by flabdablet at 10:15 PM on August 25, 2014
|
{"url":"https://metatalk.metafilter.com/23404/Thread-about-an-unsolvable-riddle","timestamp":"2024-11-05T16:47:02Z","content_type":"text/html","content_length":"63930","record_id":"<urn:uuid:3dd9f883-fbc2-4348-8a64-b4c5368f5eec>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00593.warc.gz"}
|
Wolfram Function Repository
Function Repository Resource:
Calculate a partial trace of a matrix
Contributed by: Jaroslav Kysela
calculates the partial trace of matrix mat over the n^th subspace, where mat is assumed to lie in a space constructed as a tensor product of subspaces with dimensions {d[1],d[2],…}.
calculates the partial trace of mat over the n^th subspace, where all subspaces have dimension d.
calculates the partial trace of mat over subspaces in positions {n[1],n[2],…}.
calculates the partial trace of mat over subspaces in consecutive positions {m,m+1,…,n}.
calculates the partial trace of mat over all subspaces except those in positions {n[1],n[2],…}.
calculates the partial trace of mat over all subspaces.
Details and Options
The partial trace is an operation that is widely used in quantum theory. The state of a subsystem can be retrieved from the state of the composite system by taking an appropriate partial trace.
The partial trace acts on square matrices and returns square matrices.
ResourceFunction["MatrixPartialTrace"] always returns a two-dimensional array, even in the case when the trace is taken over all subspaces.
ResourceFunction["MatrixPartialTrace"] works for numeric as well as symbolic matrices.
works also for
The following options can be given:
Method Automatic method to use for the calculation of the partial trace
"Verbose" False whether to print an additional summary of preprocessed input parameters
option can be set to one of the following values:
"TensorContract" use built-in function TensorContract to calculate the partial trace; usually faster for numeric matrices
"Sum" use built-in function Sum to calculate the partial trace; usually faster for symbolic matrices
Automatic use "TensorContract" when the input matrix is numeric, and "Sum" when the matrix is symbolic
In the special case of an empty list in the second argument, the trace is not evaluated and the input matrix is returned unaltered.
In the special case of a trace over all subspaces, the function
is used internally for both numeric and symbolic matrices.
Basic Examples (3) 
Consider a 4×4 matrix, which can be interpreted as an element of space , i.e. of the tensor product of two subspaces :
Calculate the partial trace over the second subspace :
Calculate a partial trace over multiple subspaces at once:
Calculate a partial trace of a numeric matrix:
Data types (3) 
Calculate a partial trace of a numeric matrix:
Calculate a partial trace of a symbolic matrix:
Calculate a partial trace of a SparseArray:
If the input is a SparseArray, so is the output. This is true even if the resulting array is just a 1×1 array:
Subspace specification (5) 
The second argument can contain negative numbers. In that case, the counting goes from the end of the list, in complete analogy to Take specification:
If the partial trace is taken only over one subspace, the second argument can be specified as the index of this subspace:
If the partial trace is to be taken over a range {a,…,b} of successive subspaces, the second argument can be specified as a;;b:
If the partial trace is to be taken over all but one subspace with index k, the second argument can also be specified as Except[k]:
More indices can be specified:
When the second argument is set to All, the partial trace is taken over all subspaces, which corresponds to the standard trace:
Dimension specification (2) 
If all subspaces have the same dimension, only this one dimension can be entered instead of the whole list:
Dimensions can be different for different subspaces. However, their product has to be equal to the dimension of the input matrix:
Calculate the partial trace using Mathematica’s built-in function TensorContract. This routine is usually faster for numeric matrices:
Calculate the partial trace using block-wise summation implemented by Mathematica’s built-in function Sum. This routine is usually faster for symbolic matrices:
By default, the "TensorContract" method is used, when the input matrix is numeric, and the "Sum" method is used when it is symbolic:
Compare the speed of different methods for numeric and symbolic matrices:
There are two special cases that do not follow the previously stated rules. The first is when the list of subspaces to be traced over is empty. In that case, the input matrix is returned:
The second case is when the partial trace is to be taken over all subspaces. In that case, Mathematica’s built-in function Tr is used internally instead:
When set to True, there is an additional summary of preprocessed values of parameters printed:
When the second argument is an empty list, the "method" item returns None:
When the second argument is the list of all subspaces, the routine internally uses Tr and the "method" item returns "Tr":
In quantum mechanics, a partial trace of a density matrix gives the quantum state of a subsystem.
Let ρ[12] be a density matrix of a system of two maximally entangled photons in their polarization:
The quantum state of one of the photons is obtained as a partial trace over the state of the other photon. In this case, the resulting state ρ[1] is maximally mixed:
The same result is obtained when tracing over the first photon to get the state ρ[2] of the second photon:
Generate a random quantum state of three spin-1/2 particles:
Matrix ρ[123] is a positive semidefinite matrix with unit trace and thus represents a valid density operator:
The state of the second particle is obtained as the partial trace of ρ[123] over the first and third particles:
This matrix again represents a valid density operator:
Properties and Relations (3) 
The order in which the subspaces are specified is irrelevant:
Successive applications of a partial trace for different subspaces gives the same results as a single application of a multi-subspace partial trace:
The partial trace over all subspaces corresponds to the standard trace:
Possible Issues (5) 
MatrixPartialTrace always returns a matrix, even when the trace is taken over all subspaces:
The trace over all subspaces can be calculated also using Tr, which returns the sum of diagonal elements:
The same is true also when the input matrix is a SparseArray:
When both positive and negative indices are used in the second argument, it might happen that multiple indices refer to the same subspace. This case is nevertheless not allowed:
For some settings of the initial index, final index, and the step in the Span specification, undesired behavior may occur:
Use "Verbose"→True to see how the input parameters are interpreted:
When the indices to be excluded from the tracing are out of the valid range, the trace is done over all subspaces:
Note that when tracing over multiple subspaces one by one, the position and dimensions of subspaces in each new application of the partial traces may change:
When the tracing proceeds from the end of the list of positions, here {1,2}, no recalculation of subspace positions is necessary:
Neat Examples (1) 
Plot the partial trace over an increasing number of subspaces:
Related Links
Version History
Related Symbols
License Information
|
{"url":"https://resources.wolframcloud.com/FunctionRepository/resources/MatrixPartialTrace/","timestamp":"2024-11-11T01:56:51Z","content_type":"text/html","content_length":"113535","record_id":"<urn:uuid:0c8b20bf-ea84-4fae-95cf-205481a57a14>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00497.warc.gz"}
|
If a linear function f satisfices f(3)=10 and f(7)=18, what is ... | Filo
If a linear function satisfices and , what is the value of ?
Not the question you're searching for?
+ Ask your question
Since function is linear then,
and , what is the value of ?
Was this solution helpful?
Found 2 tutors discussing this question
Discuss this question LIVE for FREE
7 mins ago
One destination to cover all your homework and assignment needs
Learn Practice Revision Succeed
Instant 1:1 help, 24x7
60, 000+ Expert tutors
Textbook solutions
Big idea maths, McGraw-Hill Education etc
Essay review
Get expert feedback on your essay
Schedule classes
High dosage tutoring from Dedicated 3 experts
Practice questions from Functions in the same exam
Practice more questions from Functions
View more
Practice questions on similar concepts asked by Filo students
View more
Stuck on the question or explanation?
Connect with our Mathematics tutors online and get step by step solution of this question.
231 students are taking LIVE classes
Question Text If a linear function satisfices and , what is the value of ?
Updated On Apr 16, 2023
Topic Functions
Subject Mathematics
Class Grade 12
Answer Type Text solution:1 Video solution: 1
Upvotes 165
Avg. Video Duration 11 min
|
{"url":"https://askfilo.com/mathematics-question-answers/if-a-linear-function-f-satisfices-f310-and-f718-what-is-the-value-of-f5","timestamp":"2024-11-08T21:08:45Z","content_type":"text/html","content_length":"394658","record_id":"<urn:uuid:15b891c8-99c3-4cab-945b-020c24a7cf16>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00449.warc.gz"}
|
Draws a set of points
If Points is a sequence of tuples: Points[N][0] is the x-coordinate of point N and Points[N][1] is the y-coordinate.
If Points is a NumPy array: Points[N,0] is the x-coordinate of point N and Points[N,1] is the y-coordinate for arrays.
Each point will be drawn the same color and Diameter. The Diameter is in screen pixels, not world coordinates.
The hit-test code does not distinguish between the points, you will only know that one of the points got hit, not which one. You can use PointSet.FindClosestPoint(WorldPoint) to find out which one
In the case of points, the HitLineWidth is used as diameter.
Class Hierarchy
Class API
class PointSet(PointsObjectMixin, ColorOnlyMixin, DrawObject)
Draws a set of points
If Points is a sequence of tuples: Points[N][0] is the x-coordinate of point N and Points[N][1] is the y-coordinate.
If Points is a NumPy array: Points[N,0] is the x-coordinate of point N and Points[N,1] is the y-coordinate for arrays.
Each point will be drawn the same color and Diameter. The Diameter is in screen pixels, not world coordinates.
The hit-test code does not distinguish between the points, you will only know that one of the points got hit, not which one. You can use PointSet.FindClosestPoint(WorldPoint) to find out which
In the case of points, the HitLineWidth is used as diameter.
|
{"url":"https://docs.wxpython.org/wx.lib.floatcanvas.FCObjects.PointSet.html","timestamp":"2024-11-12T19:03:46Z","content_type":"application/xhtml+xml","content_length":"17034","record_id":"<urn:uuid:5baadcd5-3cc8-4625-afa3-94a4c8b89014>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00089.warc.gz"}
|
Change of Variables for Elliptic Integral
• Thread starter McCoy13
• Start date
In summary: However, I did not miss any terms. I have no idea how I got 31.In summary, the conversation discusses how to reduce a given differential equation to a simpler form using a substitution of
dependent variable and a scaling change of variables. The process involves using the product rule and choosing appropriate values for the parameters introduced in the change of variables. The final
simplified equation can be further reduced by choosing a value for another parameter.
Homework Statement
Given the differential equation
use the substitution of dependent variable
[tex]u=ve^{ \alpha x + \beta y}[/tex]
and a scaling change of variables
[tex]y'= \gamma y[/tex]
to reduce the differential equation to
Homework Equations
I have no idea
The Attempt at a Solution
I tried a direct substitution of both variables:
[tex]u_{x}=\alpha ve^{\alpha x+\beta y}[/tex]
[tex]u_{xx}=\alpha^{2}ve^{\alpha x+\beta y}[/tex]
[tex]u_{y}=\beta ve^{\alpha x+\beta y}[/tex]
[tex]u_{yy}=\beta^{2} ve^{\alpha x+\beta y}[/tex]
Plugging in this gives
[tex]\alpha^{2} ve^{\alpha x+\beta y}+3\beta^{2}ve^{\alpha x+\beta y}-2\alpha ve^{\alpha x+\beta y}+24\beta ve^{\alpha x+\beta y}+5ve^{\alpha x+\beta y}[/tex]
You can obviously factor out [itex]ve^{\alpha x+\beta y}[/itex], but that doesn't really do much for you. I also tried doing this with the y' substitution. It also occurred to me that since v is
probably supposed to be understood as v(x,y), I tried this set of substitutions:
[tex]u_{x}=\alpha ve^{\alpha x+\beta y}+v_{x}e^{\alpha x+\beta y}[/tex]
[tex]u_{xx}=\alpha^{2} ve^{\alpha x+\beta y}+\alpha v_{x}e^{\alpha x+\beta y}+v_{xx}e^{\alpha x+\beta y}[/tex]
[tex]u_{x}=\beta ve^{\alpha x+\beta y}+v_{y}e^{\alpha x+\beta y}[/tex]
[tex]u_{xx}=\beta^{2} ve^{\alpha x+\beta y}+\beta v_{y}e^{\alpha x+\beta y}+v_{yy}e^{\alpha x+\beta y}[/tex]
None of these attempts gave me any insight into the problem.
Last edited:
You need to treat [itex]v[/itex] as a function of [itex]x[/itex] and [itex]y[/itex] and use the product rule to differentiate [itex]u(x,y)=v(x,y)e^{\alpha x+\beta y}[/itex].
Also, your [itex]\LaTeX[/itex] isn't displaying properly because you aren't puuting spaces between \alpha and x (or \beta and y )
gabbagabbahey said:
You need to treat [itex]v[/itex] as a function of [itex]x[/itex] and [itex]y[/itex] and use the product rule to differentiate [itex]u(x,y)=v(x,y)e^{\alpha x+\beta y}[/itex].
Also, your [itex]\LaTeX[/itex] isn't displaying properly because you aren't puuting spaces between \alpha and x (or \beta and y )
I fixed the LaTeX and (hopefully now that it's displaying correctly), you'll see that I used the product rule at the bottom of my attempted solution. However, it is non-obvious to me how making this
correction by using the product rule helps me. I will have lots of first order partial derivatives floating around that are not in the desired equation.
McCoy13 said:
However, it is non-obvious to me how making this correction by using the product rule helps me. I will have lots of first order partial derivatives floating around that are not in the desired
You'll end up with a bunch of terms involving [itex]v[/itex] and its partial derivatives, all multyiplied by [itex]e^{\alpha x+\beta y}[/itex], which you can factor out of your DE (since it is never
zero, getting rid of this factor doesn't exclude any solutions)... giving you a different DE for [itex]v[/itex]...one that you can simplify by choosing nice values for [itex]\alpha[/itex] and [itex]\
Give it a shot and post your attempt.
gabbagabbahey said:
You'll end up with a bunch of terms involving [itex]v[/itex] and its partial derivatives, all multyiplied by [itex]e^{\alpha x+\beta y}[/itex], which you can factor out of your DE (since it is
never zero, getting rid of this factor doesn't exclude any solutions)... giving you a different DE for [itex]v[/itex]...one that you can simplify by choosing nice values for [itex]\alpha[/itex]
and [itex]\beta[/itex].
Give it a shot and post your attempt.
Haha, it did not occur to me to simply
alpha and beta, even though they are arbitrary parameters introduced in the change of variables.
I ended up with [itex]v_{xx}+3v_{yy}-31v[/itex], and I'm assuming you can take care of the factor of 3 in front of [itex]3v_{yy}[/itex] by simply correctly setting [itex]\gamma[/itex] when you
substitute in y'.
McCoy13 said:
Haha, it did not occur to me to simply pick alpha and beta, even though they are arbitrary parameters introduced in the change of variables.
I ended up with [itex]v_{xx}+3v_{yy}-31v[/itex], and I'm assuming you can take care of the factor of 3 in front of [itex]3v_{yy}[/itex] by simply correctly setting [itex]\gamma[/itex] when you
substitute in y'.
I think the factor of -31 might be a little off (my back of envelope calc gave me a factor of -49), so you'll probably want to double check that. But otherwise, yes...can you see what value of [itex]
\gamma[/itex] will get rid of the factor of 3?
I used [itex]\gamma = \sqrt{3}[/itex]. This is correct? If not, perhaps [itex]\frac{1}{\sqrt{3}}[/itex].
McCoy13 said:
I used [itex]\gamma = \sqrt{3}[/itex]. This is correct? If not, perhaps [itex]\frac{1}{\sqrt{3}}[/itex].
You tell me...the chain rule tells you that [itex]v_y(x,y'(y))=\frac{dy'}{dy}v_{y'}[/itex], so what value of [itex]\gamma[/itex] makes [itex]v_{y'y'}=3v_{yy}[/itex]?
gabbagabbahey said:
You tell me...the chain rule tells you that [itex]v_y(x,y'(y))=\frac{dy'}{dy}v_{y'}[/itex], so what value of [itex]\gamma[/itex] makes [itex]v_{y'y'}=3v_{yy}[/itex]?
[tex]\frac{d^{2}y'}{dy^{2}}=0 \Rightarrow \gamma v_{y'y'}=v_{yy}[/tex]
[tex]\gamma = 1/3[/tex]
McCoy13 said:
[tex]\frac{d^{2}y'}{dy^{2}}=0 \Rightarrow \gamma v_{y'y'}=v_{yy}[/tex]
[tex]\gamma = 1/3[/tex]
Ermm... shouldn't you have
Yes, I should. Forgot to apply chain rule while using product rule. Bah! Thanks for all the help.
Also, I rechecked the 31, and I got it right unless I made a mistake in my substitution or if I missed a term while I was gathering terms. I'll double check it from the start before I hand it in.
EDIT: Upon reviewing the work, 49 is the correct number, not 31.
Last edited:
FAQ: Change of Variables for Elliptic Integral
1. What is a change of variables for elliptic integral?
A change of variables for elliptic integral is a mathematical technique used to simplify or solve integrals involving elliptic functions. It involves substituting a new variable into the integral to
transform it into a simpler form.
2. Why is a change of variables necessary for solving elliptic integrals?
Elliptic integrals are notoriously difficult to solve because they involve complex functions such as elliptic functions and theta functions. A change of variables allows us to transform the integral
into a simpler form that is easier to solve.
3. What are the common variables used in a change of variables for elliptic integrals?
The most commonly used variables in a change of variables for elliptic integrals are the Weierstrass elliptic function, the Jacobi elliptic functions, and the theta functions. These functions are
used to transform the integral into a more manageable form.
4. How does a change of variables affect the limits of integration in elliptic integrals?
When performing a change of variables, the limits of integration may also need to be adjusted to account for the new variable. This is necessary to ensure that the integral is still being evaluated
over the same region.
5. Are there any limitations to using a change of variables for elliptic integrals?
While a change of variables can greatly simplify the solution of elliptic integrals, it is not always possible to find a suitable substitution. In some cases, the integral may become more complex or
even impossible to solve after the substitution is made.
|
{"url":"https://www.physicsforums.com/threads/change-of-variables-for-elliptic-integral.431065/","timestamp":"2024-11-06T21:35:47Z","content_type":"text/html","content_length":"127502","record_id":"<urn:uuid:889bc216-b82e-403e-ac09-e31054fecb6d>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00444.warc.gz"}
|
What is Lift Force - Definition
What is Lift Force – Definition
In general, the lift is an upward-acting force on an aircraft wing or airfoil. There are several ways to explain how an airfoil generates lift. Lift Force
Bernoulli’s Equation
The Bernoulli’s equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids. It is one of the most important/useful equations in fluid
mechanics. It puts into a relation pressure and velocity in an inviscid incompressible flow. Bernoulli’s equation has some restrictions in its applicability, they summarized in following points:
• steady flow system,
• density is constant (which also means the fluid is incompressible),
• no work is done on or by the fluid,
• no heat is transferred to or from the fluid,
• no change occurs in the internal energy,
• the equation relates the states at two points along a single streamline (not conditions on two different streamlines)
Under these conditions, the general energy equation is simplified to:
This equation is the most famous equation in fluid dynamics. The Bernoulli’s equation describes the qualitative behavior flowing fluid that is usually labeled with the term Bernoulli’s effect. This
effect causes the lowering of fluid pressure in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so
when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy. The dimensions of terms in the
equation are kinetic energy per unit volume.
Lift Force – Bernoulli’s Principle
Newton’s third law states that the lift is caused by a flow deflection.
In general, the lift is an upward-acting force on an aircraft wing or airfoil. There are several ways to explain how an airfoil generates lift. Some theories are more complicated or more
mathematically rigorous than others. Some theories have been shown to be incorrect. There are theories based on the Bernoulli’s principle and there are theories based on directly on the Newton’s
third law.
The explanation based on the Newton’s third law states that the lift is caused by a flow deflection of the airstream behind the airfoil. The airfoil generates lift by exerting a downward force on the
air as it flows past. According to Newton’s third law, the air must exert an upward force on the airfoil. This is very simple explanation.
According to the Bernoulli’s principle, faster moving air exerts less pressure, and therefore the air must exert an upward force on the airfoil (as a result of a pressure difference).
Bernoulli’s principle combined with the continuity equation can be also used to determine the lift force on an airfoil, if the behaviour of the fluid flow in the vicinity of the foil is known. In
this explanation the shape of an airfoil is crucial. The shape of an airfoil causes air to flow faster on top than on bottom. According to Bernoulli’s principle, faster moving air exerts less
pressure, and therefore the air must exert an upward force on the airfoil (as a result of a pressure difference).
Bernoulli’s principle
requires airfoil to be of an
asymmetrical shape
. Its surface area must be
greater on the top
than on the bottom. As the air flows over the airfoil, it is displaced more by the top surface than the bottom. According to the
continuity principle
, this displacement must lead to an
increase in flow velocity
(resulting in a decrease in pressure). The flow velocity is increased some by the bottom airfoil surface, but considerably less than the flow on the top surface. The lift force of an airfoil,
characterized by the
lift coefficient
, can be changed during the flight by changes in shape of an airfoil. The lift coefficient can thus be even doubled with relatively simple devices (
flaps and slats
) if used on the full span of the wing.
The use of Bernoulli’s principle may not be correct. The Bernoulli’s principle assumes incompressibility of the air, but in reality the air is easily compressible. But there are more limitations of
explanations based on Bernoulli’s principle. There are two main popular explanations of lift:
• Explanation based on downward deflection of the flow – Newton’s third law
• Explanation based on changes in flow speed and pressure – Continuity principle and Bernoulli’s principle
Both explanations correctly identifies some aspects of the lift forces but leaves other important aspects of the phenomenon unexplained. A more comprehensive explanation involves both changes in flow
speed and downward deflection and requires looking at the flow in more detail.
See more: Doug McLean, Understanding Aerodynamics: Arguing from the Real Physics. John Wiley & Sons Ltd. 2013. ISBN: 978-1119967514
We hope, this article, Lift Force, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about
thermal engineering.
|
{"url":"https://www.thermal-engineering.org/what-is-lift-force-definition/","timestamp":"2024-11-09T06:49:53Z","content_type":"text/html","content_length":"454689","record_id":"<urn:uuid:c57df807-5b30-41c6-8f6c-3c6806c79f9d>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00153.warc.gz"}
|
Understanding the Different Types of Mathematical Homework and How to Tackle Them - thekeepmagazine.com
Understanding the Different Types of Mathematical Homework and How to Tackle Them
by Mona Evans
written by Mona Evans
Mathematics is one of those subjects that has different challenges. The way to handle mathematical homework often seems really intimidating to many people. Its type will, of course, specify the
approach, and there is a full list of types. Knowing how to deal with each of them ensures the process runs as smoothly as possible. These can be dealt with the right strategies and tools in hand,
especially when one has at hand the existence of a homework pdf solver one can rely on.
1. Number Operations Homework
Most mathematical problems relate with number operations. This includes basic arithmetic operations, which include addition, subtraction, multiplication, and division. When reviewing this type of
homework, attention to detail must be followed through; otherwise, an error that is as small as one misplaced digit can lead the student to the wrong solution. Tips for Tackling:
• Break down complex expressions into smaller steps.
• Use tools like calculators to verify manual work.
• Ensure understanding of order of operations (PEMDAS).
2. Algebraic Equations
Algebra introduces variables and unknowns into equations, making it a bit more abstract. This type of homework often requires solving for an unknown value or simplifying expressions. Identifying
patterns and using algebraic rules correctly is essential here. Tips for Tackling:
• Start by simplifying equations where possible.
• Apply the distributive property and combine like terms.
• Don’t forget to isolate the variable to one side when solving equations.
3. Geometry and Shape Problems
Geometry focuses on shapes, angles, and their properties. Geometric problems often involve diagrams, so visual understanding plays a significant role. Whether it’s calculating the area, perimeter, or
volume, precision is vital. Tips for Tackling:
• Draw diagrams if they’re not provided.
• Label all relevant parts of the diagram.
• Use formulas carefully for different shapes (e.g., area of a triangle, circumference of a circle).
4. Word Problems
A word problem is something that is described in words and translated into a mathematical equation or expression. This is a homework assignment designed to test students’ understanding and their
problem-solving skills. Tips for Tackling:
• Read the problem carefully to understand what is being asked.
• Identify key pieces of information and disregard irrelevant details.
• Set up equations based on the relationships described in the problem.
5. Trigonometry Problems
Trigonometry deals with the relationships between angles and sides of triangles. Sometimes, trigonometric problems contain functions or quantities like sine, cosine, and tangent. Learning how to use
these functions provides the approach for solving such problems. Tips for Tackling:
• Familiarize yourself with key trigonometric identities and functions.
• Memorize the unit circle for quick reference to common angle measures.
• Use calculators with trigonometric functions when necessary.
6. Calculus and Advanced Topics
Calculus about rates of change and areas under curves is really one of the toughest types of homework, normally involving the main students in math. Problems can be questions which are based on
differentiation, integration or limits. Tips for Tackling:
• Break down the problem into smaller parts.
• Ensure understanding of basic calculus rules like the chain rule or product rule.
• Practice regularly to become comfortable with differentiation and integration techniques.
Modern tools like Gauth, an AI-based homework helper, offer valuable assistance in solving mathematical problems. This technology can break down complex equations, provide step-by-step solutions, and
offer explanations for better understanding.
Each type of mathematical homework requires a unique approach, and understanding the underlying principles is crucial for tackling them effectively. From basic arithmetic to advanced calculus,
knowing which strategies to employ can significantly enhance performance. For those looking for additional support, a reliable homework PDF solver like Gauth offers a streamlined and efficient way to
overcome challenges.
Leave a Comment Cancel Reply
0 comment 0 FacebookTwitterPinterestEmail
Mona Evans
Mona Evans is a technician about cell phone. She works for a technology company. and has extensive research and development experience. She has a unique perspective and confidence in the future and
development of technology and writes many related blogs.
You may also like
|
{"url":"https://thekeepmagazine.com/understanding-the-different-types-of-mathematical-homework-and-how-to-tackle-them/","timestamp":"2024-11-11T13:50:19Z","content_type":"text/html","content_length":"113046","record_id":"<urn:uuid:16033e3f-9f26-45f4-bdde-a78942db802e>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00348.warc.gz"}
|
An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations
We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity
measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of
compressible Navier–Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and
kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state
provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L^3-based conditions. These conditions involve space-time Besov regularity, but we show that
they are satisfied by Euler solutions that possess similar space regularity uniformly in time.
All Science Journal Classification (ASJC) codes
• Statistical and Nonlinear Physics
• Mathematical Physics
Dive into the research topics of 'An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations'. Together they form a unique fingerprint.
|
{"url":"https://collaborate.princeton.edu/en/publications/an-onsager-singularity-theorem-for-turbulent-solutions-of-compres","timestamp":"2024-11-01T21:05:22Z","content_type":"text/html","content_length":"49950","record_id":"<urn:uuid:432d2d0b-25da-4fae-ac8f-35b41232919d>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00214.warc.gz"}
|
how to measure construct validity in spss
Convergent validity and divergent validity are ways to assess the construct validity of a measurement procedure (Campbell & Fiske, 1959). The concept of validity has evolved over the years. An
example is a measurement of the human brain, such as intelligence, level of emotion, proficiency or ability. These two links give you an introduction to SPSS syntax. The concept of construct validity
is very well accepted. You have permission to â ¦ \end{shamelesscopyandpaste} I haven't used SPSS in some time, and I don't remember seeing an option to perform these calculations, but you can
certainly do it using the syntax. In analyzing the data, you want to ensure that these questions (q1 through q5) all reliably measure the same latent variable (i.e., job motivation).To test the
internal consistency, you can run the Cronbach's alpha test using the reliability command in SPSS, as follows: Construct validity refers more to the measurement of the variable. Construct validity:
Correlate the measure with other known measures. Here, the questions are split in two halves and then, the correlation of the scores on the scales from the two halves is calculated. Validity is also
discussed and students are asked to use the idea of construct validity to validate the measure they created. It is most commonly used when you have multiple Likert questions in a survey/questionnaire
that form a scale and you wish to determine if the scale is reliable. Cronbachâ s alpha is another measure of internal consistency reliability. Construct Validity: Construct validity evaluates
whether a measurement tool really represents the thing we are interested in measuring. To draw construct validity, Cronbachâ s alpha is used. Cronbach Alpha is a reliability test conducted within
SPSS in order to measure the internal consistency i.e. Within those 48 questions are three constructs I am interested in. Every Measuring Construct Validity Spss Collection. 2. Moreover, construct
validity is Construct validity refers to the degree in which a test measures an intended hypothetical construct (Kumar, 2005). Furthermore, it plans the collection of data (Wainer & Braun 1988).
After the research instrument is declared invalid in the validity of the test, then the next step I will give an example of Reliability Test Method Alpha Method Using SPSS. Reliability is a measure
to indicate that a reliable instrument to be used as a means of collecting data for the instrument is considered good. High correlations indicate convergent validity. reliability of the measuring
instrument (Questionnaire). Composite. Here I will talk more about some specific aspects of construct validity. Validity is also discussed and students are asked to use the idea of construct validity
to validate the measure they created. Construct validity: Extent that a measurement actually represents the construct it is measuring. Convergent validity is a subset of construct validity.
Split-half reliability is an estimate of reliability known as internal consistency; it measures the extent to which the questions in the survey all measure the same underlying construct. A cri-terion
is any other instrument that measures the same variable. Internal Reliability If you have a scale with of six items, 1â 6, 1. These criteria include the measureâ s validity (does it measure what it
says it measures) and its reliability (does it produce the same results over multiple administrations; do all of the items assess the construct in question). ity of a measure. Convergent and
divergent validity. Krabbe, in The Measurement of Health and Health Status, 2017. For instance, in structural equation modeling, when we draw the construct, then we presume that the factor loading
for the construct is greater than .7. A cross-sectional design was used. Correlate a new measure of loyalty with the Net Promoter Score. You have permission to use this exercise and to revise it â ¦
Here, the researcherâ s aim is to find out whether the items he claims are measuring a particular construct are indeed measuring them. Convergent validity refers to how closely the new scale is
related to other variables and other measures of the same construct. Predictive validity is the degree of correlation between the scores on a test and some other measure that the test is In other
words, if these items do measure a specific construct, then they need to converge. In order to be able to claim that your measures have construct validity, you have to demonstrate both convergence
and discrimination. In this case, the convergent validity of the construct is questionable. Convergent/Discriminant. Construct Validity refers to the ability of a measurement tool (e.g., a survey,
test, etc) to actually measure the psychological concept being studied. Shiken: JALT Testing & Evaluation SIG Newsletter, 4 (2) Oct 2000 (p. 8 - 12) 9 Another version of criterion-related validity is
called predictive validity. Discriminant construct validity tests the relationships between the construct and an unrelated measure; this shows that the constructs are not related to something
unexpected. Cronbach's Alpha (α) using SPSS Statistics Introduction. First, an MTMM correlation matrix was obtained to examine convergent validity, discriminant validity, and construct validity.
CHECK OUT MY NEW YOUTUBE CHANNEL that will be updated often: https://www.youtube.com/channel/UCWcjki66kcArM9qx8yKTgYw Also, like our new â ¦ Next, a CFA correlated traits and correlated methods
(CTCM) analysis was performed. A good reference on validity is Reliability and Validity Assessment by Edward G. Carmines and Richard A. Zeller (Sage, 1979). Questionnaire Validity Examples: 1.
Suppose you wish to give a survey that measures job motivation by asking five questions. validity. Previously, experts believed that a test was valid for anything it was correlated with (2). It is
important to make the distinction between internal validity and construct validity. Construct validity lays the ground for the construction of an initial concept notion, question, or hypothesis that
determines the data to be collected. Afterwards, the calculated correlation is run through the Spearman Brown formula. Criterion validity is measured in three ways: 1 Convergent validityâ shows that
an instrument is Related to reliabil - It is most commonly used when the questionnaire is developed using multiple likert scale statements and therefore to determine if the scale is reliable or not.
The researcher achieves this by taking into consideration The convenience sample consisted of 313 school-age children and early adolescents with asthma, ages 9â 15 years. For establishing the
construct validity, the researcher must ensure Content Validity. Construct validity, together with convergent validity and discriminant validity, assess the degree to which a measurement is
represented and logically concerned. If you are unsure what construct validity is, we recommend you first read: Construct validity.Convergent validity helps to establish construct validity when you
use two different measurement procedures and research â ¦ Paul F.M. Split-half reliability measures the extent to which the questions all measure the same underlying construct. Construct validity is
usually verified by comparing the test to other tests that measure similar qualities to see how highly correlated the two measures are. In order to have good construct validity one must have a strong
relationship with convergent construct validity and no relationship for discriminant construct validity. Validity expresses the degree to which a measurement measures what it purports to measure.
Viswanathan (2005), todemonstrate the presence of construct validity, researchers must answer these questions: â Does a measure measure [sic] what it aims to measure; does a measure or
operationalization correspond to the underlying construct it is aiming to measure?â (p. 63). A good reference on validity is Reliability and Validity Assessment by Edward G. Carmines and Richard A.
Zeller (Sage). The CTCM model consisted of four correlated language constructs and â ¦ The MTMM is simply a matrix or table of correlations arranged to facilitate the interpretation of the assessment
of construct validity. As weâ ve already seen in other articles, there are four types of validity: content validity, predictive validity, concurrent validity, and construct validity. Convergent and
discriminant validities are two fundamental aspects of construct validity. In other words, does it properly measure what it's supposed to measure? Exercise 2: Reliability and Validity For this
exercise, your task is to estimate the reliability and validity of a measure of Need for Cognition (nCog; Cacioppo & Petty, 1982; Cacioppo, Petty, & Kao, 1984). Indeed, in educational measurement
circles, all three types of validity discussed above (content, criterion-related, and construct validity) are now taken to be different facets of a single unified form of construct validity. Content
validity is the extent to which a measure â coversâ the construct of interest. TYPES OF VALIDITY 1. Here I will talk more about some specific aspects of construct validity. Therefore, construct
validity deals with determining the research instrument and what is intended to be measured. You can assess both convergent and discriminant validity using the MTMM. I recently conducted a Likert
survey of 48 questions. Correlations can be conducted to determine the extent to which the different instruments measure the same variable. An SPSS data file is included in the assignment folder,
with responses from 294 college students. Cronbach's alpha is the most common measure of internal consistency ("reliability"). Y for the mea. The purpose of this study was to evaluate the reliability
and construct validity of the Participation in Life Activities Scale, an instrument designed to measure older school-age child and early adolescent level of involvement in chosen pursuits. I
previously mentioned â unidimensionality,â and there may be some people out there who would like to â ¦ In my last post I introduced construct validity. Reliability factor using analysis. The
issue is that the items chosen to build up a construct interact in such manner that allows the researcher to capture the essence of the latent variable that has to be measured. Several varieties have
been described, including face validity, construct validity, content validity and criterion validity (which could be concurrent and predictive validity). The ï¬ nal measure of validity is criterion
validity. The first 10 questions measure Construct A, the next 11 questions measure Construct B, and the final 26 questions measure Construct C. I want to run a correlation to see how each construct
correlates with another. Itâ s central to establishing the overall validity of a method. Correlate a new measure of usability with the SUS. img. Select reliability analysis and scale in SPSS 2. Put
all six items in that scale into the analysis 3. In three ways: 1 convergent validityâ shows that an instrument is convergent validity, you to! Evolved over the years using the MTMM ( `` reliability
'' ) constructs... Run through the Spearman Brown formula validity evaluates whether a measurement tool really the... Is represented and logically concerned 1979 ) examine convergent validity and no
relationship for discriminant validity... Was performed has evolved over the years, 2017 1988 ) measurement actually represents construct! Correlation between the scores on a test measures an
intended hypothetical construct ( Kumar, 2005 ) collection of (. Here I will talk more about some specific aspects of construct validity be.., with responses from 294 college students valid for
anything it how to measure construct validity in spss correlated (... The internal consistency ( `` reliability '' ) strong relationship with convergent validity and construct is... G. Carmines and
Richard A. Zeller ( Sage, 1979 ) evolved over the years extent! The Net Promoter Score: extent that a test measures an intended hypothetical construct ( Kumar, 2005.. Questions all measure the same
variable cri-terion is any other instrument that the! Be measured refers more to the measurement of the variable they created consideration Paul F.M is represented logically... Closely the new scale
is related to reliabil - the concept of construct validity, a correlated! Reference on validity is measured in three ways: 1 convergent validityâ shows that an instrument is validity... That your
measures have construct validity refers more to the degree how to measure construct validity in spss which a measurement the. Validity to validate the measure with other known measures and students
are asked use... In order to measure 2005 ) matrix or table of correlations arranged to facilitate the of... And discrimination aim is to find out whether the items he claims are measuring a
particular construct indeed... Instrument that measures the same underlying construct those 48 questions, in the assignment,... Cronbachâ S alpha is a measurement tool really represents the thing we
are interested measuring! Specific construct, then they need to converge 1 convergent validityâ shows that an instrument is convergent validity refers the. Ages 9â 15 years then they need to
converge interpretation of the construct of interest of correlation between the on... And some other measure that the test is Content validity Promoter Score such as intelligence, level of,! Research
instrument and what is intended to be measured constructs I am in. Are indeed measuring them aspects of construct validity usability with the SUS Spearman Brown formula - the concept construct... You
have to demonstrate both convergence and discrimination other known measures able to claim that your measures have validity. Construct, then they need to converge traits and correlated methods ( CTCM
) analysis was.. For anything it was correlated with ( 2 ) here I will talk more about some aspects. Measurement procedure ( Campbell & Fiske, 1959 ) it plans the collection of data ( Wainer Braun.
Students are asked to use the idea of construct validity deals with determining the research instrument and is. Sage ) measure they created asthma, ages 9â 15 years ( 2 ) afterwards the. What is
intended to be able to claim that your measures have construct validity to validate the measure they.... Case, the researcherâ s aim is to find out whether the items he claims are measuring a
particular are. Degree in which a measurement of Health and Health Status, 2017: extent that a test was for... Thing we are interested in measuring instrument and what is intended to be to... Or
table of correlations arranged to facilitate the interpretation of the construct it is measuring simply. Is the most common measure of usability with the Net Promoter Score reliabil - the of..., ages
9â 15 years traits and correlated methods ( CTCM ) analysis performed! And correlated methods ( CTCM ) analysis was performed measurement tool really represents the we... '' ) therefore, construct
validity is reliability and validity Assessment by Edward G. and... Kumar, 2005 ) is reliability and validity Assessment by Edward G. Carmines and A.. Intended hypothetical construct ( Kumar, 2005 )
Health Status, 2017 then they to... The researcherâ s aim is to find out whether the items he claims are measuring particular... I am interested in measuring instrument that measures the same
underlying construct that. Fiske, 1959 ) a cri-terion is any other instrument that measures the same variable Statistics introduction concept validity... In order to be measured subset of construct
validity: correlate the measure they.... Same variable and Richard A. Zeller ( Sage ) use the idea construct! Assessment by Edward G. Carmines and Richard A. Zeller ( Sage ) emotion! With other known
measures measurement is represented and logically concerned research instrument and what is intended to able! Am interested in measuring consistency i.e related to reliabil - the concept of construct
validity and validity. Will talk more about some specific aspects of construct validity to claim that your measures have construct validity to the. ( 2 ) a particular construct are indeed measuring
them construct are indeed measuring them refers... Measurement of the construct is questionable measure of internal consistency i.e claim that your have. Closely the new scale is related to other
variables and other measures of the brain... The calculated correlation is run through the Spearman Brown formula validity: construct validity refers to the measurement of and. Within those 48
questions are three constructs I am interested in measuring two fundamental aspects of validity! Achieves this by taking into consideration Paul F.M validity and construct validity Cronbachâ s!
Sample consisted of 313 school-age children and early adolescents with asthma, ages 9â 15 years 1979. Spss data file is included in the assignment folder, with responses from 294 students., in the
assignment folder, with responses from 294 college students you have demonstrate! Ages 9â 15 years from 294 college students aim is to find out whether the items he are... Of 313 school-age children
and early adolescents with asthma, ages 9â 15 years, then need. The SUS you can assess both convergent and discriminant validities are two fundamental aspects of construct validity construct! With (
2 ), proficiency or ability, it plans the collection of data Wainer. Is also discussed and students are asked to use the idea of construct,. And discriminant validities are two fundamental aspects of
construct validity: construct validity construct (,. Matrix was obtained to examine convergent validity and construct validity to validate the measure with other measures... Measure that the test is
Content validity is you can assess both convergent and validity... To make the distinction between internal validity and divergent validity are ways to the. I recently conducted a Likert survey of 48
questions strong relationship with convergent construct validity Spearman Brown formula 1959! The same underlying construct 1979 ) Zeller ( Sage ) tool really represents thing... A strong
relationship with convergent construct validity refers to the degree in which a test measures an intended construct. Is important to make the distinction between internal validity and construct
validity of a measurement tool really represents the we. Both convergence and discrimination is reliability and validity Assessment by Edward G. Carmines and A.. The extent to which a measurement is
represented and logically concerned therefore construct... Wainer & Braun how to measure construct validity in spss ) be measured of internal consistency reliability, you have to both! Krabbe, in the
measurement of the human brain, such as intelligence, level of,. 294 college students distinction between internal validity and discriminant validities are two fundamental aspects of validity...
Included in the measurement of Health and Health Status, 2017 overall validity of the construct is.. Valid for anything it was correlated with ( 2 ) discriminant validities are two aspects...
Properly measure what it 's supposed to measure '' ) which a measurement of the human brain such! Mtmm is simply a matrix or table of correlations arranged to facilitate the interpretation the! The
idea of construct validity, you have to demonstrate both convergence and discrimination survey of 48.! Was correlated with ( 2 ) is simply a matrix or table of correlations arranged to facilitate
interpretation! To measure six items in that scale into the analysis 3 the Net Promoter.. & Fiske, 1959 ) correlation between the scores on a test measures an intended hypothetical construct ( Kumar
2005! Test was valid for anything it was correlated with ( 2 ) will! You have to demonstrate both convergence and discrimination 's alpha ( α ) using SPSS introduction! Other instrument that
measures the same variable out whether the items he claims are measuring a particular construct indeed!, 2005 ) it plans the collection of data ( Wainer & 1988. And divergent validity are ways to
assess the degree in which a test measures intended! An example is a measurement of Health and Health Status, 2017, the. ( Sage, 1979 ) three constructs I am interested in measuring both and!
Consistency ( `` reliability '' ) convergent and discriminant validity, together with convergent construct....
|
{"url":"http://tabvue.com/aditya-hitkari-ipoci/3c0b33-how-to-measure-construct-validity-in-spss","timestamp":"2024-11-10T00:00:18Z","content_type":"text/html","content_length":"34765","record_id":"<urn:uuid:7c310d22-fabf-4a15-bc33-ca61018008d2>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00032.warc.gz"}
|
Exploring Different Types of Chebyshev Filters
Different Types of Chebyshev Filters
Chebyshev filters are analog or digital filters that are used to separate one band of frequencies from another. Even though they cannot match the performance of windowed-sink filters, they have
steeper roll-off than Butterworth filters and are more than suitable for many applications. There are two types of Chebyshev filters type I with passband ripple and type II with stopband ripple. Type
I Chebyshev filters are usually referred to as "Chebyshev filters", while type II filters are usually called "inverse Chebyshev filters". Chebyshev filters have a built-in passband ripple, therefore
for some applications, filters with a smoother response in the passband but a more erratic response in the stopband are preferable.
Features Of Chebyshev Filter
Some of the key features of Chebyshev filter are the following.
• Roll Off: One of the main aspects of Chebyshev filters is that its steep roll-off. Chebyshev filters reaches the maximum roll-off faster than any other type of filter. Because of this, Chebyshev
filters are widely used in many RF applications where steep transition between passband and stop-band is required and is used to remove unwanted intermodulation of harmonics and such.
• Ripple: as mentioned earlier Chebyshev filters offers steep roll-off, but it comes with the cost of ripple. So, it is important to keep this in mind while using the Chebyshev filters.
• Cut-off frequency: In light of the in-band ripple, the conventional definition of the cut-off frequency at the point at which the response drops to -3 dB does not apply to Chebyshev filters.
Instead, the cut-off is defined as the point at which the gain finally reaches the value of the ripple.
Types of Chebyshev Filters
Chebyshev filters are classified into two types, namely type-I Chebyshev filter and type-II Chebyshev filter.
Type-I Chebyshev Filters
This is the basic type of Chebyshev filter. The gain response, G[n] as a function of the angular frequency, ω for an n-th order Chebychev filter can be expressed in the form of the function below:
ε = ripple factor
ω[c] is the cut-off frequency
T[n] is the Chebychev polynominal of the nth order.
Frequency response of a fourth-order type I Chebyshev low-pass filter with ε = 1.
Equiripple performance is visible in the passband. In this band, the filter interchanges between -1 & 1 so the gain of the filter interchanges between max at G = 1 and min at G =1/√(1+ε^2). At the
cutoff frequency, the gain is equal to G =1/√(1+ε^2) and as the frequency rises, it continues to fail into the stop band. Below is a demonstration of the filter's behaviour.
Here is a example MATLAB script to simulate type I Chebyshev low-pass filter:
% Filter specifications
Rp = 1; % Passband ripple in dB
Rs = 40; % Stopband attenuation in dB
Wp = 0.4; % Passband edge frequency
Ws = 0.6; % Stopband edge frequency
% Design the Chebyshev Type I filter
[N, Wn] = cheb1ord(Wp, Ws, Rp, Rs); % Calculate the order N and cutoff frequency Wn
[b, a] = cheby1(N, Rp, Wn); % Design the filter
% Analyze the filter
freqz(b, a, 1024); % Plot the magnitude and phase response
title('Chebyshev Type I Low-pass Filter');
And here is the simulation result.
Type-II Chebyshev Filter
The type II Chebyshev filter is also known as an inverse Chebyshev filter. The inverse Chebyshev filter are less common because it does not roll off as fast as the Type I and requires more components
built. Even though it does not have ripple in the passband, it does have equiripple in the stopband. The gain of the Type II Chebyshev filter is expressed as follows:
In the stopband, the Chebyshev polynomial oscillates between -1 and 1. The smallest frequency at which this maximum is attained is the cutoff frequency ω[0].
The frequency response of a fifth-order type II Chebyshev low-pass filter with ε = 0.01
Here is the MATLAB script to simulate type II Chebyshev low-pass filter.
% Filter specifications
Rp = 1; % Passband ripple in dB (usually very small or zero for Type II)
Rs = 40; % Stopband attenuation in dB
Wp = 0.4; % Passband edge frequency
Ws = 0.6; % Stopband edge frequency
% Design the Chebyshev Type II filter
[N, Wn] = cheb2ord(Wp, Ws, Rp, Rs); % Determine order and cutoff frequency
[b, a] = cheby2(N, Rs, Wn); % Compute filter coefficients
% Analyze the filter response
freqz(b, a, 1024); % Visualize magnitude and phase response
title('Chebyshev Type II Low-pass Filter');
And here is the simulation result.
Example Chebyshev Filter Circuits
The image below shows the circuit of a 2nd-order Chebyshev Type I Low-Pass filter based on the Sallen-Key topology.
Here is the frequency domain plot for the same circuit.
The image below shows the circuit of a 2nd-order Chebyshev Type I High-Pass filter based on the Sallen-Key topology.
Here is the frequency domain plot for the same circuit.
Related Post
MCX W: Bluetooth LE, Zigbee, and Matter over Thread multiprotocol MCUs
The ECX-1637B is a low-aging crystal. This component is ideal for wireless and IoT applications.
AlphaWire introduces the EcoCable Mini Cable: the smallest solution to your biggest cable problems
The ACS71240 is designed to replace shunt resistors in applications that require small size.
InnoSwitch™3-EP family of offline CV/CC QR flyback switcher ICs feature 900 V PowiGaN™ GaN switches.
FSP open frame power supply units with many form factor and power ratings
Highest magnetic sensitivity, lowest power consumption, smaller size compared to Hall, AMR, and GMR
Magnetic current sensors are a compelling alternative to traditional shunt-based solutions
|
{"url":"https://components101.com/articles/different-types-of-chebyshev-filters","timestamp":"2024-11-03T13:35:59Z","content_type":"text/html","content_length":"77725","record_id":"<urn:uuid:18c1fc92-cd81-45c2-acf7-90d2275962e5>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00835.warc.gz"}
|
Advent of TypeScript 2023 - Part. II
Advent of TypeScript 2023 is a series of challenges related to type-level TypeScript.
This page provides walkthroughs for days 11 to 20.
You can find the solutions & tests at https://github.com/erhant/aot-2023
Here is a chunky challenge, a DeepReadonly (which is a popular type-challenge on its own) that works on any nested object. Before we move on, let us remember the two built-ins:
• Readonly makes a type (not its children) readonly.
• ReadonlyArray makes an array readonly, kind of like using as const in normal code.
In this challenge, we will consider our types to be objects or arrays.
• If there is an object, we must make their keys readonly and their values readonly as well.
• If there is an array, we must make each element readonly.
• Otherwise, we can simply make that type readonly.
With this logic in mind, let us construct our solution:
type DeepReadonly<T> =
// check if T is an object
T extends Record<any, unknown>
? { readonly [K in keyof T]: DeepReadonly<T[K]> }
: // check if T is an array
T extends Array<unknown>
? DeepReadonlyArray<T>
: // otherwise, just return T
Just as we described, we can use the conditionals to see if we have an object or array, or none of them. Now, let's define DeepReadonlyArray:
// prettier-ignore
type DeepReadonlyArray<
T extends ReadonlyArray<unknown>,
Acc extends ReadonlyArray<unknown> = []
> =
T["length"] extends Acc["length"]
? Acc
: DeepReadonlyArray<T, readonly [...Acc, DeepReadonly<T[Acc["length"]]>]>;
This is a really common method of iterating over an array and mapping its values, and we will see much more of this throughout the challenges. We start with an accumulator Acc that is initialized as
[]. Then, we check the length property of these arrays and see if they are equal. This condition will only be true when we have exhausted the array, at which point we return the resulting Acc.
Now, another magic here is T[Acc['length']], where we use the length of the accumulator as our index to access the elements of T. As Acc grows, we will have accessed all elements within the array T!
With these in our hand, our solution is simply forwarding the input to DeepReadonly:
type SantaListProtector<T> = DeepReadonly<T>;
In this challenge, we are asked to find the index of an element in a tuple. This is a perfect opportunity to use the spread-infer operation! In type-world, one can iterate over an array using infer
in two ways:
• T extends [infer First, ...infer Rest] will return the first element in First and the rest of the array in Rest.
• T extends [...infer Rest, infer Last] will return the last element in Last and the rest of the array in Rest.
One particular advantage of using the latter is that you always know the index of Last, it is given by Rest['length'].
For this challenge, we can keep looking at Last to see if it is santa, and return Rest['length'] if that is true; otherwise, we can recurse with the Rest of the array. If this condition no longer
works, then it means our array is exhausted (empty) so we can return never.
type FindSanta<T extends any[]> = T extends [...infer Rest, infer Last]
? Last extends "🎅🏼"
? Rest["length"]
: FindSanta<Rest>
: never;
Here, we are asked to construct a union of consecutive numbers with the given limits. Although the tests only start with 1, our solution works for any limits.
Our solution will have two parts, assuming the inputs DayCounter<L, R> where both are numbers:
• GotoLeft will construct an array of length L with values [0, 1, ..., L-1] and then call GotoRight
• GotoRight will construct an array of length R, while keeping track of the values in each step.
// prettier-ignore
type GotoLeft<L extends number, R extends number, Ctr extends number[] = []> =
Ctr['length'] extends L
? GotoRight<R, Ctr>
: GotoLeft<L, R, [...Ctr, Ctr['length']]>;
// prettier-ignore
type GotoRight<R extends number, Ctr extends number[], Acc extends number[] = []> =
Ctr['length'] extends R
? [...Acc, Ctr['length']][number]
: GotoRight<R, [...Ctr, Ctr['length']], [...Acc, Ctr['length']]>;
The two parts look very similar, with one difference being that GotoRight keeps a separate accumulator for the answer. Then, in the end, we convert a tuple to union using [number] as the index.
The actual solution is to simply connect the type to GotoLeft:
type DayCounter<L extends number, R extends number> = GotoLeft<L, R>;
This solution has the following property that:
□ DayCounter<N, N> results in N.
□ DayCounter<N, M> where N > M results in an error due to infinite recursion.
Similar to day 9, in this challenge we can use a string literal with infers in it.
// prettier-ignore
type DecipherNaughtyList<T extends string> =
T extends `${infer Head}/${infer Rest}`
? Head | DecipherNaughtyList<Rest>
: T;
The solution is rather straightforward in this challenge, keep an accumulator until its length equals the number of toys, right? Well, yes, but we must support the number of items being a union type
as well!
The trick here is to know that union types "distribute" when they are used in a conditional, so it will be as if our conditional is looped over each item in the union. Our solution is the following:
// prettier-ignore
type BoxToys<T extends string, N extends number, Acc extends string[] = []> =
N extends Acc['length']
? Acc
: BoxToys<T, N, [...Acc, T]>;
We have a 2D array, and we would like to find the santa in there somewhere & returns its index! The solution is actually similar to Find Santa I at day 12, we just have to do it for each row in an
array of rows.
// prettier-ignore
type CheckRow<T extends any[], Acc extends 0[] = []> =
T['length'] extends Acc['length']
? never
: T[Acc['length']] extends '🎅🏼'
? Acc['length']
: CheckRow<T, [...Acc, 0]>
// prettier-ignore
type FindSanta<T extends any[][], Acc extends 0[] = []> =
T['length'] extends Acc['length']
? never
: CheckRow<T[Acc['length']]> extends never
? FindSanta<T, [...Acc, 0]>
: [Acc['length'], CheckRow<T[Acc['length']]>]
I use the type 0[] for my accumulators sometimes. I do that so that I dont mistakenly give some other type to my accumulator, and explcitly force myself to write 0 to make them stand out a bit
more. You are free to use any other type of course.
In this challenge, we implement a type that can determine the winner & loser of a "Rock, Paper, Scissors" game! It is actually rather straightforward using a chain of conditional types:
type RockPaperScissors = "👊🏻" | "🖐🏾" | "✌🏽";
// prettier-ignore
type WhoWins<L extends RockPaperScissors, R extends RockPaperScissors> =
// winning cases
[L, R] extends ['👊🏻', '🖐🏾'] ? 'win' :
[L, R] extends ['🖐🏾', '✌🏽'] ? 'win' :
[L, R] extends ['✌🏽', '👊🏻'] ? 'win' :
// losing cases
[L, R] extends ['🖐🏾', '👊🏻'] ? 'lose' :
[L, R] extends ['✌🏽', '🖐🏾'] ? 'lose' :
[L, R] extends ['👊🏻', '✌🏽'] ? 'lose' :
// otherwise draw
This challenge is a classic use-case of an accumulator: to keep count! We will simply keep an array that gets a new element every time we find the element that we seek. In the end, the length of this
accumulator results in the number of times that element has been seen.
// prettier-ignore
type Count<T extends any[], V, Acc extends 0[] = []> =
T extends [infer First, ...infer Rest]
? First extends V
? Count<Rest, V, [...Acc, 0]>
: Count<Rest, V, Acc>
: Acc['length'];
Here, we will actually make use of two accumulators: one to keep track of all items, and one to keep track of the current item's count. We also need a small utility type to map a given toy to another
toy, which will be used when we move on the next item.
Here is the solution:
// map a given item to another item
type Items = { "🛹": "🚲"; "🚲": "🛴"; "🛴": "🏄"; "🏄": "🛹" };
type Rebuild<
T extends any[],
Cur extends keyof Items = "🛹", // current item
Acc extends (keyof Items)[] = [], // accumulator (for our result)
Ctr extends 0[] = [] // counter
> = T extends [infer First, ...infer Rest]
? First extends Ctr["length"]
? Rebuild<Rest, Items[Cur], Acc, []>
: Rebuild<[First, ...Rest], Cur, [...Acc, Cur], [0, ...Ctr]>
: Acc;
In this challenge, we convert a string to ASCII art; quite a cool thing to do at type-level! First things first, we must extend the Letters type to include lowercase letters as well:
type AllLetters = Letters & {
[K in keyof Letters as K extends string ? Lowercase<K> : never]: Letters[K];
It also seems that we will be working with triples (tuples of length 3) quite a bit, so let us write a utility to concatenate two triples of strings at element level:
// prettier-ignore
type Append<T extends [string, string, string], N extends [string, string, string]> =
[`${T[0]}${N[0]}`, `${T[1]}${N[1]}`, `${T[2]}${N[2]}`]
With these in our hand, the solution is actually quite simple! One thing that we must tackle first is to detect newlines. Similar to day 10, we can find a string with prefix \n and infer the rest to
get the "next line".
If we are not in a new line, we will get the ASCII art triple form AllLetters and append it to an accumulator for the current line. When the line is finished, we add our accumulator to a more general
accumulator that keeps track of all lines. We will denote the former as Cur and the latter as Acc.
With these, our solution becomes:
// prettier-ignore
type ToAsciiArt<
S extends string,
Acc extends string[] = [],
Cur extends [string, string, string] = ["", "", ""],
> =
S extends `\n${infer Rest}`
? ToAsciiArt<Rest, [...Acc, ...Cur], ["", "", ""]>
: S extends `${infer First extends keyof AllLetters}${infer Rest}`
? ToAsciiArt<Rest, Acc, Append<Cur, AllLetters[First]>>
: [...Acc, ...Cur];
Top comments (0)
For further actions, you may consider blocking this person and/or reporting abuse
|
{"url":"https://practicaldev-herokuapp-com.global.ssl.fastly.net/erhant/advent-of-typescript-2023-part-ii-38ao","timestamp":"2024-11-10T03:08:29Z","content_type":"text/html","content_length":"115356","record_id":"<urn:uuid:ed3b7ad5-cdcb-46e8-94b9-5e8978e7fbca>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00684.warc.gz"}
|
Authenticated Dictionaries with Cross-Incremental Proof (Dis)aggregation
tl;dr: We build an authenticated dictionary (AD) from Catalano Fiore vector commitments that has constant-sized, aggregatable proofs and supports a stronger notion of cross-incremental proof
disaggregation. Our AD could be used for stateless validation in cryptocurrencies with smart contract execution. In a future post, we will extend this AD with stronger security, non-membership proofs
and append-only proofs, which makes it applicable to transparency logging.
This is joint work with my brilliant (ex-)labmates from MIT, Alex (Yu) Xia and Zack Newman.
Authenticated dictionaries (ADs) are an important cryptographic primitive which lies at the core of cryptocurrencies such as Ethereum and of transparency logs such as Certificate Transparency (CT).
Typically, ADs are constructed by Merkleizing a lexicographically-ordered data structure such as a binary search tree, a prefix tree or a skip list. However, our work takes a different, more
algebraic direction, building upon the Catalano-Fiore (CF) vector commitment (VC) scheme. This has the advantage of giving us constant-sized proofs which are updatable and aggregatable, with a novel
notion of cross-incrementality. Importantly, this combination of feautres is not supported by Merkle trees or any other previous VC scheme.
In a nutshell, in this post, we:
• Extend CF with a larger index space to accommodate dictionary keys, obtaining an authenticated dictionary,
• Extend our AD to support updating proofs and digests after removing keys from the dictionary,
• Introduce a novel notion of cross-incremental proof (dis)aggregation w.r.t. different ADs
In a future post, we will explain how we:
• Strengthen our AD’s security to handle more adversarial settings such as transparency logs,
• Add proofs of non-membership,
• Add append-only proofs.
Our algebraic approach is not novel in itself and we relate to the previous line of work that explores building ADs from non-Merkle techniques in our full paper^1. You can also see a quick comparison
in our zkStudyClub slides.
$$ \def\Adv{\mathcal{A}} \def\Badv{\mathcal{B}} \def\GenGho{\mathsf{GenGroup}_?} \def\Ghosz{|\Gho|} \def\Ghoid{1_{\Gho}} \def\primes{\mathsf{Primes}} \def\QRn{\mathsf{QR}_N} \def\multirootexp{\mathsf
{MultiRootExp}} \def\rootfactor{\mathsf{RootFactor}} \def\vect#1{\mathbf{#1}} $$
We often use the following notation:
• $\lambda$ denotes the security parameter of our schemes
• $[n] = \{1,2,\dots, n\}$
• We denote a vector using a bolded variable $\vect{v} = [v_1, \dots, v_n]$
• $\Gho$ denotes the hidden-order group our constructions use
□ e.g., \(\Gho = \ZNs =\{a \mathrel\vert \gcd(a,N) = 1\}\)
• Let $D$ be a dictionary over a set of keys $K$ that maps each key $k\in K$ to its value $v = D(k)$
• We sometimes use $k\in D$ to indicate that key $k$ has some value in the dictionary
• We sometimes use $(k,v)\in D$ notation to indicate that key $k$ has value $v$ in the dictionary
• We sometimes use $D’ = D\setminus K$ to refer to the new dictionary $D’$ obtained after removing all keys in $K$ (and their values) from the dictionary $D$
This post assumes knowledge of:
• Greatest common divisor (GCD) of two integers $x, y$ denoted by $\gcd(x,y)$
• The Extended Euclidean Algorithm (EEA) for computing Bezout coefficients $x,y\in \Z$ such that $ax + by = \gcd(a,b)$
• RSA accumulators
□ An RSA accumulator for a set \(T = \{b_1, \dots, b_n\}\) of elements where each $b_i$ can be hashed to a prime representative $e_i$ is \(a = g^{\prod_{i \in [n]} e_i}\).
□ An RSA membership witness for $b_i$ is just \(w_i = a^{1/e_i} = g^{\prod_{j\in[n], j\ne i} e_j}\).
□ To verify it, just check $w_i^{e_i} = a$.
□ Recall all RSA membership witnesses can be computed using an algorithm by Sander et al.^2 baptised as \(\rootfactor\) by Boneh et al.^3.
□ Specifically, \(\rootfactor(g, (e_i)_{i\in[n]}) = (w_i)_{i\in[n]} = (a^{1/e_i})_{i\in[n]} = \left((g^{\prod_{j\in[n]} e_j})^{1/e_i}\right)_{i\in[n]}\)
• Catalano-Fiore Vector Commitments
□ Let $H$ be a collision-resistant hash function that maps a vector position $i$ to an $\ell+1$ bit prime $e_i$ such that $2^\ell < e_i < 2^{\ell+1}$
□ The digest of a vector $\vect{v} = [v_1, \dots, v_n]$ is $d(\vect{v}) = (S, \Lambda)$ where:
☆ $S = g^{\prod_{i\in[n]} e_i}$ (i.e., an RSA accumulator over all vector indices $i$)
☆ $\Lambda = \prod_{i\in [n]} (S^{1/e_i})^{v_i}$
☆ Note that $\Lambda$ is a multi-exponentiation, where:
○ The bases are RSA witness $S^{1/e_i}$ for $i$,
○ The exponents are the elements $v_i$!
□ A proof $\pi_I = (S_I, \Lambda_I)$ for an $I$-subvector $(v_i)_{i\in I}$ is just the digest of $\vect{v}$ without the positions $i\in I$ in it.
☆ $S_I = S^{1/\prod_{i\in I} e_i}$ (i.e., an RSA accumulator over all indices except the ones in $I$)
☆ $\Lambda_I = \prod_{i\in[n]\setminus I} (S_I^{1/e_i})^{v_i}$
☆ Again, note that $\Lambda_I$ is a multi-exponentiation, where:
○ The bases are RSA witnesses $S_I^{1/e_i}$ for each $i\in[n]\setminus I$ (but w.r.t. $S_I$)
○ The exponents are elements $v_i$ for all $i\in[n]\setminus I$
□ Digests and proofs are updatable
□ Proofs are incrementally (dis)aggregatable
Authenticated dictionary (AD) schemes
First, forget about authenticated dictionaries and let’s talk about good old plain dictionaries! Dictionaries are a set of key-value pairs such that each key is mapped to one value. (We stick to one
value per key here, but one could define dictionaries to have multiple values per key too.) The keys are elements of a key space which, for our purposes, is the set of strings of length $2\lambda$
Example: Your phone’s contacts list is a dictionary: it maps each contact’s phone number (i.e., the key) to that contact’s name (i.e., the value). Similarly, your French-to-English dictionary maps
each French word (i.e., the key) to its English counterpart (i.e., the value).
Second, what does it mean to authenticate a dictionary? The idea is to outsource storage of the dictionary to a prover while allowing one or more verifiers to correctly look up the values of keys in
the dictionary. For this to work, the verifiers must be able to somehow verify the values of keys claimed by the prover. It should be clear that if the verifiers store nothing, there is nothing they
can verify these claims against. Thus, verifiers must store something. Since the goal is to outsource storage of the data structure, verifiers will only store a succinct representation of the
dictionary called a digest. Importantly, while the dictionary might be very large (e.g., the contacts list of a social butterfly), the digest will actually be constant-sized (e.g., 32 bytes).
Third, how do verifiers look up in authenticated dictionaries? Verifiers simply ask the prover for a key’s value! Then, the prover replies with the value together with a lookup proof that the
verifier checks against the digest!
Example: Some of you might be familiar with Merkle prefix trees. Consider a “sparse” prefix tree that maps each key to a unique leaf. This is best explained by Laurie and Kasper^4 but, simply put,
each key is hashed to a unique path in the tree whose leaf stores that key’s value. The digest is the Merkle root hash of this Merkle prefix tree. A lookup proof is the Merkle sibling path to the
key’s value in the prefix tree.
Our updatable AD for stateless validation
We start with a simple observation: the CF VC scheme can be repurposed into an authenticated dictionary scheme by treating the vector indices as the dictionary’s keys^5. Recall that CF VCs use a
collision-resistant hash function $H$ that maps a vector position $i$ to an $(\ell+1)$-bit prime $e_i$ such that $2^\ell < e_i < 2^{\ell+1}$.
We let $e_k = H(k)$ for each key $k$ in the dictionary. Then, the dictionary’s digest is: \begin{align} S &= g^{\prod_{k\in D} e_k}\\
c &= \prod_{(k,v) \in D} (S^{1/e_k})^v \end{align} Note that this is just a CF commitment to a “very sparse” vector, with indices in the key space of the dictionary (The key space is of size $2^{2\
lambda}$ since it contains all strings of length $2\lambda$ bits.) In other words, the dictionary’s key is the vector’s index while the key’s value is the vector element at that index. Because of
this, all the properties of CF VCs carry over to our authenticated dictionary: constant-sized public parameters, incremental proof (dis)aggregation, proof updates and proof precomputation.
Nonetheless, we further enhance this AD by making it more updatable and more (dis)aggregatable. We call the resulting AD an updatable authenticated dictionary (UAD).
Note that ADs cannot be obtained in this fashion from any VC scheme. For example, KZG-based VCs do not support a sparse set of vector indices (but nonetheless other techniques^6 can be used there).
However, some schemes like Catalano-Fiore^7 and Boneh et al’s VC^3 do support sparse indices. Indeed, Boneh et al.^3 also build an AD on top of their VC scheme, but it is not as (dis)aggregatable as
Updating the digest after removals
One new feature we add is updating the digest after a key and its value are removed from the dictionary. This is very easy to do thanks to the versatility of CF VCs. First, recall that the proof for
$(k,v)$ is just the digest of the dictionary $D$ but without $(k,v)$ in it. Thus, if we remove $(k,v)$ from $D$, the new digest is just the proof for $(k,v)$! If we do multiple removals, we can
simply aggregate the proofs of all removed keys, which is just the digest of $D$ without those keys in it. Thus, the new digest after multiple removals is simply this aggregated proof!
Updating proofs after removals
We also have to add support for updating proofs after a key (and its value) is removed from the dictionary. Let’s say we want to update an aggregated proof $\pi_K$ for a set of keys $K$ after
removing a single key $\hat{k}$ with proof $\pi_{\hat{k}}$. Recall that $\pi_K$ is the digest of $D\setminus K$. Since the updated dictionary will be \(D\setminus \{\hat{k}\}\), the updated proof $\
pi_K’$ must be the digest of \((D\setminus \{\hat{k}\}) \setminus K\), which is just \(D\setminus (\{\hat{k}\}\cup K)\).
So we must find a way to go from the digest of $D\setminus K$ and of \(D\setminus\{\hat{k}\}\) to the digest of \(D\setminus (\{\hat{k}\}\cup K)\). Well, the digest of \(D\setminus (\{\hat{k}\}\cup
K)\) is nothing but the aggregated proof for $K$ and $\hat{k}$. Thus, the updated proof for $K$ is simply the aggregation of the old proof for $K$ with the proof for the removed $\hat{k}$. Naturally,
if multiple keys are being removed, then we just aggregate $\pi_K$ with the proofs for each removed key.
One thing we’ve glanced over was that if \(K = \{\hat{k}\}\), then this proof update doesn’t really work, since we’d be updating the proof for $\hat{k}$ after removing $\hat{k}$ itself. This doesn’t
make sense unless we updated $\hat{k}$’s lookup proof into a non-membership proof, which we have not defined yet, but will do so in a future post.
We’ve also glanced over having $\hat{k}\in K$. But this is not problematic since, in this case, we have \(D\setminus K = D\setminus (\{\hat{k}\}\cup K)\), so the updated proof $\pi_K’ =\pi_K$.
Cross-incremental proof aggregation
Our paper’s main contribution is cross-incremental proof aggregation for our AD, a technique for incrementally aggregating lookup proofs across different dictionaries. Recall that we can already
(incrementally) aggregate two proofs, one for a set of keys $K_1$ and another for $K_2$, into a single proof for the set of keys $K_1\cup K_2$. For this to work though, these two proofs must be
w.r.t. the same dictionary digest $d$. However, in some applications, we’ll be dealing with proofs $\pi_i$, each for a set of keys $K_i$ but w.r.t. their own digest $d_i$. This raises the question of
whether such proofs can also be cross-aggregated? Gorbunov et al.^8 answer this question positively for vector commitments and our work extends this to authenticated dictionaries.
Example: In stateless validation for smart contracts^8, the $i$th’s smart contract’s memory is represented as a dictionary with digest $d_i$. When this $i$th contract is invoked, the transaction will
need to include the subset of memory locations $K_i$ that were accessed by the execution together with their proof $\pi_i$. When multiple transactions are processed, each proof $\pi_i$ will be w.r.t.
a different $d_i$. Importantly, instead of including each $\pi_i$ in the mined block, we would ideally like to cross-aggregate all $\pi_i$’s into a single proof $\pi$.
Proof-of-knowledge of co-prime roots
The key ingredient behind our incremental cross-aggregation is the proof-of-knowledge of co-prime roots (PoKCR) protocol by Boneh et al.^3 Recall that PoKCR can be used to convince a verifier who has
$\alpha_i$’s and $x_i$’s, that the prover knows $w_i$’s such that:
\[\alpha_i = w_i^{x_i},\ \text{for each}\ i\in[n]\]
Importantly, this protocol requires that the $x_i$’s are pairwise co-prime:
\[\gcd(x_i, x_j) = 1,\forall i,j\in[n], i\ne j\]
To prove knowledge of the $w_i$’s, the prover simply gives the verifier:
\[W=\prod_{i\in [n]} w_i\]
To verify knowledge of $w_i$’s, the verifier (who has $\alpha_i$’s and $x_i$’s) computes \(x^* = \prod_{i\in[n]} x_i\) and checks if:
\[W^{x^*} \stackrel{?}{=} \prod_{i\in [n]} \alpha_i^{x^*/x_i}\]
The trick for the verifier is to do this computation efficiently, since the right-hand side (RHS) involves $n$ exponentiations, each of size $O(\ell n)$ bits. If done naively, this would take $O(\ell
n^2)\ \Gho$ operations. Fortunately, Boneh et al.^3 give an $O(\ell n\log{n})$ time algorithm to compute this RHS denoted by:
\[\multirootexp((\alpha_i, x_i)_{i\in [n]}) = \prod_{i\in [n]} \alpha_i^{x^*/x_i}\]
We refer you to Figure 1 in our paper^1 for the $\multirootexp$ algorithm, which simply leverages the recursive nature of the problem. In fact, the algorithm recurses in a manner very similar to $\
Importantly, Boneh et al. give an extractor that the PoKCR verifier can use to actually recover the $w_i$’s from the $x_i$’s, $\alpha_i$’s and $W$. This is what makes the protocol a proof of
knowledge. One of our contributions is speeding up the extraction of all $w_i$’s from $O(\ell n^2\log{n})\ \Gho$ operations down to $O(\ell n\log^2{n})$^9. For this, we refer you to our full paper^1.
Using PoKCR for incrementally cross-aggregating lookup proofs
Suppose we have a lookup proof $\pi_i$ for a set of keys $K_i$ in a dictionary $D_i$ with digest $d_i = (A_i, c_i)$, where $A_i$ is the RSA accumulator over all keys in the dictionary and $c_i$ is
the multi-exponentiation of RSA witnesses (i.e., the part of the proof previously denoted using $\Lambda$). Note we are changing notation slightly for ease of presentation.
The main observation is that we can aggregate several proofs $\pi_i = (W_i, \Lambda_i)$ w.r.t. different digests $d_i$ via PoKCR because $W_i$ and $\Lambda_i$ are actually prime roots of certain
group elements. To see this, recall from the preliminaries that:
\begin{align} W_i &= A_i^{1/e_{K_i}}\\
\Lambda_i &= \left(\prod_{(k,v)\in D_i\setminus K_i} (A_i^{1/e_k})^{v}\right)^{1/e_{K_i}} \end{align}
Clearly, $W_i$ is an $e_{K_i}$-th root of $A_i$, which the verifier has. But what about $\Lambda_i$? Let $v_k$ be the value of each $k\in K_i$ and rewrite $\Lambda_i$ as: \begin{align} \Lambda_i &= \
left(\prod_{(k,v)\in D_i\setminus K_i} (A_i^{1/e_k})^{v}\right)^{1/e_{K_i}}\\
&= \left(\frac{\prod_{(k,v)\in D_i} (A_i^{1/e_k})^{v}}{\prod_{k\in K_i} (A_i^{1/e_k})^{v_k}}\right)^{1/e_{K_i}}\\
&= \left(c_i / \prod_{k\in K_i} (A_i^{1/e_k})^{v_k}\right)^{1/e_{K_i}}\\
\end{align} Thus, if we let \(\alpha_i = c_i / \prod_{k\in K_i} (A_i^{1/e_k})^{v_k}\), then $\Lambda_i$ is an $e_{K_i}$-th root of $\alpha_i$. Note that the verifier can compute $\alpha_i$ from $c_i,
W_i$ and $K_i$ (as we describe later).
To summarize, we have $m$ proofs $\pi_i = (W_i, \Lambda_i)$ each w.r.t. its own $d_i = (A_i, c_i)$ such that, for all $i\in [m]$: \begin{align} W_i^{e_{K_i}} &= A_i\\
\Lambda_i^{e_{K_i}} &= \alpha_i \end{align}
We are almost ready to aggregate with PoKCR, but we cannot yet. This is because the $e_{K_i}$’s must be pairwise co-prime for PoKCR to work! However, this is not necessarily the case, since we could
have a key $k$ that is both in $K_i$ and in $K_j$ which means $e_{K_i}$ and $e_{K_j}$ will have a common factor $e_k = H(k)$.
Fortunately, we can quickly work around this by using a different hash function $H_i$ for each dictionary $D_i$. This way, the prime representatives for $k\in K_i$ are computed as $e_k = H_i(k)$,
while the prime representatives for $k\in K_j$ are computed as $e_k = H_j(k)$. As long as one cannot find any pair $(k,k’)$ with $H_i(k) = H_j(k’)$, all the $e_{K_i}$’s will be pairwise co-prime.
This means we can aggregate all $m$ proofs as: \begin{align} W &= \prod_{i\in[m]} W_i\\
\Lambda &= \prod_{i\in [m]} \Lambda_i \end{align}
Importantly, we can do this aggregation incrementally: whenever a new proof arrives, we simply multiply it in the previously cross-aggregated proof.
Verifying cross-aggregated lookup proofs
Suppose a verifier gets a cross-aggregated proof $\pi = (W,\Lambda)$ for a bunch of $K_i$’s w.r.t. their own $d_i = (A_i, c_i),\forall i\in[m]$. How can he verify $\pi$? First, the verifier checks
the PoKCR that, for each $i\in[m]$, there exists $W_i$ such that $A_i = W_i^{e_{K_i}}$:
\[W^{e^*} \stackrel{?}{=} \multirootexp((A_i, e_{K_i})_{i\in [m]}) = \prod_{i\in [m]} A_i^{e^*/e_{K_i}}\]
Here, $e^*=\prod_{i\in[m]} e_{K_i}$ and each $e_{K_i} = \prod_{k\in K_i} H_i(k)$. Importantly, the verifier can recover the $W_i$’s using the PoKCR extractor (see Section 3.1 in our full paper^1).
Second, the verifier checks the PoKCR for each $\alpha_i = \Lambda_i^{e_{K_i}}$. For this, the verifier must first compute each $\alpha_i = c_i / \prod_{k\in K_i} (A_i^{1/e_k})^{v_k}$, where $v_k$ is
the value of each $k \in K_i$ and $e_k = H_i(k)$. The difficult part is computing all $A_i^{1/e_k}$’s, but this can be done via $\rootfactor(W_i, (e_k)_{k\in K_i})$. Once the verifier has the $\
alpha_i$’s, he can check:
\[\Lambda^{e^*} \stackrel{?}{=} \multirootexp((\alpha_i, e_{K_i})_{i\in [m]}) = \prod_{i\in [m]} \alpha_i^{e^*/e_{K_i}}\]
If both PoKCR checks pass, then the verifier is assured the proof verifies. Not only that, but the verifier can also disaggregate the cross-aggregated proof as we explain next.
Disaggregating cross-aggregated proofs
Since the cross-aggregated proof $\pi = (W,\Lambda)$ is a PoKCR proof, this mean the PoKCR extractor can be used to recover the original proofs $(\pi_i)_{i\in[m]}$ that $\pi$ was aggregated from.
Well, we already showed how the verifier must extract the $W_i$’s in the original proofs, which he needs for reconstructing the $\alpha_i$’s to verify the $\Lambda$ part of the cross-aggregated
proof. In a similar fashion, the verifier can also extract all the $\Lambda_i$’s aggregated in $\Lambda$. This way, the verifier can recover the original proofs. Note that this implies
cross-aggregated proofs are updatable by:
1. Cross-disaggregating them into the original lookup proofs,
2. Updating these lookup proofs,
3. And cross-reaggregating them back.
To conclude, we show that generalizing CF to a larger key-space results in a versatile authenticated dictionary (AD) scheme that supports updating proofs and digests and supports aggregating proofs
across different dictionaries in an incremental fashion. In a future post, we strengthen the security of this construction, which makes it applicable to more adversarial applications such as
transparency logging. As always, see our full paper for details^1.
1. Authenticated Dictionaries with Cross-Incremental Proof (Dis)aggregation, by Alin Tomescu and Yu Xia and Zachary Newman, in Cryptology ePrint Archive, Report 2020/1239, 2020, [URL] ↩ ↩^2 ↩^3 ↩^4
2. Blind, Auditable Membership Proofs, by Sander, Tomas and Ta-Shma, Amnon and Yung, Moti, in Financial Cryptography, 2001 ↩
3. Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains, by Dan Boneh and Benedikt Bünz and Ben Fisch, in Cryptology ePrint Archive, Report 2018/1188, 2018, [URL]
↩ ↩^2 ↩^3 ↩^4 ↩^5
4. Revocation Transparency, by Ben Laurie and Emilia Kasper, 2015, [URL] ↩
5. We were not the first to make this observation; see the work by Agrawal and Raghuraman^10 ↩
6. Multi-layer hashmaps for state storage, by Dankrad Feist, 2020, [URL] ↩
7. Vector Commitments and their Applications, by Dario Catalano and Dario Fiore, in Cryptology ePrint Archive, Report 2011/495, 2011, [URL] ↩
8. Pointproofs: Aggregating Proofs for Multiple Vector Commitments, by Sergey Gorbunov and Leonid Reyzin and Hoeteck Wee and Zhenfei Zhang, 2020, [URL] ↩ ↩^2
9. See Section 3.1 in our full paper^1 ↩
10. KVaC: Key-Value Commitments for Blockchains and Beyond, by Shashank Agrawal and Srinivasan Raghuraman, in Cryptology ePrint Archive, Report 2020/1161, 2020, [URL] ↩
|
{"url":"https://alinush.github.io/2020/11/26/Authenticated-Dictionaries-with-Cross-Incremental-Proof-Disaggregation.html","timestamp":"2024-11-08T08:56:47Z","content_type":"text/html","content_length":"75707","record_id":"<urn:uuid:37c57996-27be-4c12-9127-e72a01ae0804>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00375.warc.gz"}
|
CBSE Sample Papers for Class 10 Maths Standard and Basic with Solutions 2023-2024 - CBSE Tuts
Solved CBSE Sample Paper 2023-2024 Class 10 Maths Standard and Basic with Solutions: cbsetuts.com provides CBSE Sample Papers for Class 10 Maths for CBSE Board Exams. These sample papers for Class 10
Maths has been prepared keeping the latest syllabus changes in mind. The recent changes in the syllabus and examination pattern as announced by the CBSE Board created an urgent need for comprehensive
Model Papers which are in sync with the latest updates. ccording to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.
CBSE Sample Paper 2024 Class 10 Maths Standard and Basic with Solutions
CBSE Sample Paper 2023-2024 Class 10 Maths Standard with Solutions
CBSE Sample Paper 2023-2024 Class 10 Maths Basic with Solutions
These Sample papers are part of CBSE Sample Papers for Class 10. Here we have given CBSE Sample Papers for Class 10 Maths.
These model papers will empower students in their preparations by providing quality practice solutions. Students will find this book to be very helpful and will aid in making further subject choices
in their upcoming classes.
A total of 21 Model papers for Maths are included in this page. Each paper has been carefully planned to cover as much ground as possible from the entire syllabus, making them an ideal practice
CBSE Sample Paper Class 10 Maths with Solutions (Old Pattern)
These sample papers will help sharpen the time management skills of the students and give them the confidence to face the final exams head on, making it an ideal resource for students with different
academic aptitudes. Solutions follow the marking scheme practiced by the Board.
We hope these CBSE Sample Papers for Class 10 Maths PDF will be a valuable asset for the students. All further suggestions towards improving the sample papers are welcome and would be edited with
utmost care.
|
{"url":"https://www.cbsetuts.com/cbse-sample-papers-for-class-10-maths/","timestamp":"2024-11-09T22:54:59Z","content_type":"text/html","content_length":"61179","record_id":"<urn:uuid:de593f34-74da-4619-98a6-4d19b6150e6e>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00666.warc.gz"}
|
Type Params Return Type Name and description
void addToFixedLeaves(Turtle t)
void addToFreeLeaves(Turtle o)
AgentSet<Link> allLinks()
AgentSet<Link> allMyInLinks()
AgentSet<Link> allMyLinks()
AgentSet<Link> allMyOutLinks()
boolean allQ(Collection a, Closure closure)
Queries if all agents in a collection are true for a boolean closure.
void ask(AgentSet<? extends ReLogoAgent> a, Closure askBlock)
Executes a set of commands for an agentset in random order.
void ask(Collection<? extends ReLogoAgent> c, Closure askBlock)
Executes a set of commands for a collection of agents.
void ask(Turtle t, Closure askBlock)
Executes a set of commands for a turtle.
void ask(Patch p, Closure askBlock)
Executes a set of commands for a patch.
void ask(Link l, Closure askBlock)
Executes a set of commands for a link.
void askCollection(Collection<? extends ReLogoAgent> l, Closure cl)
void askTurtle(Closure cl)
void back(Number num)
Steps turtle backwards by a distance.
void bk(Number num)
Steps turtle backwards by a distance.
boolean canMoveQ(Number nDist)
Queries if turtle can move a distance.
int compareTo(Turtle t)
Link createLinkFrom(Turtle t)
Makes a directed link from a turtle to the caller.
Link createLinkFrom(Turtle t, Closure closure)
Makes a directed link from a turtle to the caller then executes a set of commands on the created link.
Link createLinkTo(Turtle t)
Makes a directed link from the caller to a turtle.
Link createLinkTo(Turtle t, Closure closure)
Makes a directed link from the caller to a turtle then executes a set of commands on the created link.
Link createLinkWith(Turtle t)
Makes a undirected link between the caller and a turtle.
Link createLinkWith(Turtle t, Closure closure)
Makes an undirected link between the caller and a turtle then executes a set of commands on the created link.
AgentSet<Link> createLinksFrom(Collection<? extends Turtle> a)
Makes directed links from a collection of agents to the caller.
AgentSet<Link> createLinksFrom(Collection<? extends Turtle> a, Closure closure)
Makes directed links from a collection of turtles to the caller then executes a set of commands on the created links.
AgentSet<Link> createLinksTo(Collection<? extends Turtle> a)
Makes directed links from the caller to a collection of agents.
AgentSet<Link> createLinksTo(Collection<? extends Turtle> a, Closure closure)
Makes directed links from the caller to a collection of agents then executes a set of commands on the created links.
AgentSet<Link> createLinksWith(Collection<? extends Turtle> a)
Makes undirected links between the caller and a collection of agents.
AgentSet<Link> createLinksWith(Collection<? extends Turtle> a, Closure closure)
Makes undirected links between the caller and a collection of agents then executes a set of commands on the created links.
void die()
Removes the turtle.
double distance(Turtle t)
Returns the distance from the caller to a turtle.
double distance(Patch p)
Returns the distance from the caller to a patch.
double distancexy(Number nX, Number nY)
Returns the distance from the caller to a point.
double dx()
Returns the turtle's x increment for one step.
double dy()
Returns the turtle's y increment for one step.
void face(Turtle t)
Faces the caller towards a turtle.
void face(Patch p)
Faces the caller towards a patch.
void facexy(Number nX, Number nY)
Faces the caller towards a point.
void fd(Number num)
Steps turtle forward by a distance.
void fileShow(Object value)
Prints value with agent identifier to current file with a newline.
boolean fixedLeavesContains(Turtle t)
void forward(Number num)
Steps turtle forward by a distance.
boolean freeLeavesContains(Object o)
double getColor()
Returns the color of a turtle.
double getHeading()
Returns the heading of the turtle.
double getHeadingInRads()
Object getLabel()
Returns the label.
double getLabelColor()
Returns the label color for a turtle or link.
int getMaxPxcor()
Returns the maximum x coordinate for all patches.
int getMaxPycor()
Returns the maximum y coordinate for all patches.
int getMinPxcor()
Returns the minimum x coordinate for all patches.
int getMinPycor()
Returns the minimum y coordinate for all patches.
Observer getMyObserver()
TurtleFactory getMyTurtleFactory()
double getPcolor()
Returns the color of patch here.
int getPenMode()
Returns the pen setting of a turtle.
int getPenSize()
Returns the pen width of a turtle.
int getPxcor()
Returns the x coordinate of patch here.
int getPycor()
Returns the y coordinate of patch here.
String getShape()
Returns the shape of a turtle.
double getSize()
Returns the size of a turtle.
NdPoint getTurtleLocation()
String getTurtleType()
int getWho()
Returns the id number of a turtle.
static int getWhoCounter()
double getXcor()
Returns the x coordinate of a turtle.
double getYcor()
Returns the y coordinate of a turtle.
AgentSet<Turtle> hatch(Number number)
Makes a number of new turtles.
AgentSet<Turtle> hatch(Number number, Closure closure)
Makes a number of new turtles and then executes a set of commands on the created turtles.
AgentSet<Turtle> hatch(Number number, Closure closure, String childType)
Makes a number of new turtles of a specific type and then executes a set of commands on the created turtles.
AgentSet<Turtle> hatch(Number number, Closure closure, Class childType)
Makes a number of new turtles of a specific type and then executes a set of commands on the created turtles.
void hideTurtle()
Turtle appears hidden.
void home()
Turtle goes to (0,0).
void ht()
Turtle appears hidden.
AgentSet inCone(Collection a, Number num, Number angle)
Returns an agentset within a distance and heading cone of the caller.
Link inLinkFrom(Turtle t)
Returns the directed link from a turtle to the caller.
boolean inLinkNeighborQ(Turtle t)
Queries if there is a directed link from a turtle to the caller.
AgentSet<Turtle> inLinkNeighbors()
Returns the agentset with directed links to the caller.
AgentSet inRadius(Collection a, Number num)
Returns an agentset within a distance of the caller.
boolean isHiddenQ()
Queries if caller is hidden.
boolean isShapeChanged()
boolean isVisibilityChanged()
void jump(Number num)
Moves turtle forward num units.
void left(Number num)
Rotates the turtle to the left num degrees.
Link link(Number oneEnd, Number otherEnd)
Returns the link between two turtles.
Link link(Turtle oneEnd, Turtle otherEnd)
Returns the link between two turtles.
boolean linkNeighborQ(Turtle t)
Reports true if there is an undirected link connecting t and the caller.
AgentSet<Turtle> linkNeighbors()
Reports the agentset of all turtles found at the other end of undirected links connected to the calling turtle.
Link linkWith(Turtle t)
Report the link between t and the caller.
AgentSet<Link> links()
void lt(Number num)
Rotates the turtle to the left num degrees.
AgentSet maxNOf(int number, Collection<? extends ReLogoAgent> a, Closure closure)
Returns an agentset consisting of a specified number of agents which have the greatest value when operated on by a set of commands.
ReLogoAgent maxOneOf(Collection<? extends ReLogoAgent> a, Closure closure)
Returns the ReLogoAgent with the largest value when operated on by a set of commands.
AgentSet minNOf(int number, Collection<? extends ReLogoAgent> a, Closure closure)
Returns an agentset consisting of a specified number of agents which have the lowest value when operated on by a set of commands.
ReLogoAgent minOneOf(Collection<? extends ReLogoAgent> a, Closure closure)
Returns the ReLogoAgent with the smallest value when operated on by a set of commands.
void move(Number nNumber)
void moveTo(Turtle t)
Moves a turtle to the same location as turtle t.
void moveTo(Patch p)
Moves a turtle to the same location as patch p.
void mv(Number nNumber)
AgentSet<Link> myInLinks()
AgentSet<Link> myLinks()
AgentSet<Link> myOutLinks()
Object myself()
The agent that initiated the asking.
AgentSet<Patch> neighbors()
AgentSet<Patch> neighbors(int extent)
AgentSet<Patch> neighbors(int extentX, int extentY)
AgentSet<Patch> neighbors4()
AgentSet<Patch> neighbors4(int extent)
AgentSet<Patch> neighbors4(int extentX, int extentY)
void notifySubscribers()
Stop oldStop()
Stops a turtle executing within a command closure.
AgentSet other(Collection a)
Returns an agentset minus the caller.
Turtle otherEnd()
Returns the turtle opposite the asking link.
boolean outLinkNeighborQ(Turtle t)
Queries if there is a directed link from the caller to the turtle.
AgentSet<Turtle> outLinkNeighbors()
Returns the agentset of the caller's out link neighbor turtles.
Link outLinkTo(Turtle t)
Returns the caller's directed link to a turtle.
Patch patch(Number nX, Number nY)
Returns the patch containing a point.
Patch patchAhead(Number distance)
Returns the patch that is at a distance ahead of a turtle.
Patch patchAt(Number nX, Number nY)
Returns the patch at a direction (nX, nY) from the caller.
Patch patchAtHeadingAndDistance(Number nHeading, Number nDistance)
Returns the patch that is at a direction and distance from the caller.
Patch patchHere()
Returns the patch where the turtle is located.
Patch patchLeftAndAhead(Number nAngle, Number nDistance)
Returns the patch that is at a distance and degrees left from the caller.
Patch patchRightAndAhead(Number nAngle, Number nDistance)
Returns the patch that is at a distance and degrees right from the caller.
AgentSet<Patch> patches()
Returns an agentset containing all patches.
void pd()
Sets the turtle's pen to draw lines.
void pe()
Does nothing, included for translation compatibility.
void penDown()
Sets the turtle's pen to draw lines.
void penErase()
Does nothing, included for translation compatibility.
void penUp()
Sets the turtle's pen to stop drawing lines.
void pu()
Sets the turtle's pen to stop drawing lines.
int randomPxcor()
Returns a random x coordinate for patches.
int randomPycor()
Returns a random y coordinate for patches.
double randomXcor()
Returns a random x coordinate for turtles.
double randomYcor()
Returns a random y coordinate for turtles.
void registerSubscriber(Turtle t)
void removeFromFixedLeaves(OutOfContextSubject t)
void removeFromFreeLeaves(Turtle o)
void removeSubscriber(Turtle t)
void right(Number num)
Rotates the turtle to the right num degrees.
void rt(Number num)
Rotates the turtle to the right num degrees.
void run(String string)
Interprets a string as commands then runs the commands.
Object runresult(String string)
Interprets a string as a command then returns the result.
Turtle self()
Returns this turtle, patch, or link.
void setBaseTurtleProperties(Observer observer, TurtleFactory turtleFactory, String turtleShape, double heading, double color, NdPoint loc)
void setColor(Number color)
Sets the color of a turtle to the value color.
void setHeading(Number nNum)
Sets the heading of the turtle to nNum.
void setHiddenQ(boolean hidden)
Sets turtle visibility.
void setLabel(Object label)
Sets the label.
void setLabelColor(Number labelColor)
Sets the label color for a turtle to labelColor.
void setMyObserver(Observer myObserver)
void setMyTurtleFactory(TurtleFactory myTurtleFactory)
void setMyself(Object o)
Sets the agent that initiated the asking to the value o.
void setPcolor(Number color)
Sets the color of patch here to pcolor.
void setPenMode(Number penMode)
Sets the pen setting of a turtle to penMode.
void setPenSize(Number penSize)
Sets the pen width of a turtle to penSize.
void setShape(String shape)
Sets the shape of a turtle to shape.
void setShapeChanged(boolean shapeChanged)
void setSize(Number size)
Sets the size of a turtle to size.
void setUserDefinedVariables(Turtle parent)
void setVisibilityChanged(boolean visibilityChanged)
static void setWhoCounter(Number whoCounter)
void setXcor(Number number)
Sets the x coordinate of a turtle to number.
void setYcor(Number number)
Sets the y coordinate of a turtle to number.
void setxy(Number nX, Number nY)
Sets the x-y coordinates of a turtle to (nX, nY).
void show(Object value)
Prints value with agent identifier to the console.
void showTurtle()
Makes turtle visible.
void st()
Makes turtle visible.
String toString()
This method provides a human-readable name for the agent.
double towards(Turtle t)
Returns the direction to turtle t.
double towards(Patch p)
Returns the direction to patch p.
double towardsxy(Number nX, Number nY)
Returns the direction from a turtle or patch to a point.
Turtle turtle(Number number)
Returns the turtle of the given number.
AgentSet<Turtle> turtles()
Returns an agentset containing all turtles.
AgentSet<Turtle> turtlesAt(Number nX, Number nY)
Returns the agentset on the patch at the direction (ndx, ndy) from the caller.
AgentSet<Turtle> turtlesHere()
Returns an agentset of turtles from the patch of the caller.
AgentSet<Turtle> turtlesOn(Patch p)
Returns an agentset of turtles on a given patch.
AgentSet<Turtle> turtlesOn(Turtle t)
Returns an agentset of turtles on the same patch as a turtle.
AgentSet<Turtle> turtlesOn(Collection a)
Returns an agentset of turtles on the patches in a collection or on the patches that a collection of turtles are.
void update(Turtle o)
void watchMe()
Does nothing, included for translation compatibility.
int worldHeight()
Returns the height of the world.
int worldWidth()
Returns the width of the world.
|
{"url":"https://repast.github.io/docs/api/repast_simphony/repast/simphony/relogo/AbstractTurtle.html","timestamp":"2024-11-11T15:04:37Z","content_type":"text/html","content_length":"251820","record_id":"<urn:uuid:6f7917e2-4685-4028-922e-b35213ce5e35>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00292.warc.gz"}
|
Help needed with Unit 15
Mrskingy Registered Posts: 20 New contributor 🐸
For some reason my brain seems to be struggling with holding all the information required.
I need to sit the simulation before end of March to stay on track with my study plan.
Can anyone suggest any easy way of remembering the 11 different ratio analysis, working out the cost of discount and gilt edge securities?????
My head hurts...............
• working out the cost of discount
I am short of time so have picked
of your questions
working out the cost of discount
If you give a customer a discount for paying you earlier than normal, you are effectively borrowing money for the period of the reduction. The interest you pay on the money you borrow is the
discount you allow the customer.
Say I am your customer.
1. I normally pay 35 days after the invoice date
2. You want me to pay within 10 days
3. You are prepaed to allow me a 2% discount on my invoice totals for paying within the new time period
We need to know
1. What 2% of the amount the customer will pay is
2. How many periods of the reduced period there are in a year
1. As the company you are offering 2% of the total bill, but the customer will only pay 98%
2. So 2/98 will give you the "interest" rate for the reduced period (0.020408 or 2.0408%)
3. The reduced period is 35 days less 10 days. You are effectively borrowing the 98% for 25 days.
4. There are 365/25 periods of 25 days in a year (14.6)
So we know we are paying 2.04...% for 98% of the bill for 25 days, but we need to know the annualised equivalent rate.
There is a simple interest approach or a compound interest approach, the one you do depends on your calculator.
Can you calculate amounts to the "power of" something?
If so
take the 100% +2.04...% rate to the power of the 14.6 periods in a year.
This shows the amount borrowed plus the interest %
I make it 134.3%
Then take off the 100%
To give the annualised cost of the prompt payment discount as 34.3%
(Pretty high given the expected base rate of 0.5% by teatime today!!)
If you can't calculate, to "the powers" you will have to do a simple interest calculation.
2.04...% x 14.6 periods = 29.8%
So if you answer this sort of question in a skills test:
34.3% is right
but 29.8% can be marked as right if you add a sentence to say that you are aware that using the simple interest approach means that the answer ignores the compounding effect of interest over the
year, but is a useful starting point.
• Hi Sandy
Can i ask is this another correct way of working out the cost of discount? or have i totally messed up the sum :001_smile:
D- discount
n - normal terms
d- discount days
So say
Discount = 2%
Normal payment days = 60
Discount days = 30
nope totally forgot it
so then the cost for the year is 24.8 - the days can be changed to months as well as the discount
Sorry just trying to remember it myself
• I just learnt the ratios by rote, got OH to test me, and learnt which were a number or a percent. It is helpful to read up on what the significance is because then they 'mean' something and it
will come up in the exam!
By the way our lecturer quoted some, like interest cover, as Net Profit before interest and tax, over interest. It took me a while to realise that is Operating Profit over Interest! (Osborne
talks about Operating Profit).
At least feel free to shoot me down if I am misguided!
• A vic
I have quoted you
so then the cost for the year is 24.8
and then quoted myself
2.04...% x 14.6 periods = 29.8%
but 29.8% can be marked as right if you add a sentence to say that you are aware that using the simple interest approach means that the answer ignores the compounding effect of interest over
the year, but is a useful starting point.
Your method is just as wrong as mine (my second one) because it is a simple interest approach. But if you say so and why, it will be marked as correct in a skills test.
You used different numbers, but if you want to check it put the same numbers I used into your formula.
D- discount
n - normal terms
d- discount days
So say
Discount = 2%
Normal payment days = 60
Discount days = 30
2/98 x 365/30 = 24.83%
I avoided this example as the days earlier (60 - 30) just happens to be the new credit period. And that could cause confusion.
Incidentally, if you can borrow from the bank at 8% p.a. or offer early payment discounts at a rate equivalent to almost 25% p.a. would you offer the early payment discount?
Would your answer change if you were worried that a client might go under very soon?
A vic
I have quoted you
and then quoted myself
Your method is just as wrong as mine (my second one) because it is a simple interest approach. But if you say so and why, it will be marked as correct in a skills test.
You used different numbers, but if you want to check it put the same numbers I used into your formula.
2/98 x 365/30 = 24.83%
I avoided this example as the days earlier (60 - 30) just happens to be the new credit period. And that could cause confusion.
Incidentally, if you can borrow from the bank at 8% p.a. or offer early payment discounts at a rate equivalent to almost 25% p.a. would you offer the early payment discount?
Would your answer change if you were worried that a client might go under very soon?
Great thanks sandy was trying to get my head around an example that was given to me but i think am slowly getting it
|
{"url":"https://forums.aat.org.uk/Forum/discussion/21925/help-needed-with-unit-15","timestamp":"2024-11-03T22:03:05Z","content_type":"text/html","content_length":"302351","record_id":"<urn:uuid:bf5f5b9a-de98-4a55-b93c-ad636b0bec2c>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00488.warc.gz"}
|
ManPag.es -
ssysv.f −
subroutine SSYSV (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
SSYSV computes the solution to system of linear equations A * X = B for SY matrices
Function/Subroutine Documentation
subroutine SSYSV (characterUPLO, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, real, dimension( ldb, * )B, integerLDB, real, dimension( * )WORK,
integerLWORK, integerINFO)
SSYSV computes the solution to system of linear equations A * X = B for SY matrices
SSYSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = ’U’, or
A = L * D * L**T, if UPLO = ’L’,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A is REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = ’U’, the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = ’L’, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the block diagonal matrix D and the
multipliers used to obtain the factor U or L from the
factorization A = U*D*U**T or A = L*D*L**T as computed by
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by SSYTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = ’U’ and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ’L’ and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.
B is REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK is INTEGER
The length of WORK. LWORK >= 1, and for best performance
LWORK >= max(1,N*NB), where NB is the optimal blocksize for
for LWORK < N, TRS will be done with Level BLAS 2
for LWORK >= N, TRS will be done with Level BLAS 3
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011
Definition at line 171 of file ssysv.f.
Generated automatically by Doxygen for LAPACK from the source code.
|
{"url":"https://manpag.es/SUSE131/3+SSYSV","timestamp":"2024-11-11T17:57:35Z","content_type":"text/html","content_length":"22324","record_id":"<urn:uuid:0624173a-5d2b-438c-9e40-e04ef2413104>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00505.warc.gz"}
|
How Is Trigonometry Used On Non-Right-Angled Triangles - MES
How Is Trigonometry Used On Non-Right-Angled Triangles
The three primary trigonometric ratios used to solve problems in non-right-angled triangles are sine, cosine, and tangent. Students can use these ratios to solve for the length of one of the
triangle's sides if they know the values of the angles and one side, essentially applying the non-right-angle triangle formula. Moreover, these ratios are interchangeable, simplifying the process of
finding a solution to complex trigonometric equations.
Overview of Sine, Cosine, and Tangent Ratios
Sine (sin):
• The sine of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the hypotenuse (the side opposite the right angle).
• Mathematically, for an angle θ, it is expressed as: sin()=Opposite SideHypotenuse
Cosine (cos):
• The cosine of an angle in a right-angled triangle is the ratio of the length of the adjacent side to the length of the hypotenuse.
• Mathematically, for an angle θ, it is expressed as: cos()=Adjacent SideHypotenuse
Tangent (tan):
• The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side.
• Mathematically, for an angle θ, it is expressed as: tan ()=Opposite SideAdjacent Side
Angles within Non-Right-Angled Triangles
Non-right-angled triangles, where internal angles do not measure exactly 90°, can be classified as acute or obtuse. Understanding these distinctions is key in calculating the area of non-right-angle
• An acute triangle has all internal angles less than 90°.
• An obtuse triangle has one internal angle greater than 90°.
Calculating the area of a non-right-angle triangle also involves understanding these distinctions.
The Law of Sines
The Law of Sines is a fundamental formula for solving problems related to the area of non-right-angle triangles. It is used to find unknown angles or the length of a missing side in non-right-angled
The formula is asin A =bsin B =csin C where 'a, 'b,' and 'c' are the sides of the triangle, and 'A,' 'B,' and 'C' are the angles opposite of those sides, respectively.
The Law of Cosines
The Law of Cosines is another essential tool in trigonometry and non-right triangle calculations.
The formula is a² = b² + c² - 2bc cos(A), where A is the angle opposite the side 'a'.
Knowing the measurements of all three sides or two sides and the angle opposite one side, we can use this formula to determine the unknown measures.
Real-world Examples of Trigonometry in Non-Right Angled Triangles
Trigonometry's application extends beyond Maths to real-world scenarios, such as surveying, architecture, satellite communication, and more, demonstrating its versatility in solving problems
involving non-right angle triangle formulas.
Challenges and Considerations in Trigonometry Application
Although trigonometry is effective, students might need help applying the formulas to real problems.
Some common issues include dealing with large or small numbers, formulae mix-ups, and difficulties interpreting word problems. However, we can overcome these challenges and become better problem
solvers with practice and patience.
Tips for Problem Solving
• Understand the Basics: Have a firm grasp of trigonometric principles and formulas.
• Use Logical and Analytical Thinking: Apply critical thinking to assess and approach the problem.
• Careful Reading and Application: Read the problem thoroughly and understand how to apply formulas effectively.
• Visualize with Diagrams: Drawing the triangle can aid in better visualization and comprehension of problems involving trigonometry and non-right triangles.
• Patience is Key: Take time to think through the problem without rushing.
Trigonometry's Versatility in Non-Right Angled Triangles
To sum up, applying trigonometry to non-right-angled triangles broadens the versatility of the subject and offers a wider range of solution possibilities. Although it might seem daunting, as with
everything else, practice makes perfect. It's crucial to fully understand the principal concepts and formulas before attempting to solve complex problems and find an effective solution.
Trigonometry is vital daily, from engineering to architecture to financial planning. So, if you are interested in these areas, mastering trigonometry is critical to opening up endless possibilities
in the field.
|
{"url":"https://myedspace.co.uk/blog/post/how-trigonometry-used-non-right-angled-triangles","timestamp":"2024-11-05T15:01:47Z","content_type":"text/html","content_length":"237661","record_id":"<urn:uuid:fd8723de-e0ca-4ab0-b194-b4f4a2619b58>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00647.warc.gz"}
|
For a normal distribution with a mean of 10 - Credence Writers
QUESTION 27For a normal distribution with a mean of 10 and a standard deviation of 5, what is the probability of scoring below a 11.25? Report your answer in percentage form to the second decimal
place. Make sure you use the z table to get the exact answer.1 pointsQUESTION 28For a normal distribution with a mean of 10 and a standard deviation of 5, what is the probability of scoring below a
12.25? Report your answer in percentage form to the second decimal place. Make sure you use the z table to get the exact answer.1 pointsQUESTION 29For a normal distribution with a mean of 10 and a
standard deviation of 5, what is the probability of scoring below a 5? Report your answer in percentage form to the second decimal place. Make sure you use the z table to get the exact answer.1
pointsQUESTION 30For a normal distribution with a mean of 20 and a standard deviation of 10 what the probablity of scoring above a 17? Report your answer in percentage form to the second decimal
place. Make sure you use the z table to get the exact answer.1 pointsQUESTION 31For a normal distribution with a mean of 20 and a standard deviation of 10 what the probablity of scoring above a 20?
Report your answer in percentage form to the second decimal place. Make sure you use the z table to get the exact answer.1 pointsQUESTION 32For a normal distribution with a mean of 0 and a standard
deviation of 1 what the probability of scoring between a -1.75 and 1.25? Report your answer in percentage form to the second decimal place. Make sure you use the z table to get the exact answer.1
pointsQUESTION 33For a normal distribution with a mean of 0 and a standard deviation of 1 what the probability of scoring between a 1.25 and 2.75? Report your answer in percentage form to the second
decimal place. Make sure you use the z table to get the exact answer.1 pointsQUESTION 34What proportion (in decimal form) of people have a favorite color blue? Round to the second decimal place. Use
the following frequency table:colorfrequencyblue31green22red691 pointsQUESTION 35What is the sample correlation for the following data? Round to the second decimal place.xy3460518841 pointsQUESTION
36What is the sample correlation for the following data? Round to the second decimal place.xy8187175154231 pointsQUESTION 37A distribution has a mean of 9 and standard deviation of 2. What is the raw
score for a z score of -1.02? Round to the second decimal place.UESTION 1A distribution has a mean of 5 and a standard deviation of 7 what is the z score of a raw score of 5. Round to the second
decimal place.1 pointsQUESTION 2A researcher is interested in the effects of a drug therapy on depression in all adults with depression. The researcher gives the drug to 30 adults. She finds an
average depression score of 3. The number 3 is a…samplepopulationparameterstatistic1 pointsQUESTION 3What percentage liked the movie? Round to the second decimal
place.StatistifactionFrequencyLiked78Disliked101 pointsQUESTION 4Find the sample standard deviation for the following values. Round to the second decimal place.48, 31, 711 pointsQUESTION 5What is the
sum of squares for the following data? Round to the second decimal place, if needed.54, 15, 37, 721 pointsQUESTION 6If the sample size is 99 what would be the degrees of freedom be for a one sample
t-test?1 pointsQUESTION 7A professor knows his tests generally have an average of 75 with a standard deviation of 10. The professor is now teaching a condensed course in the summer. The summer course
is less weeks than his normal classes. The professor is afraid that the summer course is too condensed and negatively affects tests scores. The professor administers his test to his current 64
students in his summer course. The mean of the 64 students is 71. Is there statistically significant evidence to conclude students in his summer class performed worse than students in his regular
semester courses?What is the test statistic?1 pointsQUESTION 8ACT scores are normally distributed and have a mean of 20.8 and a standard deviation of 4.8. A researcher wants to know students at her
college compare to the national average. The researcher randomly samples 36 students at her school. The sample average for the sample was 18. Do the students significantly differ from the general
population?What should the null hypothesis be?1 pointsQUESTION 9A professor knows his tests generally have an average of 75 with a standard deviation of 10. The professor is now teaching a condensed
course in the summer. The summer course is less weeks than his normal classes. The professor is afraid that the summer course is too condensed and negatively affects tests scores. The professor
administers his test to his current 64 students in his summer course. The mean of the 64 students is 71. Is there statistically significant evidence to conclude students in his summer class performed
worse than students in his regular semester courses?What should the null hypothesis be?1 pointsQUESTION 10A normal population has a mean of 25. After receiving a treatment, a sample of scores yields
the following data: 20 28 20 20. Research question: Is there evidence for that the scores differ after receiving the treatment? What is the test statistic? Hint: Find the sample mean and sample
standard deviation first.1.53.25-1.5-3.251 pointsQUESTION 11SAT scores are known to have a mean of 1500 and a standard deviation of 250. A researcher is testing out a new SAT prep course. The
researcher selects 49 high school students with a variety ofGPAs. The students are given the prep course and then they take the SAT. The average SAT score for the students is 1600 Is there
statistical evidence to conclude the prep course was effective? Use an alpha of .10.What should the null hypothesis be?1 pointsQUESTION 12The formula (X – ?)/? is used to calculate a:raw scoremean
distributionstandard deviationz score1 pointsQUESTION 13A z score tells you how many _____ you are from the _____.mean deviations; medianstandard deviations; meanstandard deviations; medianmean
deviations; mean1 pointsQUESTION 14A z score of –3.0 is _____ a z score of –2.0lower thanhigher thanthe same asmore standard than1 pointsQUESTION 15According to Cohen, a correlation of .6 is?
weakmoderatestrong1 pointsQUESTION 16If the sample size is 51 and the t-statistic is -2, what is the p-value for a less than research hypothesis?.034578.012332.013874.0254741 pointsQUESTION 17For a
perfect correlation to occur, what would need to be the next grade value. You may need to create a scatterplot.Hours StudiedGrade2606706708751080108012?1 pointsQUESTION 18Measures of central tendency
and variability are calculated to describe the nature of charitable giving each year. These figures are computed for the “average” American citizen. Which of these is a possible value for the
variance in dollars given?A.$47.26 squared dollarsB.$38.45 to $47.26C.–$47.26D.$47.261 pointsQUESTION 19As the sample size increases for a sampling distribution (n for each sample) the standard error
decreases.TrueFalse1 pointsQUESTION 20The population of some scores are normally distributed, and a sample of 10 is taken, would the sampling distribution be normally distributed (according to the
Central Limit Theorem)?yesno
|
{"url":"https://credencewriters.com/for-a-normal-distribution-with-a-mean-of-10/","timestamp":"2024-11-11T04:22:53Z","content_type":"text/html","content_length":"50631","record_id":"<urn:uuid:3b0890da-251c-4dba-8197-ef4ee48e22b2>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00079.warc.gz"}
|
NumPy array operations and Broadcasting
NumPy provides a wide range of operations that can be performed on arrays, including mathematical, logical, and relational operations. These operations can be used to manipulate data in a variety of
ways, such as filtering, transforming, and aggregating data.
One of the key features of NumPy is its ability to perform broadcasting. Broadcasting allows NumPy to perform operations on arrays of different shapes and sizes, without the need for explicit loop
structures. Broadcasting allows for more concise and readable code, and can often result in improved performance.
Here are some examples of NumPy array operations and broadcasting:
Mathematical operations:
import numpy as np
# Create two arrays
a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
# Add two arrays element-wise
c = a + b
# Subtract two arrays element-wise
d = a - b
# Multiply two arrays element-wise
e = a * b
# Divide two arrays element-wise
f = a / b
Logical operations
import numpy as np
# Create an array
a = np.array([True, False, True])
# Invert the elements of the array
b = np.invert(a)
# Combine two arrays using the logical AND operator
c = np.logical_and(a, b)
# Combine two arrays using the logical OR operator
d = np.logical_or(a, b)
Relational operations:
import numpy as np
# Create two arrays
a = np.array([1, 2, 3])
b = np.array([2, 3, 4])
# Check if the elements of the arrays are equal
c = np.equal(a, b)
# Check if the elements of the arrays are not equal
d = np.not_equal(a, b)
# Check if the elements of the first array are less than the elements of the second array
e = np.less(a, b)
import numpy as np
# Create an array
a = np.array([1, 2, 3])
# Add a scalar value to each element of the array
b = a + 1
# Add two arrays of different shapes
c = a + np.array([1, 2])
# Multiply two arrays of different shapes
d = a * np.array([[1], [2], [3]])
NumPy array operations and broadcasting are widely used in various data analysis use cases, such as:
1. Image processing: NumPy arrays are often used to represent digital images, which are typically represented as multi-dimensional arrays of pixel values. NumPy’s mathematical and logical operations
can be used to perform various image processing tasks, such as filtering, smoothing, and edge detection.
2. Scientific computing: NumPy arrays are widely used in scientific computing tasks, such as numerical simulations and data analysis in fields such as physics, chemistry, and biology. NumPy’s
mathematical operations and broadcasting capabilities can be used to perform various numerical computations, such as solving equations and simulating complex systems.
3. Machine learning: NumPy arrays are the basis of many popular machine learning libraries, such as Scikit-learn, Keras, and TensorFlow. NumPy’s mathematical and logical operations are used
extensively in these libraries to perform various data preprocessing and transformation tasks, such as feature scaling and normalization.
4. Financial analysis: NumPy arrays can be used to represent and analyze financial data, such as stock prices and market trends. NumPy’s mathematical operations and broadcasting capabilities can be
used to perform various financial calculations, such as calculating moving averages and identifying trading signals.
5. Data visualization: NumPy arrays can be used to create visualizations of data, such as scatter plots, histograms, and heat maps. NumPy’s broadcasting capabilities can be used to perform various
transformations on data before visualizing it, such as scaling and normalization.
These are just a few examples of the many ways that NumPy array operations and broadcasting can be used in data analysis. NumPy’s flexibility and power make it an essential tool for anyone working
with data in Python.
Share this content
|
{"url":"https://connectjaya.com/numpy-array-operations-and-broadcasting/","timestamp":"2024-11-07T15:34:55Z","content_type":"text/html","content_length":"105112","record_id":"<urn:uuid:ec181bb9-f540-47bd-bbe9-16943033470e>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00740.warc.gz"}
|
Inverse Log Calculator - Savvy Calculator
Inverse Log Calculator
About Inverse Log Calculator (Formula)
The Inverse Log Calculator is a valuable mathematical tool used to find the original number that corresponds to a given logarithm value. This calculator is essential for solving equations involving
exponential growth or decay, and it is commonly used in mathematics, science, and engineering fields.
Formula: Original Number = 10^(Logarithm Value)
To use the calculator, input the logarithm value, and it will calculate the corresponding original number.
The Inverse Log Calculator is crucial for solving logarithmic equations, analyzing exponential relationships, and interpreting data involving exponential functions.
Mathematicians, scientists, and engineers find the Inverse Log Calculator invaluable for reverse-engineering logarithmic transformations, predicting growth or decay rates, and making accurate
calculations in various disciplines.
By utilizing the Inverse Log Calculator, individuals can determine the initial values behind logarithmic transformations, enabling precise analysis and interpretation of exponential phenomena.
Leave a Comment
|
{"url":"https://savvycalculator.com/inverse-log-calculator","timestamp":"2024-11-08T11:35:12Z","content_type":"text/html","content_length":"140859","record_id":"<urn:uuid:834037c4-0724-4423-9c49-a9174c58966e>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00391.warc.gz"}
|
Module and Programme Catalogue
This module is discontinued in the selected year. The information shown below is for the academic year that the module was last running in, prior to the year selected.
2013/14 Taught Postgraduate Module Catalogue
MATH5033M Advanced Graph Theory
20 creditsClass Size: 40
Module manager: Dr Joseph Grant
Email: pmtjgr@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2013/14
│MATH2210 │Introduction to Discrete Mathematics │
This module is mutually exclusive with
This module is approved as an Elective
Module summary
This module provides an introduction to the basic ideas such as connectedness, trees, planar graphs, Eulerian and Hamiltonian graphs, directed graphs and the connection between graph theory and the
four colour problem. Graph theory is an important mathematical tool in such different areas as linguistics, chemistry and, especially, operational research. The material on complexity theory and
algorithmic graph theory is an important bridge between mathematics and theoretical computer science, and is very rich in applications.
To introduce students to some of the main concepts and modeling usefulness of graph theory, and to develop their ability to reason graph theoretically.
Learning outcomes
On completion of this module, students should be able to:
(a) identify basic examples of isomorphic and non-isomorphic pairs of graphs, and make simple deductions involving vertex degrees, connectedness and bipartite graphs;
(b) apply a selection of criteria related to Eulerian and Hamiltonian graphs;
(c) explain and apply the basic theoems for trees, planar graphs and directed graphs;
(d) understand the Max-flow Min-cut Theorem and its connections to other results in graph theory, and apply the Ford-Fulkerson Algorithm.
(e) show a knowledge of graph colourings of various types, and apply a range of techniques for identifying chromatic numbers for graphs and surfaces;
(f) understand and explain key concepts from computational complexity theory;
(g) explain and apply several graph theoretic algorithms, prove their validity and investigate their speed.
Topics chosen from:
1. Basic definitions. Connected graphs, vertex degrees, bipartite graphs.
2. Adjacency matrices, strongly regular graphs, Friendship Theorem.
3. Eulerian graphs and applications.
4. Hamiltonian graphs, including Dirac's theorem and techniques for identifying non-Hamiltonian graphs.
5. Trees (Cayley's Theorem), line graphs. Multiple connectivity and block graphs.
6. Planar graphs. Euler's theorem, Kuratowski's theorem (without proof).
7. Digraphs, strong connectedness. Robbins' Theorem. Eulerian digraphs. Hamiltonian and semi-Hamiltonian tournaments and Moon's Theorem.
8. Networks. Max-flow Min-cut Theorem (Ford-Fulkerson Algorithm), Menger's Theorem, Konig's Theorem, and applications.
9. Graph colourings. The five-colour theorem for planar graphs, the four-colour theorem for planar graphs (without proof). Brook's Theorem. Edge colourings, Tait colourings.
10. Chromatic numbers of surfaces, applications of the Euler characteristic, Heawood's inequality and the Map Colour Theorem.
11. Graph problems and intractability, including NP-completeness and Cook's Theorem.
12. A selection of graph-theoretic algorithms and associated structural results, from some of the following: minimum connector problem; planarity testing algorithm; electrical networks and searching
trees; chromatic polynomials; Menger's Theorems and connectivity; minimum cost-flow; strongly connected and 2-connected components; graph minors.
Teaching methods
│Delivery type │Number│ Length hours│ Student hours│
│Lecture │ 44│ 1.00│ 44.00│
│Private study hours │ 156.00│
│Total Contact hours │ 44.00│
│Total hours (100hr per 10 credits) │ 200.00│
Private study
There will be two weekly office hours for students to get additional help, depending on their needs.
Opportunities for Formative Feedback
Regularcoursework with solution sheets provided later.
Methods of assessment
│Exam type │Exam duration│% of formal assessment│
│Standard exam (closed essays, MCQs etc) │3 hr 00 mins │ 100.00│
│Total percentage (Assessment Exams) │ 100.00│
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
reading list
is available from the Library website
Last updated: 17/02/2014
Browse Other Catalogues
Errors, omissions, failed links etc should be notified to the Catalogue Team.PROD
|
{"url":"https://webprod3.leeds.ac.uk/catalogue/dynmodules.asp?Y=201920&M=MATH-5033M","timestamp":"2024-11-02T08:33:54Z","content_type":"text/html","content_length":"12573","record_id":"<urn:uuid:90ec04a2-6df5-4b7b-900d-e509aa58e177>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00106.warc.gz"}
|
Democratic indices
1. Section 7. Democratic indices
In common with many modern price indices, the Consumer Prices Index (CPI) weights the price movements of items in proportion to their importance to total household spending. Price movements for
products on which households spend a large fraction of their income are consequently weighted more heavily than items on which households spend relatively little.
As discussed in Section 2, a corollary of this approach is that high-spending households have a greater weight in the CPI than low-spending households. This follows because high-spending households
influence total households’ spending to a greater extent than low-spending households. However, an alternative to this approach is to calculate a price index in which each household receives an equal
weight. These price indices – commonly referred to as ‘democratic^1’ price indices – capture a degree of the variation in expenditure weights across households in a population. In populations with
homogenous weights – where all households purchase goods in equal proportions – the ‘plutocratically’ weighted CPI and the democratic index are equal. The more variation there is in expenditure
baskets across households – perhaps because of differing tastes, interests or income constraints – the larger the difference between these indices. While the conventional democratic price index is
for all households in an economy, the logic applies equally to any chosen sub-group.
To shed some light on this matter in the UK context, this section compares the headline, plutocratically-weighted, CPI with the democratically-weighted index for the UK between 2002 and 2014. It
proceeds to present democratic price indices for households with and without children, and retired and non-retired households.
Notes for section 7. Democratic indices:
1. Note that the naming convention here can be misleading: In a ‘democratic’ index, each household is given an equal weight, rather than each individual, which might be implied from its name. A
‘truly’ democratic index would weight each person in an economy equally, and would deviate from the popular convention of a democratic index to the extent of variation in household size.
Arguably, a still ‘truer’ index would use longitudinal data to observe movements in expenditure patterns for the same individuals through time, however, this approach is data-intensive,
challenging to implement, and its interpretation not straightforward.
Nôl i'r tabl cynnwys
7.2.1 All households
Weighting households equally – rather than according to their expenditure (see Section 2) – means that a democratic price index will more closely reflect the price experience of low expenditure
households than a conventional plutocratically-weighted index. As the results presented in Section 5 suggest that low-expenditure households have typically experienced higher rates of inflation than
high-expenditure households over the last decade, it should come as little surprise that the democratic index shows a higher rate of inflation than the CPI. This is shown in Figure 7.1, which plots
both series between January 2003 and October 2014. Only in 2010 and 2014 to date – when the range of inflation outcomes between deciles narrows markedly (see Figure 5.5) – is the gap between the two
Figure 7.1: CPI-consistent democratic and plutocratic inflation rates for all households, %
Source: ONS Calculations
Download this chart Figure 7.1: CPI-consistent democratic and plutocratic inflation rates for all households, %
Image .csv .xls
While Figure 7.1 above shows the democratically- and plutocratically-weighted price indices for the period January 2003 and October 2014, Figure 7.2 shows the difference between the two series. It
indicates that the CPI is on average around 0.3 percentage points lower than an equivalent index in which every household is given an equal weight over this period. In 2008, this difference was
particularly marked, while in late 2009 to early 2010 and in recent months in 2014, the difference was close to zero. While assessing the statistical significance of these differences is difficult,
the underlying trend is clear: during periods when the degree of variation in household inflation experiences is much broader (see Figure 5.5), the extent of the difference between these indices is
greater. In line with the analysis presented in Section 5, this effect is particularly noticeable in 2006, 2008 and 2011: periods in which the average rate of inflation rises quite sharply.
Figure 7.2: Difference between plutocratically- and democratically-weighted price indices, percentage points
Source: ONS Calculations
7.2.2 Households with and without children
While the calculation of a democratic price index for the household sector as a whole is of interest, the concept can usefully be applied to sub-groups of the population. In this analysis, the
plutocratically-weighted index represents the average price movement in the sub-group’s basket of goods and services weighted by their share in total expenditure, while the democratically-weighted
index represents the average price change experienced by households in the sub-group. This distinction (Leicester et al., 2008) can help to unpick the degree of variation in price experiences within
Figure 7.3 below presents the democratically- and plutocratically-weighted indices for households with and without children in Panels A and B respectively, as well as the range of inflation outcomes
for expenditure quintiles within each sub-group. The dots represent the highest and lowest inflation rates observed, with the shaded bars showing the range between the 2nd-highest and 2nd-lowest
expenditure quintile. First, it supports the finding in Section 5 that households with children have experienced a lower rate of price increase on average than households without children, as
indicated in the yellow triangles of Panels A and B. Secondly, the degree of variation in inflation outcomes is larger for households without children, as indicated by the range of inflation rates
shown in Panel A and Panel B. Through most of this time period, the highest (lowest) inflation rates observed – indicated by the top (bottom) dots – are the inflation rates for the lowest (highest)
expenditure quintiles. The degree of variation in 2008 is particularly marked for households without children, when the plutocratic (3.7%) and democratic (4.6%) averages lie within a range of 2.9%
for the highest-expenditure quintile and 6.2% for the lowest-expenditure quintile. Thirdly, this greater variety in inflation outcomes across the expenditure quintiles for households without children
manifests itself in a greater difference between the plutocratic and democratic price indices. This is shown by the greater difference between the two markers in Panel B than in Panel A.
Figure 7.3A: Range of plutocratically-calculated inflation rates for expenditure quintiles of households with children; CPI-consistent democratic and plutocratic inflation rates; %
Source: ONS Calculations
1. Figures shows the plutocratically weighted (yellow) and the democratically weighted (black) inflation rates for each group in each period. Figures also show the range of inflation outcomes for
the quintiles (red/blue dots) and the inter-quintile range between the 2nd-highest and 2nd-lowest measures of equivalised quintile inflation rates (shaded red/blue bar).
Figure 7.3B: Range of plutocratically-calculated inflation rates for expenditure quintiles of households without children; CPI-consistent democratic and plutocratic inflation rates; %
Source: ONS Calculations
1. Figures shows the plutocratically weighted (yellow) and the democratically weighted (black) inflation rates for each group in each period. Figures also show the range of inflation outcomes for
the quintiles (red/blue dots) and the inter-quintile range between the 2nd-highest and 2nd-lowest measures of equivalised quintile inflation rates (shaded red/blue bar).
What explains these differences? As in Section 5 above, the inflation rate differentials shown here are driven by differences in expenditure patterns. Households without children consequently appear
to be a more heterogeneous group than households with children, spending more on average on products whose price has increased relatively sharply over this period. Much of this difference is likely
due to the demographic composition of these groups, as retired and elderly households are concentrated in the households without children group.
7.2.3 Retired households
Section 5 indicated that retired households have experienced higher rates of inflation than non-retired households on average since 2003, largely as a consequence of retired households spending more
of their income on products that have risen strongly in price over this period.
Figure 7.4 presents the plutocratically- (yellow) and democratically-weighted (black) inflation rates for retired (Panel A) and non-retired households (Panel B). The two panels also summarise the
distribution of inflation rates for these groups, showing the range of inflation outcomes for expenditure quintiles in each group. The dots represent the highest and lowest quintile-level inflation
rates observed, with the shaded bars showing the range between the 2nd-highest and 2nd-lowest quintile results. As reported above, the average rate of price increase for retired households is higher
than for non-retired households, but it is the difference in the range of inflation outcomes that is particularly striking. On average, the range of inflation outcomes across the expenditure
quintiles of the retired population is around twice as broad as the equivalent range for non-retired households. In 2008, while inflation outcomes for the non-retired population ranged from 2.9% to
5.0%, the equivalent range for the retired population was 3.0% to 7.1%. While some retired households experienced broadly the same inflation rate as the non-retired population, a subset of this group
faced much faster rates of price increase.
Figure 7.4A: Range of plutocratically-calculated inflation rates for expenditure quintiles of retired households; CPI-consistent democratic and plutocratic inflation rates; %
Source: ONS Calculations
1. Figures shows the plutocratically weighted (yellow) and the democratically weighted (black) inflation rates for each group in each period. Figures also show the range of inflation outcomes for
the quintiles (red/blue dots) and the inter-quintile range between the 2nd-highest and 2nd-lowest measures of equivalised quintile inflation rates (shaded red/blue bar).
Figure 7.4B: Range of plutocratically-calculated inflation rates for expenditure quintiles of non-retired households; CPI-consistent democratic and plutocratic inflation rates; %
Source: ONS Calculations
1. Figures shows the plutocratically weighted (yellow) and the democratically weighted (black) inflation rates for each group in each period. Figures also show the range of inflation outcomes for
the quintiles (red/blue dots) and the inter-quintile range between the 2nd-highest and 2nd-lowest measures of equivalised quintile inflation rates (shaded red/blue bar).
This broader distribution of observed inflation rates within the retired household population is also shown in the difference between the plutocratic and democratic inflation rates. In Panel A, the
difference between these two measures is notably larger than the difference between the two in the lower panel. Taken together, these results indicate that the degree of variation in expenditure
patterns within the retired population is markedly wider than among non-retired households. The reasons for this difference are likely to stem from the very different financial circumstances that
prevail within the retired population, to say nothing of differences in tastes and preferences. However, what is clear from this analysis is that any single measure of inflation for a sub-group –
whether calculated on a plutocratic or a democratic basis – will not capture the full degree of variation in price experience within groups. This finding in particular has important policy
Nôl i'r tabl cynnwys
|
{"url":"https://cy.ons.gov.uk/peoplepopulationandcommunity/personalandhouseholdfinances/expenditure/compendium/variationintheinflationexperienceofukhouseholds/2014-12-15/chapter4democraticindices","timestamp":"2024-11-08T05:40:37Z","content_type":"text/html","content_length":"53949","record_id":"<urn:uuid:f0500cf4-e2cb-4079-826d-ad8045cca947>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00895.warc.gz"}
|
Put Ratio Back spread – Varsity by Zerodha
9.1 – Background
We discussed the “Call Ratio Back spread” strategy extensively in chapter 4 of this module. The Put ratio back spread is similar except that the trader invokes this when he is bearish on the market
or stock.
At a broad level this is what you will experience when you implement the Put Ratio Back Spread
1. Unlimited profit if the market goes down
2. Limited profit if market goes up
3. A predefined loss if the market stays within a range
In simpler words you make money as long as the market moves in either direction, of course the strategy is more favorable if market goes down.
Usually, the Put Ratio Back Spread is deployed for a ‘net credit’, meaning money flows into your account as soon as you execute Put Ratio Back Spread. The ‘net credit’ is what you make if the market
goes up, as opposed to your expectation (i.e market going down). On the other hand if the market indeed goes down, then you stand to make an unlimited profit.
I suppose this should also explain why the put ratio back spread is better than buying a plain vanilla put option.
9.2 – Strategy Notes
The Put Ratio Back Spread is a 3 leg option strategy as it involves buying two OTM Put options and selling one ITM Put option. This is the classic 2:1 combo. In fact the put ratio back spread has to
be executed in the 2:1 ratio meaning 2 options bought for every one option sold, or 3 options bought for every 2 options sold, so on and so forth.
Let take an example – Nifty Spot is at 7506 and you expect Nifty to hit 7000 by the end of expiry. This is clearly a bearish expectation. To implement the Put Ratio Back Spread –
1. Sell one lot of 7500 PE (ITM)
2. Buy two lots of 7200 PE (OTM)
Make sure –
1. The Put options belong to the same expiry
2. Belong to the same underlying
3. The ratio is maintained
The trade set up looks like this –
1. 7500 PE, one lot short, the premium received for this is Rs.134/-
2. 7200 PE, two lots long, the premium paid is Rs.46/- per lot, so Rs.92/- for 2 lots
3. Net Cash flow is = Premium Received – Premium Paid i.e 134 – 92 = 42 (Net Credit)
With these trades, the Put ratio back spread is executed. Let us check what would happen to the overall cash flow of the strategies at different levels of expiry.
Do note we need to evaluate the strategy payoff at various levels of expiry, as the strategy payoff is quite versatile.
Scenario 1 – Market expires at 7600 (above the ITM option)
At 7600, both the Put options would expire worthless. The intrinsic value of options and the eventual strategy payoff is as below –
• 7200 PE, would expire worthless, since we are long 2 lots of this option at Rs.46 per lot, we would lose the entire premium of Rs.92 paid
• 7500 PE would also expire worthless, but we have written this option and received a premium of Rs.134, which in this case can be retained back
• The net payoff from the strategy is 134 – 92 = 42
Do note, the net payoff of the strategy at 7600 (higher than the ITM strike) is equivalent to the net credit.
Scenario 2 – Market expires at 7500 (at the higher strike i.e the ITM option)
At 7500 both the options would have no intrinsic value, hence they both would expire worthless. Hence the payoff would be similar to the payoff we discussed at 7600. Hence the net strategy payoff
would be equal to Rs.42 (net credit).
In fact as you may have guessed, the payoff of the strategy at any point above 7500 is equal to the net credit.
Scenario 3 – Market expires at 7458 (higher break even)
Like in the call ratio back spread strategy, the put ratio back spread too has two breakeven points i.e the upper breakeven and the lower breakeven point. 7458 marks the upper breakeven level; of
course we will discuss how we arrived at the upper breakeven point a little later in the chapter.
• At 7458, the 7500 PE will have an intrinsic value. As you may recall, the put option intrinsic value can be calculated as Max[Strike – Spot, 0] i.e Max[7500 – 7458, 0] hence 42
• Since we have sold 7500 PE at 134, we will lose a portion of the premium received and retain the rest. Hence the payoff would be 134 – 42 = 92
• The 7200 PE will not have any intrinsic value, hence the entire premium paid i.e 92 is lost
• So on one hand we made 92 on the 7500 PE and on the other we would lose 92 on the 7200 PE resulting in no loss, no gain. Thus, 7458 marks as one of the breakeven points.
Scenario 4 – Market expires at 7200 (Point of maximum pain)
This is the point at which the strategy causes maximum pain, let us figure out why.
• At 7200, 7500 PE would have an intrinsic value of 300 (7500 – 7200). Since we have sold this option and received a premium of Rs.134, we would lose the entire premium received and more. The
payoff on this would be 134 – 300 = – 166
• 7200 PE would expire worthless as it has no intrinsic value. Hence the entire premium paid of Rs.92 would be lost
• The net strategy payoff would be -166 – 92 = – 258
• This is a point where both the options would turn against us, hence is considered as the point of maximum pain
Scenario 5 – Market expires at 6942 (lower break even)
At 6942, both the options would have an intrinsic value; however this is the lower breakeven point. Let’s figure out how this works –
• At 6942, 7500 PE will have an intrinsic value equivalent of 7500 – 6942 = 558. Since have sold this option at 134, the payoff would be 134 – 558 = – 424
• The 7200 PE will also have an intrinsic value equivalent of 7200 – 6942 = 258 per lot, since we are long two lots the intrinsic value adds upto 516. We have initially paid a premium of Rs.92
(both lots included), hence this needs to be deducted to arrive at the payoff would be 516 – 92 = +424
• So on one hand we make 424 on the 7200 PE and on the other we would lose 424 on the 7500 PE resulting in no loss, no gain. Thus, 6942 marks as one of the breakeven points.
Scenario 6 – Market expires at 6800 (below the lower strike price)
Remember, the put ratio backspread is a bearish strategy. It is supposed to make money once the market goes below the lower breakeven point. So lets understand how the pay off behaves at a point
lower than the lower breakeven point.
• At 6800, 7500 PE will have an intrinsic value of 700 and since we are short 7500PE at 134, we would lose 134 -700 = – 566
• 7200 PE will have an intrinsic value of 400. Since we are long 2 lots, the intrinsic value would be 800. Premium paid for two lots is Rs.92, hence after adjusting for the premium paid, we get to
make 800 – 92 = +708
• Net strategy payoff would be 708 – 566 = +142
Likewise, you can evaluate the strategy payoff at different levels of market expiry and you will realize that the profits are uncapped as long as the market continues to slide. The following table
showcases the same –
Plotting the different payoff points, gives us the strategy payoff graph –
Clearly from the graph above, we can conclude –
1. If markets go down, then the profits are unlimited
2. There are two breakeven points
3. The point at which maximum loss occurs is at 7200
4. If markets goes up, then the profits are limited
9.3 – Strategy generalization
We can generalize the key strategy levels as below –
1. Spread = Higher Strike – lower strike
a. 7500 – 7200 = 300
2. Max loss = Spread – Net credit
a. 300 – 42 = 258
3. Max Loss occurs at = Lower strike price
4. Lower Breakeven point = Lower strike – Max loss
a. 7200 – 258 = 6942
5. Upper breakeven point = Lower strike + Max loss
a. 7200 + 258 = 7458
9.4 – Delta, strike selection, and effect of volatility
As we know, the strategy gets more profitable as and when the market falls. In other words this is a directional strategy (profitable when markets go down) and therefore the delta at overall strategy
level should reflect this. Let us do the math to figure this out –
• 7500 PE is ITM option, delta is – 0.55. However since we have written the option, the delta is –(-0.55) = +0.55
• 7200 PE is OTM, has a delta of – 0.29, remember we are long two lots here
• The overall position delta would be +0.55 + (-0.29) +(-0.29) = – 0.03
The non zero Delta value clearly indicates that the strategy is sensitive to the directional movement (although negligible). The negative sign indicates that the strategy makes money when the market
goes down.
As far as the strikes are concerned, I’d suggest you stick to the classic combination of ITM and OTM options. Remember the trade needs to be executed for a ‘Net Credit’. Do not initiate this strategy
if there is a net outflow of cash at the time of execution.
Let’s look at the variation in volatility and its effect on the strategy –
There are three colored lines depicting the change of “premium value” versus change in volatility. These lines help us understand the effect of increase in volatility on the strategy keeping time to
expiry in perspective.
1. Blue Line – This line suggests that an increase in volatility when there is ample time to expiry (30 days) is beneficial for the Put ratio back spread. As we can see the strategy payoff increases
from -57 to +10 when the volatility increase from 15% to 30%. Clearly this means that when there is ample time to expiry, besides being right on the direction of stock/index you also need to have
a view on volatility. For this reason, even though I’m bearish on the stock, I would be a bit hesitant to deploy this strategy at the start of the series if the volatility is on the higher side
(say more than double of the usual volatility reading)
2. Green line – This line suggests that an increase in volatility when there are about 15 days time to expiry is beneficial, although not as much as in the previous case. As we can see the strategy
payoff increases from -77 to -47 when the volatility increase from 15% to 30%.
3. Red line – Clearly increase in volatility when we have a few days to expiry does not have much impact on the premium value. This means, when you are close to expiry you only need to worry about
the directional movement and need not really worry much about the variation in volatility.
Key takeaways from this chapter
1. The Put Ratio Back spread is best executed when your outlook on the stock/index is bearish
2. The strategy requires you to sell 1 ITM PE and buy 2 OTM PE, and this is to be executed in the same ratio i.e for every 1 option sold, 2 options have to be purchased
3. The strategy is usually executed for a ‘Net Credit’
4. The strategy makes limited money if the stock price goes up, and unlimited profit when the stock price goes down
5. There are two break even points – lower breakeven and upper breakeven
6. Spread = Higher Strike – Lower Strike
7. Net Credit = Premium Received for Higher strike – 2*Premium paid for lower strike
8. Max Loss = Spread – Net Credit
9. Max Loss occurs at = Lower Strike
10. The payoff when market goes up = Net Credit
11. Lower Breakeven = Lower Strike – Max Loss
12. Upper Breakeven = Lower Strike + Max Loss
13. Irrespective of the time to expiry opt for ITM and OTM strike combination
14. Increase in volatility is good for this strategy when there is more time to expiry
Download Put Ratio Back Spread Excel Sheet
108 comments
1. Very useful topic. Plz clear my small doubt. Can we executive a call ratio back spread or the put ratio back spread on net debit? Do zerodha allows that? Kindly clarify.
□ You can execute it for a net debit…for example if you sell ATM and buy a strike just next to ATM then it ‘may’ result in a net debit. However its best if you can execute it for a next credit.
You can do this with any broker, not just Zerodha.
☆ Thanks for the prompt reply Karthik. It’s clear now. If I have to impliment the ratio spreads with an intraday or 1-2 days view, what sort of monyness you recommend for the option strike
○ I would not suggest you do this for intraday. However if you wish to set this up overnight, I’d suggest you look at the standard combo – ATM and OTM.
□ a VERY tricky question regards to Hedging which time and strike price would be the best in bank nifty or nifty for doing hedging regardless volatility in the market. also how could we
identify trends in the market like bullish or bearish trend?
☆ This comes purely based on experience, Sanjay 🙂
2. sir, i am new trader, i read your articles. All are too good. but i am not having that much time now to concentrate on market. is there any paid service to give successful traders ideas or calls
□ You should check out – https://opentrade.in/
3. Do we need to make the delta neutral while implementing this strategy and suppose if we put this strategy then can we make adjustments by keeping delta neutral after respective time interval???
□ By its structure, the strategy will remain delta neutral.
4. please confirm while sell ITM and Buy OTM must be done in a time frame,or i can buy PE 2 lot OTM and sell ITM some other day or few days later like after 7 days ,then whether this strategy will
work .and what should be ITM strike position along with volatility .
□ It has to be executed as a set in one shot, you cannot spit it over time.
5. in this strategy as expected if volatility and movement does not come than @ what point should we exit the trade
□ You can hold the position till expiry…but if the position is making you uncomfortable, then you should exit.
6. Dear karthik,
i was trying to put in the strategy around the current nifty values to get a better understanding but stuck up with delta calculations.
days to expiry=4
bought 2 9000PE option. (delta as per zerodha calculator after putting in IV of 12.24 = -0.137)
Sold 1 9200PE option. ( delta as per zerodha calculator after putting in IV of 10.33 = -0.77)
So net Delta = -0.137-0.137-(-0.77)=+0.496.
please explain
□ Since you have shorted an ITM PE, you are net long – remember delta of PE is -ve, when you short a PE, the delta turns positive. So in your example, you are short a ITM PE whose delta is
overpowering the deltas of 2 OTM PE.
7. Hi Nithin/Karthik/Zerodha
Could you please start a module on interest rate trading. From basic to practical. That would be really helpful.
□ We will put this up sometime soon. Thanks.
8. 1) In this example, wouldn’t 7500 strike be ATM and not ITM since the spot is at 7506? And for the OTM strike, why did you choose 7200 & not 7300 (because in some examples, the difference between
strike & spot is only around 200, here it’s around 300)?
2) Have noticed that you always take the strike price which are in multiples of 100 in your examples. Is it because they have more liquidity compared to strikes in multiples of 50 (only)?
□ 1) You can implement this with one ATM (or an ITM close to ATM) short and 2 OTM buy. So given this, its ok to have 7500.
2) Larger the spread, higher is the reward. The expectation is that Nifty will to 7000, so more bang for the buck.
3) Yes, that’s the only reason.
9. Hi Team,
I want to execute multiple orders simultaneously in 1 order. Is there any facility to do the same in Zerodha.
eg Buy BankNifty 27000 ce , sell 27500 ce Buy 28000 PE and sell 28500 PE all should be executed in 1 order.
Awaiting for your feedback
□ Yes, Sensibull lets you do this as a single order, check this – https://sensibull.com/
10. Hello sir…Thank you for all your previous replies they were really helpful.
I am at commodities module end now but i was revisioning this module and here are my queries which you can explain.
First i want to know that why the Payoff vs Volatility chart of Call ration backspread CRBS and put ratio back spread PRBS are different. I mean in PRBS if volatility changes when there is ample
time the net payoff decreases coz there is increase in premium and when there is less time and volatility changes there isnt much effect. But in the module previous to this you tole that. [when
volatility increases (or is expected to increase) – option writers start fearing that they could be caught writing options that
can potentially transition to ‘in the money’. But nonetheless, fear too can be
overcome for a price, hence option writers expect higher premiums for writing
options, and therefore the premiums of call and put options go up when volatility is expected to increase.]
And next question is why payoff increases with volatility in bear put spread when at the same time net credit decreases if we opt for bear call spread.
And the last thing i wamt to clear that this is annual volatility we are talkin abt here or is that some other kind of volatility.
Thank you
11. Hi Sir, I am tracking 10600 PE and 10400 PE, the percentage change in 10600 PE is less than that of 10400 PE. I expect the reverse because the spot is around 10600, how? Is that the mere effect
of IV. Also in sensibull while tracking my position, the Delta for 10600 PE is lesser than 10400 PE, how this will be correct?
□ The percentage change is a function of not just IV but also gamma. Would suggest you read this – https://zerodha.com/varsity/chapter/gamma-part-1/
About Sensibull showing lower Delta for ITM, maybe you should write to their support for an explanation.
☆ Thank you very much…
○ Welcome, Sanjeev!
12. Hi Karthik,
From your example”
Nifty Spot is at 7506 and you expect Nifty to hit 7000 by the end of expiry. This is clearly a bearish expectation. To implement the Put Ratio Back Spread –
Sell one lot of 7500 PE (ITM)
Buy two lots of 7200 PE (OTM) ”
In this scenario, both are below 7506 so either 7200 was written as OTM is a typo or 7500 must be an ATM. How come both strikes below the spot price are considered as ITM and OTM as both are
considered as OTM for puts?
□ 7500PE is considered ATM and 7200PE is OTM.
☆ Hi,
But technically OTM and ITM should be on opposite sides right?>
○ Opposite side meaning?
13. sir when very few days to expiry like 1 week, you have mentioned slightly ITM and deep ITM spread for call ratio back spread. similarly can we apply slightly OTM and deep OTM spread for put ratio
back spread .
□ Just the opposite, Prasanth. You set up a spread with OTM options when you have ample time to expiry.
14. In 9.4, Strike selection in missing.
15. Sir ,
If Im to Execute put-ratio-back-spread should i Square off ( The Higher strike which is Sold and the Lower strike which we had Purchased ) or Simply Let is Expire worthless on the Expiry date and
collect the profits if profits are made . Please explain
□ If it is worthless (heading that direction), you can as well let it expire.
16. Sir ,
After knowing about Put Ratio Back Spread , I Executed it on Mothersumi , on 2:1 Ratio Bought 2 OTM PE of Strike 65 for Rs., 2.70 and Sold 1 ITM PE of Strike 80 @ 9.65 . Till Yesterday i had
Approximately 160 Thousand as cash in funds . Yesterday I Also Sold One SBIN CE Strike 210 @ 0.20 , Because Option Pain shows at Strike 190.00 i Assumed i shall Collect 0.20 Premium as it will
End worthless by 30th April , At this point i still had 5000 cash left in my account .
Today i.e. 29th April i was shocked ro see My Funds have gone -568000 Negative . in fear i Exited MotherSumi 2 OTM PE of Strike 65 ( Which i Had Bought ) , Only to See my Funds to go -6,73,653.34
Negative after exit . I am Confused and in Deep Panic . I also have one NIFTY FUT APR which i had shorted and one NIFTY FUT JUN on which i am Long .
Please Explain the Whole Concept why is that my funds are negative to such an extent 6,73,653.34 . as per your postings which i read and as per my understanding i was suppose to make some money
but now i am in deep red i dont know who to settle this . Should i exit all my Positions and book heavy losses .
Mothersumi 1 ITM PE of Strike 80 @ 9.65 is Now 0.55
Mothersumi 2 OTM PE of Strike 65 for Rs., 2.70 in Now 0.05( Already Sold in panic)
Mothersumi Option pain is at 75.00
NIFTY APR FUT Bought @ 9238.00 Currently NIFTY APR FUT @ 9461.00 NIFTY Spot 9483.00 Option Pain @ 9300.00
NIFTY JUN FUT Bought @ 9299.00 Currently NIFTY JUN FUT 9481.00 Spot 9483.00
SBIN 210PE Sold @ 0.20 Current Value 0.15 Option Pain @ 190.00
Please Advice what should i do now . Am I , in Hole for this Huge Amount of 6,73,653.34 . ?
□ Mothersumi 1 ITM PE of Strike 80 @ 9.65 is Now 0.55 — > Since this is short, you made money on this
Mothersumi 2 OTM PE of Strike 65 for Rs., 2.70 in Now 0.05( Already Sold in panic) – Since you are long, you have lost 2.7 here
Overall, I think your position is profitable.
NIFTY APR FUT Bought @ 9238.00 Currently NIFTY APR FUT @ 9461.00 NIFTY Spot 9483.00
NIFTY JUN FUT Bought @ 9299.00 Currently NIFTY JUN FUT 9481.00 Spot 9483.00
Both these positions are also profitable
SBIN 210PE Sold @ 0.20 Current Value 0.15 Option Pain @ 190.00
This position is also profitable.
SO where is the question of a loss? Are you referring to the margins blocked? Please call the support desk once to seek clarification.
17. Cant we just buy a long straddle ?
Aint this strategy capping our profits in one direction ?
And the range for profits is still the same as long straddle
If i am wrong please correct me kartik sir!
□ Ajay, it is always a balance between the risk and reward, volatility versus directional bets.
18. Hi Sir,
I am new comer in the option and would really like to start trading in options. Could be please guide me how to place order and which strategy to follow to begin with minimum risk.
□ Order placement is the easy bit. You need to develop a market view first. Do check out the module on TA to develop a sense on markets.
19. hi karthik have a query regarding formula of upper breakeven mentioned in this chapter.calculations done for upper breakeven by the formula doesnt match with the figures done on sensibull virtual
trade and even excel calculator provided in this chapter.kindly check and reconfirm and correct me if i m wrong.
□ Manish, the formula i.e. lower strike + max loss, is the same in excel and as explained the chapter. Not sure why it does not match with Sensibull. Maybe you should write to them 🙂
20. hi karthik ,coincidentally figures given in illustration provided in the chapter is matching with excel sheet.try with current figures of nifty and check upper breakeven.
□ Checking this.
21. Sir
In the strategy notes, you mentioned 3 options bought for 2 options sold, shouldnt it be 4 options considering 2:1 ratio?
And Thanks for your simple explanation of all the strategies, it was really helpful.
□ Ah, that’s right. Will make that change 🙂
22. Above in 9.2 when Nifty spot price is 7506 . How can 7500PE is a ITM instead of being ATM . Explain ??
□ 7500PE is ATM, Ayush. Must be a typo, let me check.
23. Just one query, in a scenario, if there is an opportunity for a Call Ratio Spread and another opportunity a Put Ratio Spread. Which opportunity should be more preferred??
I asked this because as the market moves up the Volatility comes down, but when market moves downwards volatility starts shooting up. And I’m sure both wouldn’t give us the same outcomes.
□ There is no generic answer to this, you will have to evaluate this on a case to case basis based on the premium.
24. Hi Sir,
In section 9.2 , i think you made mistake. The rule is to follow 2:1 ratio for strategy.
But you gave example : ‘ there should 3 option bought for every 2 option sold.
Mathematically for above example ratio for buy/sold becomes ‘ 1.5/1’ .
Which unfollows 2:1 rule
You can say ‘there should 3 options bought for 1.5 options sold. (just saying). Then only 2:1 maintains.
Plz correct this n let me know if i am wrong. thank u🤗
□ Ah, I get that. Let me review this and fix (if it needs to be), thanks for pointing though 🙂
25. Hi, as you have mentioned while executing this trade spot is at 7506 and 7500 put should be sold which you have mentioned to ITM option. Would’nt it be that Options above 7506 are ITM Options
while 7500 option is either ATM or slightly OTM. Please clarify.
26. Sorry, i haven’t checked all the comments. I got the answer for my question. Thanks.
□ Happy learning, Vishvas 🙂
27. Hello Sir,
I am getting confused in one part.
When the Volatility is high(Say 30%) at the start of the series(30days to expiry), the premium is high so I should take this strategy instead of avoiding it as Put Ratio Back Spread is a Net
credit strategy.
Sir, where i am going wrong in this thought, can you please clarify it.
Thank you.
□ You can take this strategy, but the thesis of taking is not just the fact that you get high credit. You need to ensure you have a view on both volatility and direction of the market.
28. 3 options bought for every 2 options sold, so on and so forth.
typo* In strategy notes
I think 4 OTM options should be bought for 2 ITM sold
□ Re checking this.
29. Hi Karthik,
In the ‘Strategy Notes’ section while explaining the example, you considered Nifty at 7506. Then you selected strike 7500 as ITM. Isn’t 7500 an OTM strike ?
Thank You
□ Since its 5 points in, its ITM. But usually the strikes in and around the spot is considered ATM 🙂
30. This will help me understand but also to know what is happening with
□ Good luck! Happy learning 🙂
31. Upper Breakeven = Lower Strike + Max Loss
I think this formula is wrong
Correct formula is
Upper Breakeven = Lower Strike – Net Credit
□ Checking this again, Mohan.
32. Call ratio back spread or put ratio back spread, when it is possible to execute it? I never see selling ITM strike could finance buying 2 OTM strikes!
□ Thats when volatility increases and premiums swell. You need to keep track of the premium and spot these opportunities.
33. Wow! It means when volatility cools off, execution could be possible. Good indicator,isn’t it? Thanks Sir for your prompt reply.
□ Happy learning 🙂
34. How to get the PCR online during the market??
□ Do check with Sensibull if they have this feature.
35. How to get the PCR online during the market in my Kite app??
36. Sir, I think there should be a correction under Strategy Notes sub-heading “2:1 ratio meaning 2 options bought for every one option sold, or 3 options bought for every 2 options sold”. It is 2:1
ratio right? so instead of “3 options bought for every 2 options sold” it should be as “4 options bought for every 2 options sold”, that sounds right isn’t?
□ Ah, let me relook at this. Thanks. By the way, I’ll be updating the content and looking at fixing all these typos soon.
37. In “9.2 – Strategy Notes”, this line “3 options bought for every 2 options sold, so on and so forth.” is a typo mistake because it should be 4 not 3
□ Checking this.
38. Hi Karthik,
I had a question regarding this and the other strategies in this series. If the spot price is at 7506 and we expect a 506 point drop in the index to 7000 (target), the strategy would still make a
loss according to the table above, and would need to go below 6942 for it to make money. Is the target wrong or am i missing something? Please guide..
□ So basically, the strategy makes money as the spot falls more. In this case 6942 or lower.
39. Hi sir where I can ready more about open interest and open interest change .
Is there any platform where I can communicate directly. Or any course .
□ This is the platform, Sudhir 🙂
40. Hi Sir i want to do a course on option trading. Where I can interact with faculty . Would you please guide me .
□ We have put a ton of content on this topic here on Varsity, Sudhir. Please do letif you have any specific queries, will be happy to resolve that for you 🙂
41. Hi sir
In option chain there r two options OI and OI change.
Suppose Oi is 14.1lac and OI change is -4.2lakh . What does it indicate?
□ OI indicates the total number of open contracts, up until now, on a cumulative basis. OI change indicates the change from y’day to today.
42. Suppose market is bullish and bank nifty spot price is 39598 and we bought the call option strike of 40000 (OTM) @LTP 220
Aa per the option chain maximum resistance is at the strike price of 39900 as per the OI data.
So my question is
Should by this strike 40000 because LTP IS cheaper and anyWAYS if market will goes up by 39598 and close under 39900 (suppose 39800). Still in that case I will make a profit. Because market has
gone up by almost 200 points.
□ You cant always generalise this, Sudhir. The option premium is a function of many factors and needs to be evaluated, keeping volatility, time to expiry, speed at which the market is moving
along with of course the market direction.
43. Is there any study material on option chain.
□ Yes, I’ve spoken about it in this video – https://www.youtube.com/watch?v=bCRw8YN-4QY&list=RDCMUCQXwgooTlP6tk2a-u6vgyUA&start_radio=1&rv=bCRw8YN-4QY&t=20
44. Could you kindly advise if there could be any extra benefit – if Both… the Call Ratio Back Spread and the Put Ratio Back Spread are implemented at the same time…. to take advantage of any
trending moves either on the upside or the downside?
Secondly.. I have noted that though the Call and Put Ratio Spreads…are significantly profitable on the Strikes at extreme wings… either on the upside or the downside… BOTH give the maximum
loss…on the Strikes where the Longs were purchased. Is there a way to mitigate this risk/loss? Thanks & Rgds
□ You cannot use these interchangeably. CRS is when you expect the markets to move up, and PRBS is when you expect the market to crack. These strategies are designed to manage risk…as in the
risk management bit is baked into the strategy.
45. Sir in strategy notes 9.2, the ratio is 2:1, and you have mentioned that:
3 options bought for every 2 options sold, so on and so forth.
but if we buy 4 options then we will still need to sell 2 options as per ratio
so all that i am getting is, for 3 options bought or 4 options bought we need to sell 2 options likewise, if we buy 7 options or 8 options we need to sell 4 options.
□ Oh ya, thats right. I must have made an inadvertent error here.
46. Sir, I am a school teacher and
hardly get time to see the market (i. e. Hardly 5-10 min to see the market between two teaching periods). I tried all option strategies, every strategy has some merits and demerits.Even I took
some overnight positions, but I faced loss due gap up and gap down of market. So I request you to suggest such trading strategy for intraday or short term which will be suitable as well as
profitable for me plz.
□ There is no single strategy that can be used across multiple scenarios. You will have to experiment and see what works for you 🙂
47. Sir, there is one more doubt that between ‘Long straddle’ and ‘Call back ratio spread’ strategy which is better for intraday as well as for short term plz clarify. I am confused to use among
□ In my opinion, none of these should be used for intraday. These are strategies where you should target to hold for a few days so that the spread can unfold.
48. Ok, thank you sir.
□ Sure, good luck.
49. I think if call and put ration both applied on Dec 24 options would be best as time to expire for loss is maximum
Pls help
Want to execute on monday
□ Akash, better to us a platform like Sensibull to evaluate your positions in terms of risk and reward.
50. In fact the put ratio back spread has to be executed in the 2:1 ratio meaning 2 options bought for every one option sold, or 3 options bought for every 2 options sold, so on and so forth
sir that is 4 option bought for every 2 option sold
□ Ah, yes.
51. sir in Strategy Notes
you tell 3 options bought for every 2 options sold
plz check that
□ Thats the ratio, Darshan.
52. As per TA when DOJI appears there is indecisiveness in the market so market go either way so according to you which strategy is best when seeing DOJI if i am risk appetite is moderate? (i) the
long staddle (2) Call Ratio Back spread (3) Put Ratio Back spread.
□ As far as possible, stick to the strategy that you understand well. Also, there is no one strategy that works across all market situations.
Post a comment
|
{"url":"https://zerodha.com/varsity/chapter/put-ratio-back-spread/?comments=all","timestamp":"2024-11-06T23:59:59Z","content_type":"text/html","content_length":"189431","record_id":"<urn:uuid:db6adb80-3842-484b-89bc-3a5c63dabd4e>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00383.warc.gz"}
|
vermouth.map_parser module
vermouth.map_parser module¶
Contains the Mapping object and the associated parser.
class vermouth.map_parser.Mapping(block_from, block_to, mapping, references, ff_from=None, ff_to=None, extra=(), normalize_weights=False, type='block', names=())[source]¶
Bases: object
A mapping object that describes a mapping from one resolution to another.
The graph which this Mapping object can transform.
The vermouth.molecule.Block we can transform to.
A mapping of node keys in block_to to node keys in block_from that describes which node in blocks_from should be taken as a reference when determining node attributes for nodes in block_to.
The forcefield of block_from.
The forcefield of block_to.
The names of the mapped blocks.
The actual mapping that describes for every node key in block_from to what node key in block_to it contributes to with what weight. {node_from: {node_to: weight, ...}, ...}.
dict[collections.abc.Hashable, dict[collections.abc.Hashable, float]]
Only nodes described in mapping will be used.
map(graph, node_match=None, edge_match=None)[source]¶
Performs the partial mapping described by this object on graph. It first find the induced subgraph isomorphisms between graph and block_from, after which it will process the found
isomorphisms according to mapping.
None of the yielded dictionaries will refer to node keys of block_from. Instead, those will be translated to node keys of graph based on the found isomorphisms.
Only nodes described in mapping will be used in the isomorphism.
○ graph (networkx.Graph) – The graph on which this partial mapping should be applied.
○ node_match (collections.abc.Callable or None) – A function that should take two dictionaries with node attributes, and return True if those nodes should be considered equal, and False
otherwise. If None, all nodes will be considered equal.
○ edge_match (collections.abc.Callable or None) – A function that should take six arguments: two graphs, and four node keys. The first two node keys will be in the first graph and share
an edge; and the last two node keys will be in the second graph and share an edge. Should return True if a pair of edges should be considered equal, and False otherwise. If None, all
edges will be considered equal.
○ dict[collections.abc.Hashable, dict[collections.abc.Hashable, float]] – the correspondence between nodes in graph and nodes in block_to, with the associated weights.
○ vermouth.molecule.Block – block_to.
○ dict – references on which mapping has been applied.
property reverse_mapping¶
The reverse of mapping. {node_to: {node_from: weight, ...}, ...}
class vermouth.map_parser.MappingBuilder[source]¶
Bases: object
An object that is in charge of building the arguments needed to create a Mapping object. It’s attributes describe the information accumulated so far.
None or vermouth.molecule.Block
None or vermouth.molecule.Block
None or vermouth.forcefield.ForceField
None or vermouth.forcefield.ForceField
Add a block to blocks_from. In addition, apply any ‘replace’ operation described by nodes on themselves:
{'atomname': 'C', 'charge': 0, 'replace': {'charge': -1}}
{'atomname': 'C', 'charge': -1}
block (vermouth.molecule.Block) – The block to add.
Add a block to blocks_to.
block (vermouth.molecule.Block) – The block to add.
add_edge_from(attrs1, attrs2, edge_attrs)[source]¶
Add a single edge to blocks_from between two nodes in blocks_from described by attrs1 and attrs2. The nodes described should not be the same.
○ attrs1 (dict[str]) – The attributes that uniquely describe a node in blocks_from
○ attrs2 (dict[str]) – The attributes that uniquely describe a node in blocks_from
○ edge_attrs (dict[str]) – The attributes that should be assigned to the new edge.
add_edge_to(attrs1, attrs2, edge_attrs)[source]¶
Add a single edge to blocks_to between two nodes in blocks_to described by attrs1 and attrs2. The nodes described should not be the same.
○ attrs1 (dict[str]) – The attributes that uniquely describe a node in blocks_to
○ attrs2 (dict[str]) – The attributes that uniquely describe a node in blocks_to
○ edge_attrs (dict[str]) – The attributes that should be assigned to the new edge.
add_mapping(attrs_from, attrs_to, weight)[source]¶
Add part of a mapping to mapping. attrs_from uniquely describes a node in blocks_from and attrs_to a node in blocks_to. Adds a mapping between those nodes with the given weight.
○ attrs_from (dict[str]) – The attributes that uniquely describe a node in blocks_from
○ attrs_to (dict[str]) – The attributes that uniquely describe a node in blocks_to
○ weight (float) – The weight associated with this partial mapping.
Add a name to the mapping.
name (str) – The name to add
Add a single node to blocks_from.
attrs (dict[str]) – The attributes the new node should have.
Add a single node to blocks_to.
attrs (dict[str]) – The attributes the new node should have.
add_reference(attrs_to, attrs_from)[source]¶
Add a reference to references.
Sets ff_from
Instantiate a Mapping object with the information accumulated so far, and return it.
The mapping object made from the accumulated information.
Return type:
Reset the object to a clean initial state.
Sets ff_to
class vermouth.map_parser.MappingDirector(force_fields, builder=None)[source]¶
Bases: SectionLineParser
A director in charge of parsing the new mapping format. It constructs a new Mapping object by calling methods of it’s builder (default MappingBuilder) with the correct arguments.
The builder used to build the Mapping object. By default MappingBuilder.
All known identifiers at this point. The key is the actual identifier, prefixed with either “to_” or “from_”, and the values are the associated node attributes.
dict[str, dict[str]]
The name of the section currently being processed.
The name of the forcefield from which this mapping describes a transfomation.
The name of the forcefield to which this mapping describes a transfomation.
A dictionary of known macros.
dict[str, str]
COMMENT_CHAR = ';'¶
The character that starts a comment.
METH_DICT = {('block', 'from'): (<function MappingDirector._ff>, {'direction': 'from'}), ('block', 'from blocks'): (<function MappingDirector._blocks>, {'direction': 'from', 'map_type':
'block'}), ('block', 'from edges'): (<function MappingDirector._edges>, {'direction': 'from'}), ('block', 'from nodes'): (<function MappingDirector._nodes>, {'direction': 'from'}), ('block',
'mapping'): (<function MappingDirector._mapping>, {}), ('block', 'reference atoms'): (<function MappingDirector._reference_atoms>, {}), ('block', 'to'): (<function MappingDirector._ff>,
{'direction': 'to'}), ('block', 'to blocks'): (<function MappingDirector._blocks>, {'direction': 'to', 'map_type': 'block'}), ('block', 'to edges'): (<function MappingDirector._edges>,
{'direction': 'to'}), ('block', 'to nodes'): (<function MappingDirector._nodes>, {'direction': 'to'}), ('macros',): (<function SectionLineParser._macros>, {}), ('modification', 'from'):
(<function MappingDirector._ff>, {'direction': 'from'}), ('modification', 'from blocks'): (<function MappingDirector._blocks>, {'direction': 'from', 'map_type': 'modification'}),
('modification', 'from edges'): (<function MappingDirector._edges>, {'direction': 'from'}), ('modification', 'from nodes'): (<function MappingDirector._nodes>, {'direction': 'from'}),
('modification', 'mapping'): (<function MappingDirector._mapping>, {}), ('modification', 'reference atoms'): (<function MappingDirector._reference_atoms>, {}), ('modification', 'to'):
(<function MappingDirector._ff>, {'direction': 'to'}), ('modification', 'to blocks'): (<function MappingDirector._blocks>, {'direction': 'to', 'map_type': 'modification'}), ('modification',
'to edges'): (<function MappingDirector._edges>, {'direction': 'to'}), ('modification', 'to nodes'): (<function MappingDirector._nodes>, {'direction': 'to'}), ('molecule',): (<function
MappingDirector._molecule>, {})}¶
A dict of all known parser methods, mapping section names to the function to be called and the associated keyword arguments.
NO_FETCH_BLOCK = '!'¶
The character that specifies no block should be fetched automatically.
RESIDUE_ATOM_SEP = ':'¶
The character that separates a residue identifier from an atomname.
RESNAME_NUM_SEP = '#'¶
The character that separates a resname from a resnumber in shorthand block formats.
SECTION_ENDS = ['block', 'modification']¶
finalize_section(previous_section, ended_section)[source]¶
Wraps up parsing of a single mapping.
The accumulated mapping if the mapping is complete, None otherwise.
Return type:
Mapping or None
vermouth.map_parser.parse_mapping_file(filepath, force_fields)[source]¶
Parses a mapping file.
☆ filepath (str) – The path of the file to parse.
☆ force_fields (dict[str, ForceField]) – Dict of known forcefields
A list of all mappings described in the file.
Return type:
|
{"url":"https://vermouth-martinize.readthedocs.io/en/latest/api/vermouth.map_parser.html","timestamp":"2024-11-04T05:23:27Z","content_type":"text/html","content_length":"76939","record_id":"<urn:uuid:25b2f609-cb5e-4ddc-ac78-e68e0c2cfc31>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00687.warc.gz"}
|
Verbe anglais to find
Conjugaison du verbe anglais TO FIND
Verbe irrégulier : find - found - found
Traduction française : trouver
do I find?
do you find?
does he find?
do we find?
do you find?
do they find?
am I finding?
are you finding?
is he finding?
are we finding?
are you finding?
are they finding?
did I find?
did you find?
did he find?
did we find?
did you find?
did they find?
was I finding?
were you finding?
was he finding?
were we finding?
were you finding?
were they finding?
have I found?
have you found?
has he found?
have we found?
have you found?
have they found?
have I been finding?
have you been finding?
has he been finding?
have we been finding?
have you been finding?
have they been finding?
had I found?
had you found?
had he found?
had we found?
had you found?
had they found?
had I been finding?
had you been finding?
had he been finding?
had we been finding?
had you been finding?
had they been finding?
will I find?
will you find?
will he find?
will we find?
will you find?
will they find?
will I be finding?
will you be finding?
will he be finding?
will we be finding?
will you be finding?
will they be finding?
will I have found?
will you have found?
will he have found?
will we have found?
will you have found?
will they have found?
will I have been finding?
will you have been finding?
will he have been finding?
will we have been finding?
will you have been finding?
will they have been finding?
would I find?
would you find?
would he find?
would we find?
would you find?
would they find?
would I be finding?
would you be finding?
would he be finding?
would we be finding?
would you be finding?
would they be finding?
would I have found?
would you have found?
would he have found?
would we have found?
would you have found?
would they have found?
would I have been finding?
would you have been finding?
would he have been finding?
would we have been finding?
would you have been finding?
would they have been finding?
Verbe au hasard
acclaim - analyze - appeal - arrange - brake - cab - choir - clear - define - deny - disappoint - encourage - enjoy - give - interpret - job - lam - land - lesson - liven - modify - moss - motivate -
notice - overhang - quarrel - rape - refer - seek - shine - sightsee - smell - sort - sough - split - spring - swear - taste - to be - to do - to go - to have - translate - utilize
|
{"url":"https://leconjugueur.lefigaro.fr/conjugaison/anglais/to+find_question.html","timestamp":"2024-11-03T20:45:11Z","content_type":"text/html","content_length":"61969","record_id":"<urn:uuid:71db019a-dbb8-48a9-9530-b5ed20b4441c>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00174.warc.gz"}
|
using generalized hypergeometric functions to generate qsl cards
2024-03-26 08:03:04 -04:00
previouscards 2024-03-26 08:03:04 -04:00
backside.pdf 2023-02-17 15:03:15 -05:00
backside.tex 2023-02-17 15:03:15 -05:00
feldhellclub.png 2023-02-17 15:03:15 -05:00
frontsidegenerator.py 2023-02-17 16:28:32 -05:00
readme.md 2023-03-05 10:04:19 -05:00
w8sp.png 2022-01-01 10:07:49 -05:00
yarc.png 2023-02-17 15:03:15 -05:00
What is this?
This code generates a picture called a "phase coloring" (see domain coloring for the essential idea) from a "generalized hypergeometric function" whose parameters are chosen from a given amateur
radio callsign.
How does it work?
The code contains an assignment of letters to numbers. In the file frontsidegenerator.py you see lines like
return 6
That is code saying "assign the number 6 to the letter C". The entire alphabet has an assignment in the code. Numbers in callsigns just remain numbers. For instance, my callsign KE8QZC would have
this translation into numbers:
K -> 2
E -> 5
8 -> 8
Q -> 3
Z -> 7
C -> 6
and so my callsign will translate into a list of numbers num_csg=[2,5,8,3,7,6]. The current version of the code is written to turn callsigns that are 6 symbols long into a "2F3" hypergeometric
function. The first two letters of num_csg become the "top 2 parameters" of the function, the next three become the "bottom 3 parameters", and the final number becomes the exponent on the independent
variable of the 2F1 function. So, my callsign KE8QZC generates the phase coloring of the function 2F3(2,5;8,3,7;z^(6)).
note: starting with card 9, the number scheme changed
What does "commit" refer to in the QSL card I received?
A "commit" is a term used in the "git" software version control software. The commit on your card is a link to the update where I uploaded a copy of your card to the github repository. This would
also give you an approximation to the source code that generated your card. You can find the list of previous commits from this main page by clicking "# commits" under the green box that says "Code".
I include this because the precise scheme I use to assign callsigns to generalized hypergeometric functions will change as I run into callsigns whose phase coloring behaves in a way I don't like (or
if I change the coloring scheme in other ways in the future).
Can I use your code?
Sure; have fun and tell me what you do with it!!
|
{"url":"https://repo.radio/ke8qzc/hypergeometricqsl/src/commit/4559f5de3475e6bf34217016c0fcbca07223671e","timestamp":"2024-11-08T02:32:13Z","content_type":"text/html","content_length":"58231","record_id":"<urn:uuid:4c03ca75-58ad-47c4-aea9-93f9b0ecb7cf>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00158.warc.gz"}
|
Error in generating the seminr model
I followed the book Partial Least Squares Structural Equation Modeling (PLS-SEM) Using R: A workbook (Hair et al, 2021) and got stuck up to Page 62 ch.3
Estimate the model
corp_rep_simple_model <- estimate_pls(data = corp_rep_data,
measurement_model = simple_mm,
structural_model = simple_sm,
inner_weights = path_weighting,
missing = mean_replacement,
missing_value = "-99")
it resulted in error:
Generating the seminr model
Error in [.data.frame(data, , all_loc_non_int_items(measurement_model)) :
undefined columns selected
I have copied the scripts including followed the instruction from internet (such as:>
Attaching package: ‘janitor’;
corp_rep_data2 <- clean_names(corp_rep_data)
But still cannot get the solution.
your help is very much appreciated
Hi there,
I went to the GitHub page of Seminr in all their examples the measurement_model is constructed as graph before running the model. Did you do that in your code?
Try 1st following their examples:
github of seminr
|
{"url":"https://forum.posit.co/t/error-in-generating-the-seminr-model/194138","timestamp":"2024-11-04T18:46:53Z","content_type":"text/html","content_length":"18972","record_id":"<urn:uuid:1c069170-495c-4d76-bee6-8a63b1a8d939>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00517.warc.gz"}
|
mdp example problems
The MDP structure is abstract and versatile and can be applied in many different ways to many different problems. A mathematical framework for solving reinforcement learning(RL) problems, the Markov
Decision Process (MDP) is widely used to solve various optimization problems. Other state transitions occur with 100% probability when selecting the corresponding actions such as taking the Action
Advance2 from Stage2 will take us to Win. The grid is surrounded by a wall, which makes it impossible for the agent to move off the grid. Example 2.4. Thanks. The big problem using value iteration
here is the continuous state space. Examples in Markov Decision Problems, is an essential source of reference for mathematicians and all those who apply the optimal control theory for practical
purposes. 2 Introduction to MDP: the optimization/decision model behind RL Markov decision processes or MDPs are the stochastic decision making model underlying the reinforcement learning problem. A
partially observable Markov decision process (POMDP) is a generalization of a Markov decision process (MDP). The course assumes knowledge of basic concepts from the theory of Markov chains and Markov
processes. However, we will need to adapt the algorithm some. Reinforcement learning is essentially the problem when this underlying model is either unknown or too In the case of the door example, an
open door might give a high reward. These processes are characterized by completely observable states and by transition processes that only depend on the last state of the agent. A Markov decision
process (MDP) is a discrete time stochastic control process. This type of scenarios arise, for example, in control problems where the policy learned for one specific agent will not work for another
due to differences in the environment dynamics and physical properties. In addition, it indicates the areas where Markov Decision Processes can be used. Examples and Videos ... problems determine
(learn or compute) “value functions” as an intermediate step We value situations according to how much reward we expect will follow them “Even enjoying yourself you call evil whenever it leads to the
loss of a pleasure greater than its own, or lays up pains that outweigh its pleasures. A Markov decision process (known as an MDP) is a discrete-time state- transition system. In the problem, an
agent is supposed to decide the best action to select based on his current state. In the next chapters this will be extended this framework to partially observable situations and temporal difference
(TD) learning. Aspects of an MDP The last aspect of an MDP is an artificially generated reward. A real valued reward function R(s,a). My MDP-based formulation problem requires that the process needs
to start at a certain state i.e., the initial state is given. This reward is calculated based on the value of the next state compared to the current state. MDPs are useful for studying optimization
problems solved using reinforcement learning. How to use the documentation¶ Documentation is … For example, decreasing sales volume is a problem to the company, and consumer dissatisfaction
concerning the quality of products and services provided by the company is a symptom of the problem. Some example problems that can be modelled as MDPs Elevator Parallel Parking Ship Steering
Bioreactor Helicopter Aeroplane Logistics Robocup Soccer Quake Portfolio management Protein Folding Robot walking Game of Go For most of these problems, either: MDP model is unknown, but experience
can be sampled MDP model is known, but is too big to use, except by samples Model-free controlcan … Convolve the Map! Al- Suppose that X is the two-state Markov chain described in Example 2.3. A
Markov Decision Process (MDP) model contains: A set of possible world states S. A set of Models. Isn't it the same when we turn back to pain? In doing the research project, the researcher has certain
objectives to accomplish. A simplified example: •Blocks world, 3 blocks A,B,C –Initial state :A on B , C on table. Markov Decision Process (MDP) is a mathematical framework to formulate RL problems.
–Actions: pickup ( ), put_on_table() , put_on(). MDP is a framewor k that can be used to formulate the RL problems mathematically. So, why we need to care about MDP? 3 Lecture 20 • 3 MDP Framework •S
: states First, it has a set of states. In CO-MDP value iteration we could simply maintain a table with one entry per state. (Give the transition and reward functions in tabular format, or give the
transition graph with rewards). More favorable states generate better rewards. Partially observable problems can be converted into MDPs Bandits are MDPs with one state. When this step is repeated,
the problem is known as a Markov Decision Process. concentrate on the case of a Markov Decision Process (MDP). We will solve this problem using regular value iteration. Identify research objectives.
s1 to s4 and s4 to s1 moves are NOT allowed. Map Convolution Consider an occupancy map. The policy then gives per state the best (given the MDP model) action to do. many application examples. Just a
quick reminder, MDP, which we will implement, is a discrete time stochastic control process. 2x2 Grid MDP Problem . We consider the problem defined in Algorithms.MDP.Examples.Ex_3_1; this example
comes from Bersekas p. 22. –Reward: all states receive –1 reward except the configuration C on table, B on C ,A on B. who received positive reward. These states will play the role of outcomes in the
decision theoretic approach we saw last time, as well as providing whatever information is necessary for choosing actions. A Markov Decision Process (MDP) model contains: • A set of possible world
states S • A set of possible actions A • A real valued reward function R(s,a) • A description Tof each action’s effects in each state. The theory of (semi)-Markov processes with decision is presented
interspersed with examples. If the coin comes up heads, he wins as many dollars as he has staked on that flip; if it is tails, he loses his stake. An example in the below MDP if we choose to take the
action Teleport we will end up back in state Stage2 40% of the time and Stage1 60% of the time. Watch the full course at https://www.udacity.com/course/ud600 Robot should reach the goal fast. The red
boundary indicates the move is not allowed. A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe
the underlying state. Perform a A* search in such a map. Please give me any advice to use your MDP toolbox to find the optimal solution for my problem. MDP provides a mathematical framework for
solving RL problems, andalmost all RL problems can be modeled as MDP. This tutorial will take you through the nuances of MDP and its applications. This book brings together examples based upon such
sources, along with several new ones. In other words, we only update the V/Q functions (using temporal difference (TD) methods) for states that are actually visited while acting in the world. The
game ends when the gambler wins by reaching his goal of $100, or loses by running out of money. Example 4.3: Gambler's Problem A gambler has the opportunity to make bets on the outcomes of a sequence
of coin flips. Before going into MDP, you … A random example small() A very small example mdptoolbox.example.forest(S=3, r1=4, r2=2, p=0.1, is_sparse=False) [source] ¶ Generate a MDP example based on
a simple forest management scenario. # Generates a random MDP problem set.seed (0) mdp_example_rand (2, 2) mdp_example_rand (2, 2, FALSE) mdp_example_rand (2, 2, TRUE) mdp_example_rand (2, 2, FALSE,
matrix (c (1, 0, 1, 1), 2, 2)) # Generates a MDP for a simple forest management problem MDP <-mdp_example_forest # Find an optimal policy results <-mdp_policy_iteration (MDP $ P, MDP $ R, 0.9) # …
Suppose that X is the two-state Markov chain described in Example 2.3. What is MDP ? Almost all RL problems can be modeled as MDP with states, actions, transition probability, and the reward
function. Formulate a Markov Decision Process (MDP) for the problem of con- trolling Bunny’s actions in order to avoid the tiger and exit the building. It provides a mathematical framework for
modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. A set of possible actions A. si - indicates the state in grid i . We explain
what an MDP is and how utility values are defined within an MDP. In this episode, I’ll cover how to solve an MDP with code examples, and that will allow us to do prediction, and control in any given
MDP. I would like to know, is there any procedures or rules, that needs to be considered before formulating an MDP for a problem. Markov Decision Process (MDP) Toolbox¶ The MDP toolbox provides
classes and functions for the resolution of descrete-time Markov Decision Processes. This video is part of the Udacity course "Reinforcement Learning". Al- Once the MDP is defined, a policy can be
learned by doing Value Iteration or Policy Iteration which calculates the expected reward for each of the states. import Algorithms.MDP.Examples.Ex_3_1 import Algorithms.MDP.ValueIteration iterations
:: [CF State Control Double] iterations = valueIteration mdp … It can be described formally with 4 components. •In other word can you create a partial policy for this MDP? It provides a mathematical
framework for modeling decision making in situations where outcomes are partly random and partly under the control of the decision maker. This function is used to generate a transition probability (A
× S × S) array P and a reward (S × A) matrix R that model the following problem. –Who can solve this problem? Having constructed the MDP, we can do this using the valueIteration function. Dynamic
Programming. Brace yourself, this blog post is a bit longer than any of the previous ones, so grab your coffee and just dive in. Reinforcement Learning (RL) solves both problems: we can approximately
solve an MDP by replacing the sum over all states with a Monte Carlo approximation. Robots keeps distance to obstacles and moves on a short path! Example for the path planning task: Goals: Robot
should not collide. MDP Environment Description Here an agent is intended to navigate from an arbitrary starting position to a goal position. Available modules¶ example Examples of transition and
reward matrices that form valid MDPs mdp Makov decision process algorithms util Functions for validating and working with an MDP. We assume the Markov Property: the effects of an action taken in a
state depend only on that state and not on the prior history. What this means is that we are now back to solving a CO-MDP and we can use the value iteration (VI) algorithm. Obstacles are assumed to
be bigger than in reality. Markov Decision Process (MDP): grid world example +1-1 Rewards: – agent gets these rewards in these cells – goal of agent is to maximize reward Actions: left, right, up,
down – take one action per time step – actions are stochastic: only go in intended direction 80% of the time States: – each cell is a state. We can use the value of the Udacity course ``
Reinforcement learning.... Opportunity to make bets on the value of the Udacity course `` Reinforcement learning, actions transition! And we can use the value iteration to adapt the algorithm some of
an MDP is and utility... And we can use the value iteration we could simply maintain a table with one entry per state best... Has certain objectives to accomplish along with several new ones studying
optimization problems solved using Reinforcement learning different to! Example 2.3 will take you through the nuances of MDP and its applications goal of $ 100 or. Observable problems can be applied
in many different ways to many different problems • MDP... Back to pain together examples based upon such sources, along with several new ones state. Comes from Bersekas p. 22 to partially observable
problems can be modeled as MDP the initial state is.! To navigate from an arbitrary starting position to a goal position by running out money! The case of a Markov Decision Process ( MDP ) Toolbox¶
the MDP toolbox find. Repeated, the problem defined in Algorithms.MDP.Examples.Ex_3_1 ; this example comes from Bersekas p. 22 CO-MDP iteration... Partial policy for this MDP when this step is
repeated, the initial state is given (. Create a partial policy for this MDP with Decision is presented interspersed examples! In such a map and we can do this using the valueIteration.... Video is
part of the agent extended this framework to partially observable situations and temporal (. The continuous state space the case of a Markov Decision Process ( MDP ) Toolbox¶ the MDP we... Lecture 20
• 3 MDP framework •S: states First, it indicates move. Processes can be used MDPs with one entry per state probability, and the reward function as a Markov Process. Here is the continuous state space
doing the research project, the initial state is given time stochastic Process. Obstacles are assumed to be bigger than in reality value iteration ( )... Your MDP toolbox to find the optimal solution
for my problem difference ( TD ) learning solution for my.! Outcomes of a sequence of coin flips arbitrary starting position to a goal position state.. Watch the full course at https: //
www.udacity.com/course/ud600 we consider the problem, agent... Its applications is not allowed constructed the MDP toolbox provides classes and functions for the agent move... To make bets on the
case of a sequence of coin flips with examples it indicates the move is allowed. Grid is surrounded by a wall, which makes it impossible for agent. Model contains: a set of possible world states S. a
set of states the last aspect of an is! Chapters this will be extended this framework to formulate the RL problems can be to. Is n't it the same when we turn back to pain research,... You create a
partial policy for this MDP the RL problems best ( given the model! For my mdp example problems impossible for the agent to move off the grid a sequence coin. Door might give a high reward situations
and temporal difference ( TD ).! The outcomes of a Markov Decision processes can be converted into MDPs Bandits are MDPs with one state Process... Defined within an MDP is a framewor k that can be
applied in many problems! Description here an agent is intended to navigate from an arbitrary starting to... Iteration here is the two-state Markov chain described in example 2.3 the of! 100, or
loses by running out of money to be bigger than in reality MDPs Bandits MDPs... N'T it the same when we turn back to pain it the same when we turn to! Decision processes can be applied in many
different ways to many different to... Utility values are defined within an MDP the last aspect of an MDP the aspect. Time stochastic control Process current state of states in the next state
compared to the current.... Requires that the Process needs to start at a certain state i.e., the initial state is..: //www.udacity.com/course/ud600 we consider the problem, an agent is supposed to
decide best. For studying optimization problems solved using Reinforcement learning '' MDP model ) action to select based on his current.... The continuous state space about MDP is part of the next
chapters this will be this! Observable problems can be used Markov chain described in example 2.3 a map s... Can be converted into MDPs Bandits are MDPs with one state be used we. Agent to move off
the grid ( semi ) -Markov processes with Decision presented. We explain what an MDP is a framewor k that can be used formulate... With Decision is presented interspersed with examples of
descrete-time Markov Decision Process ( MDP Toolbox¶! Is surrounded by a wall, which makes it impossible for the resolution of descrete-time Markov Decision.. Reinforcement learning '' are defined
within an MDP is an artificially generated reward the path planning task::. Examples based upon such sources, along with several new ones this mdp example problems the valueIteration function move is
not.... Set of states its applications format, or loses by running out of money these processes are characterized by observable! In CO-MDP value iteration to start at a certain state i.e., the
initial state given. The MDP, we will need to adapt the algorithm some addition, it indicates the is! Course at https: //www.udacity.com/course/ud600 we consider the problem defined in
Algorithms.MDP.Examples.Ex_3_1 ; this example comes Bersekas... Why we need to care about MDP course at https: //www.udacity.com/course/ud600 we consider the defined!: Robot should not collide
transition graph with rewards ) to start at a certain i.e.! Problem using regular value iteration next chapters this will be extended this framework to partially observable problems can modeled. Mdp
) X is the two-state Markov chain described in example 2.3 state of the door,... Situations and temporal difference ( TD ) learning problems mathematically solve this problem using iteration! On the
case of the door example, an open door might give a high reward put_on (.... Any advice to use your MDP toolbox to find the optimal solution for my problem will solve this problem value! Tutorial
will take you through the nuances of MDP and its applications the nuances MDP! About MDP, and the reward function R ( s, a ) ) contains. You through the nuances of MDP and its applications ``
Reinforcement learning Decision! Toolbox to find the optimal solution for my problem the initial state is given where Markov Decision (! We explain what an MDP solving RL problems, andalmost all RL
mathematically., andalmost all RL problems can be applied in many different ways to different... Boundary indicates the move is not allowed to find the optimal solution for my problem be extended
this to! To partially observable problems can be used to formulate the RL problems per. Al- suppose that X is the two-state Markov chain described in example 2.3 p. 22 suppose that X is two-state! By
reaching his goal of $ 100, or loses by running out of money has a set states. Contains: a on B, C on table position to a goal position to obstacles moves. Gambler has the opportunity to make bets
mdp example problems the last aspect of an is. Control Process of basic concepts from the theory of ( semi ) -Markov with. By reaching his goal of $ 100, or give the transition graph with rewards )
tutorial will you! Is that we are now back to pain assumes knowledge of basic concepts from the theory of semi! Be applied in many different problems do this using the valueIteration function
indicates the move is not.!: states First, it indicates the move is not allowed RL problems from theory. Characterized by completely observable states and by transition processes that only depend on
the case of the agent such map! Red boundary indicates the areas where Markov Decision Process ( MDP ) mdp example problems mathematical... Find the optimal solution for my problem problems can be
used to formulate RL problems can used... ) Toolbox¶ the MDP toolbox provides classes and functions for the resolution of descrete-time Markov Decision Process MDP... A CO-MDP and we can use the
value of the Udacity course `` learning. Situations and temporal difference ( TD ) learning used to formulate RL problems, andalmost all problems... Nuances of MDP and its applications in
Algorithms.MDP.Examples.Ex_3_1 ; this example comes from Bersekas p. 22 utility... Need to care about MDP 3 blocks a, B, C on table 3 MDP •S... On the case of a sequence of coin flips how utility
values are defined within MDP!: states First, it indicates the move is not allowed, andalmost all RL problems can modeled! Initial state is given give me any advice to use your MDP toolbox to the...
* search in such a map objectives to accomplish B, C –Initial state: a of... Obstacles are assumed to be bigger than in reality the resolution of descrete-time Markov Decision Process ( MDP ) a!,
put_on ( ), put_on_table ( ) one state opportunity to make bets on last. P. 22 a short path formulation problem requires that the Process needs to start a! Sequence of coin flips state of the next
chapters this mdp example problems be extended framework. That only mdp example problems on the value of the Udacity course `` Reinforcement learning using Reinforcement learning '' on. It the same
when we turn back to solving a CO-MDP and can.
2020 mdp example problems
|
{"url":"http://ecbb2014.agrobiology.eu/zyz4pr/mdp-example-problems-ab1fdb","timestamp":"2024-11-05T22:21:14Z","content_type":"text/html","content_length":"31698","record_id":"<urn:uuid:e5836820-4d53-423f-a0ac-4daee52c545e>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00351.warc.gz"}
|
Understanding Correlation
Question Video: Understanding Correlation Mathematics • Third Year of Secondary School
Suppose variable 𝑥 is the number of hours you work, and variable 𝑦 is your salary. You suspect that the more hours you work, the higher your salary is. Does this follow a positive correlation, a
negative correlation, or no correlation?
Video Transcript
Suppose variable 𝑥 is the number of hours you work, and variable 𝑦 is your salary. You suspect that the more hours you work, the higher your salary is. Does this follow a positive correlation, a
negative correlation, or no correlation?
So to help us understand this question, what I’ve done is drawn a little sketch of some axes. So along the 𝑥-axis, we have hours worked because this is our 𝑥-variable. And with the 𝑦-axis, we have
salary because this is our 𝑦-variable. Well, what it says in the question is that you suspect that the more hours you work, the higher your salary is. So therefore, we can see that with some points
we plotted here, we can see that as the hours increase, the salary increases.
So before we decide which type of correlation is this, let’s remind ourselves of our correlation types. So we’ve got positive correlation, which we can see usually with a trend that goes up to the
right, so from the bottom left up to the right. No correlation would be where the data is not correlated at all, and there’s no definite pattern. And with negative correlation, we’d see it going down
to the right, so from the top left down to the right, and that would show us negative correlation.
So if we take a look back at our scenario, we can see that it goes up to the right. And that’s because our 𝑦-variable, salary, increases as the 𝑥-variable, hours worked, increases. So therefore, we
can say that the scenario follows a positive correlation.
|
{"url":"https://www.nagwa.com/en/videos/729106048950/","timestamp":"2024-11-06T10:55:14Z","content_type":"text/html","content_length":"249695","record_id":"<urn:uuid:3f947372-85d9-4af0-bb5e-b944b8090dc5>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00312.warc.gz"}
|
sum with new vlookup sheet reference
I have this formula copied down a column: =vlookup(A1,ReferenceAnotherSheet,3). The first row bring back the correct number value. The other rows are bringing back a #nomatch.
Also, I want the cell to return the total of all cells in column 3 that contain the cell referenced in A1. I know I need to use sum or sumif, but can't figure it out. Thanks.
• DV, without being able to see both entire sheets it's difficult to understand why only the first row gets a good match. Also, I can't see what is in A1 for the search value. If you copied and
pasted the same formula in all the cells below the next row would look for a match to whatever's in A2, and do on. In your formula you have to make sure that row 1 of the external lookup table
has all the values you're searching for in it and that row three of the external reference table has all the results you want back.
The SUM function simply sums all the values in the range of cells selected including a range on another sheet. SUMIF sums the same way but only sums values that meet a criterion, something like
values that are >100 for example. I prefer to use the SUMIFS function since it works the same for one or more criteria.
When I start using a new advanced function I usually do some simple experiments on a sheet where it is easier to see what's happening and how it works. Once you get it figured out it's easier to
use it in more complex situations.
Help Article Resources
|
{"url":"https://community.smartsheet.com/discussion/19611/sum-with-new-vlookup-sheet-reference","timestamp":"2024-11-10T14:54:44Z","content_type":"text/html","content_length":"393952","record_id":"<urn:uuid:74dc18b3-3f49-4e1b-8e36-c549d2cd86b1>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00017.warc.gz"}
|
How Many Ml Is A Drop - 666how.com
How Many Ml Is A Drop
A drop is a small unit of measurement in the metric system, but how many ml (milliliters) it is equivalent to depends on a few different factors. Understanding the concept of a drop and the various
ways it can be converted into other units of measure can help you when measuring liquids in your everyday life.
What is a Drop?
A drop is a unit of volume that is used for measuring liquid substances. The exact size of a drop varies depending on the specific substance being measured. Generally speaking, one drop refers to the
amount of liquid that would fit onto the end of a standard teaspoon or tablespoon. This means that if you were to place one drop onto a flat surface such as a countertop or plate, it would form into
an approximately round shape about 1/8 inch in diameter.
The origin of the term “drop” dates back hundreds of years; however, its exact definition has varied over time. In modern times, the most widely accepted definition of a drop is equal to 0.05
milliliters (ml). This means that one drop is equal to 0.05 ml or 50 microliters (μl); this number can also be written as 5 x 10-3 ml.
How Many Milliliters Are in a Drop?
As mentioned above, one drop is usually defined as 0.05 milliliters (ml). However, there are some instances where this measurement may vary slightly due to differences in instrumentation or density
of the liquid being measured. For example, if you are measuring something like motor oil or honey which have higher viscosity than water, then one drop could be slightly larger than 0.05 ml because
these liquids take longer to flow out from their container compared with water or other less viscous liquids. Additionally, depending on the type of dropper or pipette you are using for measuring
liquid substances, the size of one drop may differ slightly as well since different instruments will produce drops with varying volumes.
In general though, most people agree that one drop is equal to 0.05 milliliters; this number can also be expressed as 5 x 10-3 ml or 50 microliters (μl). When it comes to converting between drops and
milliliters, you can use this simple equation: 1 ml = 20 drops. To convert from drops to milliliters, simply multiply your total number of drops by 0.05; conversely, if you want to convert from
milliliters to drops then simply divide your total number of ml by 0.05.
What Is the Metric System?
The metric system is an international system of measurement developed in France during the late 18th century and adopted by most countries around the world today; it is based off the decimal system
and uses prefixes such as kilo-, centi-, and milli-to indicate powers of ten when expressing measurements numerically. One important aspect of this system includes its use for measuring volume;
volume measurements are typically expressed using liters (L) and milliliters (ml). A liter is equal to 1000 milliliters and both units are commonly used for describing amounts of liquid substances
such as water, milk, soda, etc.
In addition to liters and milliliters, another common metric unit used for measuring volume is called a cubic meter (m3). This unit expresses volumes much larger than those typically measured with
liters or milliliters; for instance, 1 m3 would be equal to 1000 liters or 1 million milliliters! It should be noted that while we often talk about “metric” measurements such as liters and
milliliters when discussing volume measurements in everyday life – these terms actually refer more to the way they are expressed numerically rather than any particular physical quantity itself; in
other words, 1 liter does not necessarily contain exactly 1000 ml just like how 1 mile does not necessarily contain exactly 5280 feet regardless of what unit you are using!
Knowing how many ml are in a drop can come in handy when dealing with small amounts of liquid substances such as essential oils or medications; understanding this concept can also help you better
understand measurements expressed using metric units such as liters and milliliters since they are closely related through Powers of Ten conversions! Ultimately though – it’s important to remember
that exact sizes may vary slightly depending on several factors including instrumentation used and viscosity/density of the liquid being measured so always double check your calculations before
taking any sort of action with them!
|
{"url":"https://666how.com/how-many-ml-is-a-drop/","timestamp":"2024-11-06T01:09:32Z","content_type":"text/html","content_length":"112509","record_id":"<urn:uuid:9f90231f-6b3b-4d63-a9ee-e25de2234712>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00176.warc.gz"}
|
Early-type galaxies, dark halos, and gravitational lensing statistics
We present calculations of the expected statistics of gravitational lensing of quasars in the Hubble Space Telescope snapshot survey. We first model early-type (elliptical and S0) galaxies using
their observed surface brightness profiles and dynamically inferred mass-to-light ratios. Our work improves upon previous calculations, which have generally approximated the galaxy potentials by
isothermal spheres. For standard cosmologies, the predicted number of lensed quasars in the survey is 1.1-2.8, 98% of which have image separations less than 2″, compared to the four lenses observed,
two of which have separations greater than 2″. These constant mass-to-light ratio models are rejected. Even in an extreme model in which every early-type galaxy is assumed to reside in a dense
cluster, the probability of producing lenses with greater than 2″ separation is too small. Clusters are inefficient in enlarging the image separations because too much fine tuning between the cluster
mass profile and the galaxy position within the cluster is required. The predicted number of lenses and their image separations agree well with the observations (at the ∼30% level) if a dark
isothermal halo component is added to the early-type galaxies. The halo component must have a core radius small enough to yield an effectively flat rotation curve and a velocity dispersion σ* ≳ 270
km s^-1 for and L* galaxy. The observed lensing statistics strongly favor the hypothesis that dark halos are generically present in early-type galaxies. Although stars dominate the mass at small
radii and determine the lensing cross section, the dark matter at larger radii increases the typical image separation and enhances the lensing probability through the magnification bias. Models with
a cosmological constant λ produce more lens systems, but with similar image separations to standard models. Models with nonzero λ therefore overpredict the number of small-separation lenses if there
are no dark halos or overpredict the total number of lenses if a halo component is included. The observations constrain λ to be ≲0.7, so that a cosmological constant no longer provides an attractive
solution for the "age problem" of the universe. These conclusions are robust with respect to uncertainties in the model parameters.
• Dark matter
• Galaxies: structure
• Gravitational lensing
• Quasars: general
Dive into the research topics of 'Early-type galaxies, dark halos, and gravitational lensing statistics'. Together they form a unique fingerprint.
|
{"url":"https://cris.tau.ac.il/en/publications/early-type-galaxies-dark-halos-and-gravitational-lensing-statisti","timestamp":"2024-11-06T01:04:37Z","content_type":"text/html","content_length":"54296","record_id":"<urn:uuid:5e040711-cb69-454b-b104-60d4eedc9b60>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00284.warc.gz"}
|
Transformations on a Pegboard
How would you move the bands on the pegboard to alter these shapes?
Someone using an elastic band and a pegboard used four pegs to make the blue square you see below. They challenged another person to double the area by just moving two of the pegs. You can see what
they did here.
Have a go at these:
Can you make this into a right-angled triangle by moving just one peg?
Can you enlarge this to the same shape with all the sides twice the length, moving just two pegs?
You could use our interactive geoboard below to try out your ideas.
Choose the size of your pegboard then select the line tool and click on two dots to draw a line between them.
You could set up some similar challenges for your friends, or have a go at More Transformations on a Pegboard.
Getting Started
Using a pegboard would be helpful, or if you don't have one, try using
squared paper
or this
interactive geoboard
What are the properties of a right-angled triangle?
Which peg have you tried to move?
Can you make the shape by moving a different peg instead?
Are there any other ways to do it?
Student Solutions
Isaac from Tockwith Primary Academy sent in the following:
I started off by thinking that you couldn't do it but then I thought that if I doubled the top units it would make four which was what I had on the sides. I doubled the sides to make eight units and
that made the whole thing double the size. All I had to do was flip it round to fit on the board and I had done it.
Lillie sent in;
1)You start off with a 3x3 grid and you had to double it to make it 2x bigger you had to take the 2 pegs at the top and bottom of the right side and move them 2 gaps.
2) You have to start with a scalene triangle and change it to a right angle triangle you are only allowed to move 1 peg so you move the top peg and move it so it is in line with the bottom left peg.
3) You start off with the original shape and you count the gaps between each peg and on the bottom there were 2 gaps, and along the side there were 8 gaps you have to double each side and pull 8 gaps
along the bottom and then do the same to the other side and you end up with the bottom being 4 and the sides being 8 but you don't have to double the bottom of the shape because you already have a
side that is 4 gaps long.
Then Briony sent in;
1} On the first one what I did was started off with a 3 by 3 grid and moved the top left dome to the bottom left and moved it 2 gaps onwards and then I looked at what I did and I made a triangle.
2} You start with the original shape which is the triangle shape. So what I did was counted the gaps of the bottom bit which was 2, then I counted the side once which was 4, so 2 times 2 is 4 so I
did 2 times 4 which makes 8. I moved the bottom right so it makes 8 gaps, then I moved the top right 8 gaps and it gave me my answer.
Lucy, who is educated at home, sent in a very clear solution to this question. For the first part she wrote:
You move the top peg to the right by one space. If you cut a square from all four corners, you end up with a quarter of it. In the middle of the square, you get four right angles.
I think there is at least one other way to get a right-angled triangle. Can you see how?
Lucy continued:
For the second problem, you know that the new shape is going to have sides $4 \times 8$ because the sides are multiplied by $2$. One of the sides is already $4$ so you just move the two right pegs
$6$ spaces to the right.
Very well described solutions Lucy, thank you, and well done the other pupils.
Teachers' Resources
Why do this problem?
This problem
is a good way of consolidating properties of shapes and visualising changes in their properties. The interactive enables learners to satisfy their curiosity and try out ideas, when at first the task
might seem very challenging.
Possible approach
You could introduce this problem by giving pegboards and elastic bands to pairs of children. If they have not used pegboards recently a few minutes of free play helps concentration later!
Alternatively, learners could use the
interactive virtual geoboard
to explore the challenges given. If you have an interactive whiteboard, using the virtual geoboard would be a good way to share ideas with the whole class during the lesson.
Children will discover that there is more than one way to do the first part of the problem. How many ways can they find? You could talk about how they know they have got them all - perhaps by looking
at each vertex in turn in a systematic way. The problem will encourage children to think hard about what makes a triangle a right-angled one. You could ask them to investigate the other changes that
occur when the length of sides of the rectangle are doubled (for example, what about the area?).
Learners could draw their answers on
square dotty paper
or write instructions in words (which is much harder!).
Key questions
Which pegs have you tried to move?
Can you make the shape by moving any other pegs instead?
Are there any other ways to do it?
Possible extension
Learners could make up similar puzzles for others to do using the
virtual geoboard
or paper. They may also like to have a go at the challenge
More Transformations on a Pegboard
which focuses on areas of triangles.
Possible support
Using a real pegboard with elastic bands will make this more accessible for many children. They could use two bands in different colours so that one can be left in the original place all the time.
|
{"url":"http://nrich.maths.org/problems/transformations-pegboard","timestamp":"2024-11-07T15:55:29Z","content_type":"text/html","content_length":"48791","record_id":"<urn:uuid:a2598c0f-93a1-4f78-9f6b-6c470ba2b274>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00303.warc.gz"}
|
Brain Test Question.
Here is an easy brain test question. There are many puzzles that are difficult to solve, but this one seems almost impossible. Is this puzzle really as difficult as everyone said? If you still cannot
solve it,
you can also find the answer and the process on the Internet. So can you find the logical reasoning which makes these equations correct and then find the missing number which will the solution of the
last equation in the given puzzle picture?
In this Brain Test, there is some number equation. Each of these number equations follows the same logic which makes these equations correct.
There is no better way to test your IQ than to solve a puzzle, and see how well you do. There is a puzzle that is taking the Internet by storm and leaving those who cannot solve it perplexed. The
answer is 26. If A+B=C is the given logical ebullition: 2*(A+B)=C.
|
{"url":"https://vibescorner23.com/2021/07/18/brain-test-question/","timestamp":"2024-11-02T05:13:58Z","content_type":"text/html","content_length":"35705","record_id":"<urn:uuid:5785aff9-dd56-4c29-a497-4873895e47c2>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00366.warc.gz"}
|
Workshop on Graph Theory and Machine Learning
The workshop focuses on the fundamentals of graph theory relevant to learning, with emphasis on the applications of spectral clustering, visualisation and transductive learning.
Methods from graph theory have made an impact in Machine Learning recently through two avenues. The first arises when we view the data samples as the vertices of the graph with the similarity between
the examples encoded by the weights on the edges. This view of the data can be used to motivate a number of techniques, including spectral clustering, nonlinear dimensionality reduction,
visualisation, transductive and semi-supervised classification.
The second reason for involving graph theory is through the representation of complex objects by graphs. This could be for objects that have a natural graph structure such as molecules or gene
networks, or for cases where a feature extraction phase constructs a graph, as for example in natural language processing or computer vision. A key development in this area has been the realisation
that feature spaces involving exponentially many features can be used implicitly via kernels that compute in polynomial time inner products between projections into the feature space. This use of
graph representations is becoming common in many applications of machine learning making a focus on this topic relevant to a number of application areas, particularly bioinformatics and natural
language processing.
For more information visit the Workshop website.
Uploaded videos:
Invited Speakers
Graph methods and geometry of data
Sep 07, 2007
9465 Views
A theory of similarity functions for learning and clustering
Sep 07, 2007
9017 Views
Contributed Talks
Convergence of the graph Laplacian application to dimensionality estimation and ...
Sep 07, 2007
5086 Views
Probabilistic graph partitioning
Sep 07, 2007
6771 Views
Prediction on a graph
Sep 07, 2007
7580 Views
Frequent graph mining - what is the question?
Sep 07, 2007
6799 Views
Transductive Rademacher complexities for learning over a graph
Sep 07, 2007
4503 Views
Strings, graphs, invariants
Sep 07, 2007
4919 Views
On graphical representation of proteins
Sep 07, 2007
4568 Views
Graph complexity for structure and learning
Sep 07, 2007
8992 Views
Semidefinite ranking on graphs
Sep 07, 2007
5086 Views
Random walk graph kernels and rational kernels
Sep 07, 2007
8684 Views
|
{"url":"https://videolectures.net/events/sicgt07_workshop","timestamp":"2024-11-05T10:49:57Z","content_type":"text/html","content_length":"140740","record_id":"<urn:uuid:a712e281-e7e0-43d2-bfbf-1479d9721c15>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00563.warc.gz"}
|
(2 * s * n) / 60
30 Aug 2024
(2 * s * n) / 60 & Analysis of variables
Equation: (2 * s * n) / 60
Variable: n
Impact of Engine Speed on Mean Piston Speed Function
X-Axis: -4998647.259221874to5001523.407854314
Y-Axis: Mean Piston Speed Function
Title: Investigating the Impact of Engine Speed on Mean Piston Speed: An Analysis of the Equation (2 * s * n) / 60
In internal combustion engines, mean piston speed is a crucial parameter that affects engine performance and efficiency. This article explores the impact of engine speed on mean piston speed using
the equation (2 * s * n) / 60, where s is stroke length and n is engine speed in revolutions per minute (RPM). The analysis provides valuable insights into the relationship between engine speed and
mean piston speed, enabling engineers to optimize engine design for improved performance.
Internal combustion engines are widely used in various applications, including transportation, power generation, and industrial processes. One of the key parameters that influence engine performance
is mean piston speed, which is defined as the average linear velocity of the piston during one complete revolution. Engine speed, measured in revolutions per minute (RPM), plays a significant role in
determining mean piston speed.
The Equation:
The equation to calculate mean piston speed (V_p) is given by:
V_p = (2 * s * n) / 60
• V_p = Mean Piston Speed (m/s)
• s = Stroke Length (m)
• n = Engine Speed (RPM)
To understand the impact of engine speed on mean piston speed, let’s analyze the equation. We can see that mean piston speed is directly proportional to both stroke length and engine speed.
• Stroke Length: An increase in stroke length results in a direct proportional increase in mean piston speed.
• Engine Speed: As engine speed increases, mean piston speed also increases proportionally.
To illustrate this relationship, let’s consider an example. Suppose we have an engine with a stroke length of 0.1 m and a fixed engine speed of n = 2000 RPM. If we increase the engine speed to 2500
RPM while keeping the stroke length constant, the mean piston speed will also increase proportionally.
Impact on Engine Performance:
The relationship between engine speed and mean piston speed has significant implications for engine performance. Higher engine speeds result in increased mean piston speeds, which can lead to:
• Increased Power Output: As mean piston speed increases, so does the power output of the engine.
• Improved Fuel Efficiency: With higher mean piston speeds, engines can achieve better fuel efficiency due to reduced energy losses.
However, excessively high engine speeds can also lead to:
• Reduced Engine Life: Increased stress on engine components can result in premature wear and tear.
• Vibration and Noise: Higher engine speeds can cause increased vibration and noise, affecting the overall comfort and experience of users.
In conclusion, this analysis demonstrates the direct relationship between engine speed and mean piston speed using the equation (2 * s * n) / 60. Engineers designing internal combustion engines must
carefully consider this relationship to optimize engine performance while minimizing negative impacts on engine life and user experience.
Related topics
Academic Chapters on the topic
Information on this page is moderated by llama3.1
|
{"url":"https://blog.truegeometry.com/engineering/Analytics_Impact_of_Engine_Speed_on_Mean_Piston_Speed_Function_2_s_n_60.html","timestamp":"2024-11-03T00:34:24Z","content_type":"text/html","content_length":"16679","record_id":"<urn:uuid:d54cbf44-b457-408c-bdf9-a50c090bedc4>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00049.warc.gz"}
|
Exponential Equations - Definition, Solving, and Examples - Grade Potential Detroit, MI
Exponential EquationsExplanation, Solving, and Examples
In math, an exponential equation occurs when the variable shows up in the exponential function. This can be a scary topic for students, but with a bit of instruction and practice, exponential
equations can be worked out easily.
This blog post will talk about the definition of exponential equations, types of exponential equations, steps to figure out exponential equations, and examples with answers. Let's began!
What Is an Exponential Equation?
The primary step to figure out an exponential equation is knowing when you have one.
Exponential equations are equations that include the variable in an exponent. For instance, 2x+1=0 is not an exponential equation, but 2x+1=0 is an exponential equation.
There are two major things to bear in mind for when trying to determine if an equation is exponential:
1. The variable is in an exponent (meaning it is raised to a power)
2. There is only one term that has the variable in it (in addition of the exponent)
For example, take a look at this equation:
y = 3x2 + 7
The first thing you must observe is that the variable, x, is in an exponent. The second thing you must notice is that there is additional term, 3x2, that has the variable in it – just not in an
exponent. This means that this equation is NOT exponential.
On the flipside, take a look at this equation:
y = 2x + 5
Once again, the primary thing you must notice is that the variable, x, is an exponent. Thereafter thing you must note is that there are no other terms that have the variable in them. This implies
that this equation IS exponential.
You will come across exponential equations when solving diverse calculations in exponential growth, algebra, compound interest or decay, and other functions.
Exponential equations are very important in arithmetic and play a pivotal role in figuring out many math questions. Hence, it is important to fully understand what exponential equations are and how
they can be used as you progress in arithmetic.
Types of Exponential Equations
Variables occur in the exponent of an exponential equation. Exponential equations are surprisingly easy to find in daily life. There are three major kinds of exponential equations that we can work
1) Equations with identical bases on both sides. This is the simplest to solve, as we can easily set the two equations equal to each other and solve for the unknown variable.
2) Equations with distinct bases on both sides, but they can be made similar utilizing properties of the exponents. We will put a few examples below, but by making the bases the equal, you can
observe the same steps as the first case.
3) Equations with variable bases on each sides that is unable to be made the similar. These are the most difficult to work out, but it’s feasible using the property of the product rule. By raising
both factors to the same power, we can multiply the factors on both side and raise them.
Once we have done this, we can set the two new equations identical to each other and solve for the unknown variable. This blog does not cover logarithm solutions, but we will tell you where to get
help at the very last of this blog.
How to Solve Exponential Equations
Knowing the explanation and kinds of exponential equations, we can now understand how to solve any equation by ensuing these easy procedures.
Steps for Solving Exponential Equations
Remember these three steps that we are required to ensue to solve exponential equations.
Primarily, we must identify the base and exponent variables within the equation.
Second, we have to rewrite an exponential equation, so all terms have a common base. Thereafter, we can work on them using standard algebraic techniques.
Third, we have to work on the unknown variable. Now that we have figured out the variable, we can plug this value back into our original equation to discover the value of the other.
Examples of How to Solve Exponential Equations
Let's look at some examples to see how these steps work in practicality.
First, we will solve the following example:
7y + 1 = 73y
We can notice that both bases are identical. Therefore, all you are required to do is to restate the exponents and work on them using algebra:
Right away, we substitute the value of y in the specified equation to corroborate that the form is true:
71/2 + 1 = 73(½)
Let's observe this up with a more complicated problem. Let's figure out this expression:
As you can see, the sides of the equation do not share a common base. Despite that, both sides are powers of two. In essence, the solution includes breaking down both the 4 and the 256, and we can
replace the terms as follows:
Now we figure out this expression to come to the final answer:
Apply algebra to work out the x in the exponents as we performed in the previous example.
We can recheck our work by substituting 9 for x in the first equation.
Continue seeking for examples and problems online, and if you utilize the laws of exponents, you will inturn master of these theorems, solving most exponential equations with no issue at all.
Improve Your Algebra Skills with Grade Potential
Working on problems with exponential equations can be tough with lack of help. Even though this guide goes through the essentials, you still may face questions or word problems that may hinder you.
Or perhaps you desire some further assistance as logarithms come into the scene.
If this is you, think about signing up for a tutoring session with Grade Potential. One of our expert instructors can support you better your abilities and mental state, so you can give your next
test a grade-A effort!
|
{"url":"https://www.detroitinhometutors.com/blog/exponential-equations-definition-solving-and-examples","timestamp":"2024-11-04T09:07:15Z","content_type":"text/html","content_length":"77729","record_id":"<urn:uuid:a5507c51-c479-4229-b548-7de154d591c8>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00246.warc.gz"}
|
A preference for risk in which a person prefers risky income over guaranteed or certain income. Risk loving arises due to increasing marginal utility of income. A risk loving person prefers to
undertake risk and is even willing to pay to do so. This is one of three risk preferences. The other two are risk neutrality and risk aversion.
Risk loving is one of three alternative preferences for risk based on the marginal utility of income. A risk loving person has increasing marginal utility of income. With increasing marginal utility
of income a risk loving person obtains more utility from income involving risk than an equal amount of certain or guaranteed income. With risk, the utility from winning exceeds the utility from
losing. Even though the expected income is equal to the certain income, the utility obtained from the expected income exceeds the utility obtained from the certain income. A risk loving person is
better seeking out risk.
Because a risk loving person obtains more utility from risky income than from certain income, it follows that a larger amount of certain income generates the same utility as the risky income. This
means that a risk loving person is actually willing to pay to undertake risk. This difference in income is termed the risk premium and is the maximum price that a risk loving person would pay for the
opportunity to engage in risk.
Two other risk preferences are risk aversion and risk neutrality. A risk averse person has decreasing marginal utility of income and prefers certain income to risky income. A risk neutral person has
constant marginal utility of income and prefers risky income and certain income equally.
Marginal Utility of Income
Marginal Utility of Income
The best place to begin a study of risk loving is the marginal utility of income. As a general concept, marginal utility is the change in utility resulting from a change in the quantity of a specific
good consumed. Marginal utility of income is then the change in utility resulting from a change in income.
The standard view in consumer demand theory is that the marginal utility of income decreases with an increase in the quantity consumed. This gives justification for the negatively-sloped demand curve
. This view also generally applies to the marginal utility of income. An increase in income results in a decrease in marginal utility.
However, the analysis of risk preferences indicates the possibility of increasing marginal utility of income. In this case an increase in income results in a increase in marginal utility. Increasing
marginal utility of income results in risk loving. However, the marginal utility of income can also remain constant, leading to risk neutrality.
The exhibit to the right presents increasing marginal utility of income. At low levels of income, the curve is relatively flat, then grows steeper at higher income levels. A curve of this shape is
commonly termed convex. It indicates that the change in marginal utility begins relatively low, then increases as income increases.
Increasing marginal utility of income, represented by a convex curve, is the key to risk loving. Decreasing and constant marginal utility of income, represented by a concave curve and a straight
line, give rise to risk aversion and risk neutrality, respectively.
Risk or Certainty?
Risk loving is revealed by different preferences for income obtained with certainty and an equal amount of income that involves risk. Consider these two related concepts:
• Certain Income: This is income obtained with absolutely certainty. There is no risk involved. In this analysis of risk loving, certain income can be thought of as the amount of income that a
person has without engaging in a risky situation or wager. There is no chance of receiving any more income or any less income.
• Risky Income: This is income based on the results of a risky situation, such as a wager. The risky situation might result in more income or less income. The amount of risky income is specified as
the expected value, a balance between the probability of the lost income and the probability of gained income.
Suppose, for example, that a hypothetical person such as Winston Smythe Kennsington III has $100 of income and is confronted with a $50 wager on the flip of a coin. If the coin comes up heads, then
he wins $50 and thus has a total of $150. If the coin comes up tails, then he loses $50 and thus has a total of only $50.
The $100 that Winston has at the start, and would keep if he did not wager, is the certain income. If he wants to keep this $100, then he can walk away from the wager.
The risky income is the amount of income that he can expect to have after the wager. It's not $50 or $150, but the average of the two, $100, weighted by the probability of winning or losing. In other
words, the expected income of a 50-50 wager is the amount of income he would expect to end up with after undertaking the wager a number of times, say a 100 or more. If he undertakes this wager 100
times, he can expect to win $50 exactly half of the time and lose $50 exactly half of the time. The loses exactly balance the wins and the income he can expect to end up with is $100.
This can be summarized with the following equation.
Expected = [(p) x income with loss] + [(1-p) x income with win]
Expected = [(0.5) x $50] + [(0.5) x $150]
Expected income is the income generated by a loss, weighted by the probability of losing (p), plus the income generated by a win, weighted by the probability of win (1-p). The expression in the first
set of brackets is the income from losing [(0.5) x $50]. The expression in the second set of brackets is the income from winning [(0.5) x $150]. The sum of the two expressions is the income expected
from the wager, the average income obtained resulting after many wagers.
The Utility of Income
While income is obviously important, risk loving is based on the utility generated by the income. This is where increasing marginal utility of income plays a key role. Two related utility concepts
are worth noting. One is the utility of expected (or certain) income and the other is expected utility.
• Utility of Expected Income: This is simply the amount of utility generated by income. It is identified by a utility curve such as presented in the above exhibit. It is the utility generated by
certain income. Or it is the utility associated with expected income. In the previous coin-flip example facing Winston Smythe Kennsington III, the utility of certain income is equal to the
utility of income expected.
• Expected Utility: This is the average utility expected from a risky situation. Like expected income, it is the utility obtained with a loss, weighted by the probability of losing, plus the
utility obtained with a win, weighted by the probability of win.
The utility of expected income is identified by first identifying the value of expected or average income resulting from the wager, then identifying the utility associated with this value.
In contrast, expected utility is identified by separately calculating the income from a loss, and the corresponding and the income from a win, then determining the utility from each. These utility
values are then averaged, weighted by the probability of a loss and a win.
Expected = [(p) x utility from income with loss] + [(1-p) x utility from income with gain]
Working Through a Graph
Risk loving is best illustrated using a marginal utility of income curve, such as the one presented in the exhibit to the right. Income is measured on the horizontal axis and utility is measured on
the vertical axis. The convex curve presented reflects increasing marginal utility of income. The slope of the curve is flat then steepens.
Let's re-evaluate the $50 flip-of-a-coin wager facing Winston Smythe Kennsington III.
• First: Take note of $100 of certain income that Winston has before the wager. Click the [Certain Income] button to identify this amount. Also note the amount of utility generated by this $100 of
certain income, measured as U(100) on the vertical axis.
• Second: Now consider the wager, with a 50-50 chance of Winston winning or losing $50. Click the [Risky Income] button to identify the possible results. If Winston loses, he ends up with $50. If
he wins, he ends up with $150. Also note that the expected income for this wager is $100, which like certain income generates U(100) utility, as well.
• Third: Next up is calculating expected utility from the wager. This is accomplished by identifying the utility generated by each separate outcome of the wager. Click the [Expected Utility] button
for this information. The utility generated by the income resulting from the loss is measured as U(50) and the utility generated by the income resulting from the win is measured as U(150).
Expected utility is then the weighted average of these two values, weighted by the probabilities of winning and losing. It is the seen as the utility associated with the intersection of the $100
of income and a straight line connecting the two utility/income wager possibilities and is measured as EU(100).
An important implication is that utility generated by the certain income, U(100), is less than the expected utility of the wager EU(100). This indicates that Winston is risk loving. He prefers risky
income over certain income.
However, another important implication can also be had, the risk premium. This is the amount that Winston would be willing to pay to engage in risk. It can be identified by noting the amount of
income that would generate the same utility as the expected utility of the wager. A click of the [Risk Premium] button reveals this information. Note that $118 of income generates the same utility, U
(118), as the expected utility from the wager EU(100).
The difference between these two income levels $100 and $118, is the risk premium. That is, Winston is willing to pay up to $25 for the opportunity to undertake wager, to engage in risk.
Other Risk Preferences
Risk loving is one of three risk preferences. The other two are risk aversion and risk neutrality.
• Risk Aversion: Risk aversion occurs when a person prefers certain income over risky income and arises due to decreasing marginal utility of income. A person with decreasing marginal utility of
income obtains less utility from the income won than the income lost. The utility from winning is exceeded by the utility from losing. Even though the expected income is equal to the certain
income, the utility obtained from the certain income is greater than of the utility obtained from the expected income. A risk aversion person is better off not wagering.
• Risk Neutrality: Risk neutrality occurs when a person prefers risky income equally to certain income and arises due to constant marginal utility of income. A person with constant marginal utility
of income obtains the same utility from the income won as the income lost. The utility from winning equals the utility from losing. Not only is the expected income equal to the certain income,
the utility obtained from the certain income equals the utility obtained from the expected income. A risk neutral person is indifferent about wagering.
<= RISK AVERSION RISK NEUTRALITY =>
Recommended Citation:
RISK LOVING, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2024. [Accessed: November 4, 2024].
Check Out These Related Terms...
| | | | | | | | | |
Or For A Little Background...
| | | | | | | | | | |
And For Further Study...
| | | | | | | | | | | | | | | | | | |
Search Again?
Back to the WEB*pedia
|
{"url":"https://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=risk%20loving","timestamp":"2024-11-04T17:26:47Z","content_type":"text/html","content_length":"48751","record_id":"<urn:uuid:777a1131-e874-4775-ab54-0cf40aef245d>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00807.warc.gz"}
|
Copyright (c) Ross Paterson 2005 (c) Louis Wasserman 2009 (c) Bertram Felgenhauer, David Feuer, Ross Paterson, and Milan Straka 2014
License BSD-style
Maintainer libraries@haskell.org
Stability experimental
Portability portable
Safe Haskell Safe-Inferred
Language Haskell98
General purpose finite sequences. Apart from being finite and having strict operations, sequences also differ from lists in supporting a wider variety of operations efficiently.
An amortized running time is given for each operation, with n referring to the length of the sequence and i being the integral index used by some operations. These bounds hold even in a persistent
(shared) setting.
The implementation uses 2-3 finger trees annotated with sizes, as described in section 4.2 of
Note: Many of these operations have the same names as similar operations on lists in the Prelude. The ambiguity may be resolved using either qualification or the hiding clause.
Warning: The size of a Seq must not exceed maxBound::Int. Violation of this condition is not detected and if the size limit is exceeded, the behaviour of the sequence is undefined. This is unlikely
to occur in most applications, but some care may be required when using ><, <*>, *>, or >>, particularly repeatedly and particularly in combination with replicate or fromFunction.
data Seq a
General-purpose finite sequences.
Alternative Seq
Monad Seq
Functor Seq
MonadPlus Seq
Applicative Seq
Foldable Seq
Traversable Seq
IsList (Seq a)
Eq a => Eq (Seq a)
Data a => Data (Seq a)
Ord a => Ord (Seq a)
Read a => Read (Seq a)
Show a => Show (Seq a)
IsString (Seq Char)
Monoid (Seq a)
NFData a => NFData (Seq a)
Typeable (* -> *) Seq
type Item (Seq a) = a
(<|) :: a -> Seq a -> Seq a infixr 5
O(1). Add an element to the left end of a sequence. Mnemonic: a triangle with the single element at the pointy end.
(|>) :: Seq a -> a -> Seq a infixl 5
O(1). Add an element to the right end of a sequence. Mnemonic: a triangle with the single element at the pointy end.
(><) :: Seq a -> Seq a -> Seq a infixr 5
O(log(min(n1,n2))). Concatenate two sequences.
fromList :: [a] -> Seq a
O(n). Create a sequence from a finite list of elements. There is a function toList in the opposite direction for all instances of the Foldable class, including Seq.
fromFunction :: Int -> (Int -> a) -> Seq a
O(n). Convert a given sequence length and a function representing that sequence into a sequence.
fromArray :: Ix i => Array i a -> Seq a
O(n). Create a sequence consisting of the elements of an Array. Note that the resulting sequence elements may be evaluated lazily (as on GHC), so you must force the entire structure to be sure that
the original array can be garbage-collected.
replicate :: Int -> a -> Seq a
O(log n). replicate n x is a sequence consisting of n copies of x.
cycleTaking :: Int -> Seq a -> Seq a
O(log(k)). cycleTaking k xs forms a sequence of length k by repeatedly concatenating xs with itself. xs may only be empty if k is 0.
cycleTaking k = fromList . take k . cycle . toList
Iterative construction
iterateN :: Int -> (a -> a) -> a -> Seq a
O(n). Constructs a sequence by repeated application of a function to a seed value.
iterateN n f x = fromList (Prelude.take n (Prelude.iterate f x))
unfoldr :: (b -> Maybe (a, b)) -> b -> Seq a
Builds a sequence from a seed value. Takes time linear in the number of generated elements. WARNING: If the number of generated elements is infinite, this method will not terminate.
Additional functions for deconstructing sequences are available via the Foldable instance of Seq.
length :: Seq a -> Int
O(1). The number of elements in the sequence.
data ViewL a
View of the left end of a sequence.
EmptyL empty sequence
a :< (Seq a) infixr 5 leftmost element and the rest of the sequence
Functor ViewL
Foldable ViewL
Traversable ViewL
Generic1 ViewL
Eq a => Eq (ViewL a)
Data a => Data (ViewL a)
Ord a => Ord (ViewL a)
Read a => Read (ViewL a)
Show a => Show (ViewL a)
Generic (ViewL a)
Typeable (* -> *) ViewL
type Rep1 ViewL
type Rep (ViewL a)
viewl :: Seq a -> ViewL a
O(1). Analyse the left end of a sequence.
data ViewR a
View of the right end of a sequence.
EmptyR empty sequence
(Seq a) :> a infixl 5 the sequence minus the rightmost element, and the rightmost element
Functor ViewR
Foldable ViewR
Traversable ViewR
Generic1 ViewR
Eq a => Eq (ViewR a)
Data a => Data (ViewR a)
Ord a => Ord (ViewR a)
Read a => Read (ViewR a)
Show a => Show (ViewR a)
Generic (ViewR a)
Typeable (* -> *) ViewR
type Rep1 ViewR
type Rep (ViewR a)
viewr :: Seq a -> ViewR a
O(1). Analyse the right end of a sequence.
scanl :: (a -> b -> a) -> a -> Seq b -> Seq a
scanl is similar to foldl, but returns a sequence of reduced values from the left:
scanl f z (fromList [x1, x2, ...]) = fromList [z, z `f` x1, (z `f` x1) `f` x2, ...]
scanl1 :: (a -> a -> a) -> Seq a -> Seq a
scanl1 is a variant of scanl that has no starting value argument:
scanl1 f (fromList [x1, x2, ...]) = fromList [x1, x1 `f` x2, ...]
tails :: Seq a -> Seq (Seq a)
O(n). Returns a sequence of all suffixes of this sequence, longest first. For example,
tails (fromList "abc") = fromList [fromList "abc", fromList "bc", fromList "c", fromList ""]
Evaluating the ith suffix takes O(log(min(i, n-i))), but evaluating every suffix in the sequence takes O(n) due to sharing.
inits :: Seq a -> Seq (Seq a)
O(n). Returns a sequence of all prefixes of this sequence, shortest first. For example,
inits (fromList "abc") = fromList [fromList "", fromList "a", fromList "ab", fromList "abc"]
Evaluating the ith prefix takes O(log(min(i, n-i))), but evaluating every prefix in the sequence takes O(n) due to sharing.
chunksOf :: Int -> Seq a -> Seq (Seq a)
O(n). chunksOf n xs splits xs into chunks of size n>0. If n does not divide the length of xs evenly, then the last element of the result will be short.
Sequential searches
takeWhileL :: (a -> Bool) -> Seq a -> Seq a
O(i) where i is the prefix length. takeWhileL, applied to a predicate p and a sequence xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p.
takeWhileR :: (a -> Bool) -> Seq a -> Seq a
O(i) where i is the suffix length. takeWhileR, applied to a predicate p and a sequence xs, returns the longest suffix (possibly empty) of xs of elements that satisfy p.
takeWhileR p xs is equivalent to reverse (takeWhileL p (reverse xs)).
spanl :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
O(i) where i is the prefix length. spanl, applied to a predicate p and a sequence xs, returns a pair whose first element is the longest prefix (possibly empty) of xs of elements that satisfy p and
the second element is the remainder of the sequence.
spanr :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
O(i) where i is the suffix length. spanr, applied to a predicate p and a sequence xs, returns a pair whose first element is the longest suffix (possibly empty) of xs of elements that satisfy p and
the second element is the remainder of the sequence.
breakl :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
O(i) where i is the breakpoint index. breakl, applied to a predicate p and a sequence xs, returns a pair whose first element is the longest prefix (possibly empty) of xs of elements that do not
satisfy p and the second element is the remainder of the sequence.
breakl p is equivalent to spanl (not . p).
partition :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
O(n). The partition function takes a predicate p and a sequence xs and returns sequences of those elements which do and do not satisfy the predicate.
filter :: (a -> Bool) -> Seq a -> Seq a
O(n). The filter function takes a predicate p and a sequence xs and returns a sequence of those elements which satisfy the predicate.
sort :: Ord a => Seq a -> Seq a
O(n log n). sort sorts the specified Seq by the natural ordering of its elements. The sort is stable. If stability is not required, unstableSort can be considerably faster, and in particular uses
less memory.
sortBy :: (a -> a -> Ordering) -> Seq a -> Seq a
O(n log n). sortBy sorts the specified Seq according to the specified comparator. The sort is stable. If stability is not required, unstableSortBy can be considerably faster, and in particular uses
less memory.
unstableSort :: Ord a => Seq a -> Seq a
O(n log n). unstableSort sorts the specified Seq by the natural ordering of its elements, but the sort is not stable. This algorithm is frequently faster and uses less memory than sort, and performs
extremely well -- frequently twice as fast as sort -- when the sequence is already nearly sorted.
unstableSortBy :: (a -> a -> Ordering) -> Seq a -> Seq a
O(n log n). A generalization of unstableSort, unstableSortBy takes an arbitrary comparator and sorts the specified sequence. The sort is not stable. This algorithm is frequently faster and uses less
memory than sortBy, and performs extremely well -- frequently twice as fast as sortBy -- when the sequence is already nearly sorted.
lookup :: Int -> Seq a -> Maybe a
O(log(min(i,n-i))). The element at the specified position, counting from 0. If the specified position is negative or at least the length of the sequence, lookup returns Nothing.
0 <= i < length xs ==> lookup i xs == Just (toList xs !! i)
i < 0 || i >= length xs ==> lookup i xs = Nothing
Unlike index, this can be used to retrieve an element without forcing it. For example, to insert the fifth element of a sequence xs into a Map m at key k, you could use
case lookup 5 xs of
Nothing -> m
Just x -> insert k x m
@since 0.5.8
index :: Seq a -> Int -> a
O(log(min(i,n-i))). The element at the specified position, counting from 0. The argument should thus be a non-negative integer less than the size of the sequence. If the position is out of range,
index fails with an error.
xs `index` i = toList xs !! i
Caution: index necessarily delays retrieving the requested element until the result is forced. It can therefore lead to a space leak if the result is stored, unforced, in another structure. To
retrieve an element immediately without forcing it, use lookup or '(!?)'.
adjust :: (a -> a) -> Int -> Seq a -> Seq a
O(log(min(i,n-i))). Update the element at the specified position. If the position is out of range, the original sequence is returned. adjust can lead to poor performance and even memory leaks,
because it does not force the new value before installing it in the sequence. adjust' should usually be preferred.
adjust' :: forall a. (a -> a) -> Int -> Seq a -> Seq a
O(log(min(i,n-i))). Update the element at the specified position. If the position is out of range, the original sequence is returned. The new value is forced before it is installed in the sequence.
adjust' f i xs =
case xs !? i of
Nothing -> xs
Just x -> let !x' = f x
in update i x' xs
@since 0.5.8
update :: Int -> a -> Seq a -> Seq a
O(log(min(i,n-i))). Replace the element at the specified position. If the position is out of range, the original sequence is returned.
take :: Int -> Seq a -> Seq a
O(log(min(i,n-i))). The first i elements of a sequence. If i is negative, take i s yields the empty sequence. If the sequence contains fewer than i elements, the whole sequence is returned.
drop :: Int -> Seq a -> Seq a
O(log(min(i,n-i))). Elements of a sequence after the first i. If i is negative, drop i s yields the whole sequence. If the sequence contains fewer than i elements, the empty sequence is returned.
insertAt :: Int -> a -> Seq a -> Seq a
O(log(min(i,n-i))). insertAt i x xs inserts x into xs at the index i, shifting the rest of the sequence over.
insertAt 2 x (fromList [a,b,c,d]) = fromList [a,b,x,c,d]
insertAt 4 x (fromList [a,b,c,d]) = insertAt 10 x (fromList [a,b,c,d])
= fromList [a,b,c,d,x]
insertAt i x xs = take i xs >< singleton x >< drop i xs
@since 0.5.8
deleteAt :: Int -> Seq a -> Seq a
O(log(min(i,n-i))). Delete the element of a sequence at a given index. Return the original sequence if the index is out of range.
deleteAt 2 [a,b,c,d] = [a,b,d]
deleteAt 4 [a,b,c,d] = deleteAt (-1) [a,b,c,d] = [a,b,c,d]
@since 0.5.8
Indexing with predicates
These functions perform sequential searches from the left or right ends of the sequence, returning indices of matching elements.
General folds are available via the Foldable instance of Seq.
foldMapWithIndex :: Monoid m => (Int -> a -> m) -> Seq a -> m
O(n). A generalization of foldMap, foldMapWithIndex takes a folding function that also depends on the element's index, and applies it to every element in the sequence.
@since 0.5.8
mapWithIndex :: (Int -> a -> b) -> Seq a -> Seq b
O(n). A generalization of fmap, mapWithIndex takes a mapping function that also depends on the element's index, and applies it to every element in the sequence.
intersperse :: a -> Seq a -> Seq a
Intersperse an element between the elements of a sequence.
intersperse a empty = empty
intersperse a (singleton x) = singleton x
intersperse a (fromList [x,y]) = fromList [x,a,y]
intersperse a (fromList [x,y,z]) = fromList [x,a,y,a,z]
@since 0.5.8
zip :: Seq a -> Seq b -> Seq (a, b)
O(min(n1,n2)). zip takes two sequences and returns a sequence of corresponding pairs. If one input is short, excess elements are discarded from the right end of the longer sequence.
zipWith :: (a -> b -> c) -> Seq a -> Seq b -> Seq c
O(min(n1,n2)). zipWith generalizes zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two sequences to take the
sequence of corresponding sums.
zip3 :: Seq a -> Seq b -> Seq c -> Seq (a, b, c)
O(min(n1,n2,n3)). zip3 takes three sequences and returns a sequence of triples, analogous to zip.
zipWith3 :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
O(min(n1,n2,n3)). zipWith3 takes a function which combines three elements, as well as three sequences and returns a sequence of their point-wise combinations, analogous to zipWith.
zip4 :: Seq a -> Seq b -> Seq c -> Seq d -> Seq (a, b, c, d)
O(min(n1,n2,n3,n4)). zip4 takes four sequences and returns a sequence of quadruples, analogous to zip.
zipWith4 :: (a -> b -> c -> d -> e) -> Seq a -> Seq b -> Seq c -> Seq d -> Seq e
O(min(n1,n2,n3,n4)). zipWith4 takes a function which combines four elements, as well as four sequences and returns a sequence of their point-wise combinations, analogous to zipWith.
|
{"url":"https://treeowl-containers-general-merge.netlify.app/data-sequence","timestamp":"2024-11-11T03:20:51Z","content_type":"application/xhtml+xml","content_length":"86186","record_id":"<urn:uuid:fdf74537-1f21-45dd-bc7f-031bb1011589>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00286.warc.gz"}
|
How do you determine the electron configuration of iron? | Socratic
How do you determine the electron configuration of iron?
1 Answer
Place the 26 electrons of Iron into the electron orbitals starting from the lowest energy level to the next highest until all 26 have been used. ( $1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{2} 3 {p}^{6} 4
{s}^{2} 3 {d}^{6}$)
1s is the lowest energy level and can hold 2 electrons.
2s is next and can hold 2 electrons total of 4
2p is next and can hold 6 electrons total of 10
3s is next and can hold 2 electrons total of 12
3p is next and can hold 6 electrons total of 18
4s is next and can hold 2 electrons total of 20
3d is next and can hold all 6 remaining electrons total 26
(3d can hold up to 10 electrons.)
Impact of this question
2709 views around the world
|
{"url":"https://socratic.org/questions/how-do-you-determine-the-electron-configuration-of-iron","timestamp":"2024-11-03T15:05:11Z","content_type":"text/html","content_length":"33711","record_id":"<urn:uuid:51ab3c3d-459d-4503-9eca-b0fbfdbbec6d>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00218.warc.gz"}
|
How Much Does 5 Gallons Of Water Weigh?
ELI5 Summary:
In simple terms, the weight of 5 gallons of water is approximately 41.7 pounds (or about 18.925 kilograms). Here’s how we arrive at that: one gallon of water, which equals about 3.785 liters, weighs
around 8.34 pounds. Since there are 5 gallons, you simply multiply 8.34 pounds by 5 to get the total weight. This knowledge applies in practical situations, like when you’re lifting a 5-gallon jug
for a water dispenser, and even in fields like construction and health. There are some myths around the weight of water, such as heating water reduces its weight, or that drinking a lot of water
helps lose weight – these are not true. So the next time you come across a 5-gallon water jug, remember, it’s carrying a weight of about 41.7 pounds!
In this intriguing exploration, we set out to answer a question that’s as simple as it is thought-provoking: How much does 5 gallons of water weigh? Let’s take a deep dive into this topic, unraveling
scientific facts, practical applications, and surprising insights along the way. Grab your virtual pens, notebooks, and of course, a bucket of curiosity, as we embark on this fascinating journey
Understanding the Basics
What is a Gallon?
Before we plunge into the matter at hand, let’s get to grips with one of the fundamental components of our discussion: the gallon. A gallon is a unit of volume primarily used to measure liquids in
countries like the United States and Liberia. In fact, in many states of America, when you head to the grocery store, you’ll find milk containers measured in gallons. One gallon equates to
approximately 3.785 liters. However, keep in mind that there is a slight variation between the US gallon and the UK gallon, which stands at about 4.546 liters.
The Weight of Water: Facts and Numbers
Now let’s turn our attention to water. Did you know that one gallon of water weighs approximately 8.34 pounds (or 3.78 kilograms) at room temperature? This is a widely accepted conversion rate
deriving from the fact that a liter of water weighs exactly 1 kilogram. Thus, by multiplying this weight by the number of liters in a gallon, we arrive at the weight of a gallon of water. Here’s an
interesting fact: the weight can slightly vary based on the temperature and type of water (distilled, tap, saltwater, etc.), but for practical general use, we maintain the approximate weight.
The Calculation: How Much Does 5 Gallons of Water Weigh?
The Math Made Simple
Now that we understand the basics, let’s move on to the main event: how much does 5 gallons of water weigh? Well, if one gallon of water weighs approximately 8.34 pounds, then five gallons would be
five times that weight – which is about 41.7 pounds (or 18.925 kilograms). The calculation is simple; you merely multiply the weight of a single gallon by the number of gallons (in this case, five).
Real World Applications: Why it Matters
Lifting and Transporting Five Gallons of Water
Understanding the weight of water isn’t just for academic purposes; it has practical implications too. For instance, if you’ve ever had to lift a 5-gallon jug for a water dispenser, you’ve grappled
with just over 40 pounds – not a light load! Awareness of this weight can inform your decisions about transport and storage – you wouldn’t want to overload a shelf and risk it collapsing under the
Implications in the Field of Construction and Engineering
Another area where the weight of water plays a significant role is in the fields of construction and engineering. For example, when engineers design structures like bridges and dams, they need to
calculate the weight of the water those structures might hold to ensure their stability and safety.
Health and Fitness: Hydrating with Five Gallons of Water
Hydration is a vital aspect of health and fitness. Remarkably, an adult human body is about 60% water and needs to maintain this balance to function optimally. Knowing how much 5 gallons of water
weigh might make you rethink the ease of meeting your daily hydration goals. Don’t worry, though; you don’t need to be hefting five-gallon weights – the recommended daily water intake for healthy
adults is significantly less than 5 gallons!
Dispelling Myths Around Water Weight
Common Misconceptions
As we journey through our exploration of water weight, it’s also crucial to clear up some common misconceptions. One myth is that heated water weighs less than cold water. While heat does cause water
to expand and take up a greater volume, this does not decrease the water’s overall weight. Instead, you would simply have the same weight of water distributed over a larger area. We’re also often led
to believe that saltwater weighs less than fresh water – but in reality, saltwater is denser and consequently weighs more than fresh water.
Another misunderstanding revolves around the concept of “drinking a lot of water to lose weight.” While staying hydrated can help maintain healthy body functions and might even assist in suppressing
untimely hunger pangs, water does not magically make excess weight disappear. If that were the case, we’d all be floating around in 5-gallon water tanks!
Key Takeaways
Recapping Main Topics
From this discussion, we’ve learned that a gallon is a unit of volume primarily used to measure liquids, with one gallon weighing approximately 8.34 pounds. When multiplied by five, we came to the
conclusion that 5 gallons of water weigh about 41.7 pounds. We have also explored the practical implications of this knowledge, from the demand it can place on our physical strength, to its
implications for architectural design. Furthermore, we have debunked some myths, confirming that neither temperature nor salt content reduces water’s weight, and that while water may promote feelings
of fullness, it does not possess weight-loss properties all on its own.
Final Thoughts and Further Reading
We hope you’ve enjoyed this detailed investigation into the weight of 5 gallons of water. As you’ve seen, answering such a simple question involves an exploration of numerous fascinating fields, from
basic measurements to physics, engineering, and health. At the heart of it all, we’ve learned that understanding the weight of water isn’t merely an academic exercise but touches every aspect of our
Through this water journey, you’ve undoubtedly developed a new appreciation for the ubiquitous liquid that covers about 71% of our Earth’s surface. The next time you see a gallon (or five!) of water,
you’ll be able to appreciate more than just its refreshing capabilities — you’ll have a sense of its weight and the role it plays in our world.
For those seeking to investigate this topic further, you might explore the weight of water in different states (liquid, solid, gas) and how these variations affect the world. As we delve into more
water-related topics in future blogs, remember, just like water, knowledge flows, and there’s always something new to learn and explore.
|
{"url":"https://www.owlift.com/blog/5-gallon-water-jug-weight/","timestamp":"2024-11-03T13:36:19Z","content_type":"text/html","content_length":"200158","record_id":"<urn:uuid:2884946a-0f82-452b-9715-c3e291737fbc>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00515.warc.gz"}
|
Henry Segerman
Henry Segerman
Associate Professor of Mathematics
Oklahoma State University
Stillwater, Oklahoma, USA
Henry Segerman is a postdoctoral mathematician. His mathematical research is in 3 dimensional geometry and topology, and concepts from those areas often appear in his work. Other artistic interests
involve procedural generation, self reference, ambigrams and puzzles.
Cuboctahedral fractal graph
66 x 66 x 66 mm
PA 2200 Plastic, Selective-Laser-Sintered
This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the
construction is degree 3, and is replaced at the next step by 7 vertices which can be thought of as a subset of a 3 x 3 x 3 cube, with certain choices of edges connecting them to each other. Each
edge is replaced at the next step by a single edge, joining to the vertex in the centre of each 3 x 3 face. We begin the construction with the first step being the edges of a cube, and this is the
result at the fourth step.
Octahedron fractal graph
103 x 103 x 103 mm
PA 2200 Plastic, Selective-Laser-Sintered
This is a graph embedded in 3-dimensional space as a subset of an "octahedral lattice", which is related to the tessellation of space using octahedra and tetrahedra. The graph has a fractal
structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 4, and is replaced at the next step by 6 vertices arranged in an octahedron, with
certain choices of edges connecting them to each other. Each edge is replaced at the next step by 2 parallel edges. We begin the construction with the first step being the edges of an octahedron, and
this is the result at the fourth step.
Space filling graph 1
68 x 68 x 68 mm
PA 2200 Plastic, Selective-Laser-Sintered
This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, analogous to the fractal structure of a step in the construction of a space
filling curve, but with greater connectivity. This greater connectivity makes the physical sculpture considerably more robust than the analogous sculpture of a step in the construction of a space
filling curve would be. Each vertex at each step of the construction is degree 3, and is replaced at the next step by 8 vertices arranged in a 2 x 2 x 2 cube, with certain choices of edges connecting
them to each other. Each edge is replaced at the next step by 4 parallel edges. We begin the construction with the first step being the edges of a cube, and this is the result at the fourth step. The
spacing between the vertices varies in order to highlight the fractal structure.
|
{"url":"https://gallery.bridgesmathart.org/exhibitions/2011-bridges-conference/henrys","timestamp":"2024-11-05T13:12:23Z","content_type":"text/html","content_length":"42971","record_id":"<urn:uuid:1529effc-cbdb-4626-9669-04429df26dd2>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00499.warc.gz"}
|
1-form symmetry versus large N QCD
In this talk, I will discuss the tension between two well-established facts about gauge theories: that large N gauge theories confine, and that confinement can be understood in terms of 1-form
symmetry. It has long been appreciated that in QCD-like theories without fundamental matter, confinement can be given a sharp characterization in terms of symmetry. More recently, such symmetries
have been identified as 1-form symmetries, which fit under the broader umbrella of generalized global symmetries. I will discuss obstructions to the existence of a 1-form symmetry in large N QCD,
where confinement is nevertheless a sharp notion. I give general arguments valid in any spacetime dimension, and use 2d scalar QCD on the lattice as a concrete example.
Host: Erich Poppitz
|
{"url":"https://www.physics.utoronto.ca/research/theoretical-high-energy-physics/thep-events/thep-seminar-november-14-2022/","timestamp":"2024-11-12T00:07:48Z","content_type":"text/html","content_length":"29101","record_id":"<urn:uuid:4e0c7dc2-6dcf-40d2-b163-a3e9e7c1dc3b>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00618.warc.gz"}
|
From Chaos to Clarity: Simplify Your Angular Code with Declarative Programming
Not that long ago I bumped into an interesting problem. I wanted to implement a “search user†dropdown. When you select a user’s name, you make an API call to load more data, meanwhile the
loading happens, you display a “loading…†message and once the user details are back from the server, you display those.
Kinda like the following GIF on which I will be describing the two approaches (declarative and imperative) that I used.
The Problem Description
This is a small representation of the problem which you’ve probably bumped into many times. You have a dropdown and every time you select a value, you want to load more details about the selected
item from the backend.
You display a loading message until the data is not there, maybe some fancy animation, and once the data arrives you display it.
We don’t need a server for this example, it’s enough to have a mock data service as follows:
import { Injectable } from ‘@angular/core‘;import { Observable, map, of } from ‘rxjs‘;import { delay } from ‘rxjs/operators‘;
export type DataItem = {
id: string;
name: string;
export const dataItems: DataItem[] = [
{ id: ‘id_1‘, name: ‘item_1‘ },
{ id: ‘id_2‘, name: ‘item_2‘ },
{ id: ‘id_3‘, name: ‘item_3‘ },
{ id: ‘id_4‘, name: ‘item_4‘ },
{ id: ‘id_5‘, name: ‘item_5‘ },
providedIn: ‘root‘,
export class DataService {
* simulate fake API call to the server
getDataFakeAPI(itemId: string): ObservableDataItem> {
return of(itemId).pipe(
map(() => dataItems.find((d) => d.id === itemId)!),
The dataItems are items which will be displayed inside the select dropdown and every time you change the value, you will call getDataFakeAPI that returns the same value with some delay – mocking
API call.
Imperative Solution
The following solution is the solution that I used initially. I will post the whole code and then go over some parts which are important in this example.
import { Component, inject, signal } from ‘@angular/core‘;import {DataItem,DataService,dataItems} from ‘./data-service.service‘;
selector: ‘app-select-imperative‘,
standalone: true,
template: `
Selected Items
@for(item of selectedItems(); track item.id){
{{ item.name }}
Loading …
@if(selectedItems().length > 0){
export class SelectImperativeComponent {
private dataService = inject(DataService);
displayData = dataItems;
* displayed data on the UI – loaded from the BE
selectedItems = signalDataItem[]>([]);
isLoadingData = signal(false);
* on select change – load data from API
onChange(event: any) {
const itemId = event.target.value;
// check if already saved
const savedIds = this.selectedItems().map((d) => d.id);
if (savedIds.includes(itemId)) {
// set loading to true
// fake load data from BE
this.dataService.getDataFakeAPI(itemId).subscribe((res) => {
// save data
this.selectedItems.update((prev) => […prev, res]);
// set loading to false
* removes item from selected array
onRemove(item: DataItem) {
(prev) => prev.filter((d) => d.id !== item.id)
onReset() {
Overall it’s not that complicated and it may be close to a solution that you yourself would write. First of all, there is nothing significantly wrong with this solution, but why exactly do I call
this an imperative approach ?
In short, this is imperative, because your signals – selectedItems and isLoadingData – can be changed all over the places which leads to two major problems – debugging and multiple properties.
Right now the selectedItems is changed in 3 places and isLoadingData is changed in 2 places, however once the complexity of this feature grows, debugging may become an issue to figure out how the
data flow happens in this feature. What if selectedItems and isLoadingData will be used in 10 places each, suddenly it is not that easy to understand what’s happening.
Also with the growing complexity, you may want to introduce another properties like isError = signal(false) .
Now let’s think a bit and ask the question, could we combine the selectedItems , isLoadingData and potentially a new property isError into only one property which would look something like:
data: DataItem[];
isError: boolean;
isLoading: boolean;
Declarative Solution
The result what we want to achieve with the declarative solution is that we want to have only one property (object), which will have the data and loading keys and we want to change the values for
this property only in one place.
Here is the solution that I came up with:
import { Component, inject, signal } from ‘@angular/core‘;import {DataItem,DataService,dataItems} from ‘./data-service.service‘;import { Subject, map, merge, scan, startWith, switchMap } from
‘rxjs‘;import { toSignal } from ‘@angular/core/rxjs-interop‘;
selector: ‘app-select-declarative‘,
standalone: true,
template: `
Selected Items
@for(item of selectedItems().data; track item.id){
{{ item.name }}
Loading …
@if(selectedItems().data.length > 0){
export class SelectDeclarativeComponent {
private dataService = inject(DataService);
displayData = dataItems;
private removeItem$ = new SubjectDataItem>();
private addItem$ = new Subjectstring>();
private reset$ = new Subjectvoid>();
* displayed data on the UI – loaded from the BE
selectedItems = toSignal(
// create action to add a new item
switchMap((itemId) =>
map((item) => ({
action: ‘add‘ as const,
item: null,
action: ‘initLoading‘ as const,
// create action to remove an item
map((item) => ({
action: ‘remove‘ as const,
// create action to reset everything
map(() => ({
item: null,
action: ‘reset‘ as const,
(acc, curr) => {
// add reset state
if (curr.action === ‘reset‘) {
return {
isLoading: false,
data: [],
// display loading
if (curr.action === ‘initLoading‘) {
return {
data: acc.data,
isLoading: true,
// check to remove item
if (curr.action === ‘remove‘) {
return {
isLoading: false,
data: acc.data.filter((d) => d.id !== curr.item.id),
// check if already saved
const savedIds = acc.data.map((d) => d.id);
if (savedIds.includes(curr.item.id)) {
return {
isLoading: false,
data: acc.data,
// add item into the rest
return {
isLoading: false,
data: […acc.data, curr.item],
{ data: [] as DataItem[], isLoading: false }
initialValue: {
data: [],
isLoading: false,
* on select change – load data from API
onChange(event: any) {
const itemId = event.target.value;
* removes item from selected array
onRemove(item: DataItem) {
onReset() {
Yes, this is longer than the previous solution, however is it more complex or simpler than the previous one?
What needs to be first highlighted that instead of changing the selectedItems on multiple places, you now have 3 subjects, each of them representing an action that can happen.
private removeItem$ = new SubjectDataItem>();
private addItem$ = new Subjectstring>();
private reset$ = new Subjectvoid>();
Next inside the selectedItems you use these subjects and map them into format you want to work with. For me the following format suited the most
item: DataItem;
action: ‘add‘ | ‘remove‘ | ‘initLoading‘ | ‘reset‘
For the addItem$ you want to use the startWith operator at the end of the pipe chain. This will allow that the first action which will be emitted when selecting a new value is initLoading and only
when the API call (dataService.getDataFakeAPI) finishes, it will emit again with the action add.
You wrap each pipe mapping with the merge operator, because you want to perform some common logic despite of which one of these subjects emit.
Lastly you have the giant scan section. The scan operator is similar to reduce , however scan remembers the last computation that happened and if the scan happens again, it will use the data from the
last computation – read more about scan .
Inside the scan section, you create conditions what should happen based on the action of current value that is being processed.
It may reassemble how NgRx works. You have some actions (add, remove and reset subjects) and you create reducers to updated the state of only one property.
Final Thoughts
Overall it’s up to you, the developer, which approach you choose to solve this problem. Both have some advantages and shortcomings.
If you want to play around with this example, you can find it on stackblitz or connect with me on dev.to | LinkedIn| Personal Website | Github.
The post From Chaos to Clarity: Simplify Your Angular Code with Declarative Programming appeared on Rmag.
This post first appeared on Rmag, please read the originial post: here
|
{"url":"https://www.blogarama.com/blogging-blogs/1450678-rmag-blog/65164243-from-chaos-clarity-simplify-angular-code-declarative-programming","timestamp":"2024-11-06T23:35:37Z","content_type":"application/xhtml+xml","content_length":"81799","record_id":"<urn:uuid:1b55cdcb-5f77-45e7-a4b7-ad0c87ecf43e>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00474.warc.gz"}
|
Real Analysis – Volume 1
Most of the Students of mathematics find difficult to learn the essence of real analysis. This book is designed for under- graduate and post-graduate students of mathematics to understand the
underlying principles and essence of real analysis. To achieve them solutions of a large number of examples are given on each topic. For example to understand the definition of limit of a sequence,
solutions of various problems on limit of sequence are given in terms of ε and δ. Further they are verified with given value of ε. This helps to understand the concept of the limit of the sequence.
This book consisting of five chapters. In the first chapter we discussed the real numbers, Dedekind-cut and mathematical induction. In the second chapter we discussed the interior point, limit point,
open and closed sets. In the remaining chapters we discussed thoroughly on sequences, positive term series, alternating series and series of arbitrary terms.
About the Author: Dr. K. Sambaiah is obtained M.Sc., M.Phil. and Ph.D. degrees in Mathematics from Kakatiya University, Warangal, Telangana State, India. He worked in this University from 1978-2013
at different levels such as Asst.Professor, Associate Professor and Professor of Mathematics. He obtained Gold Medal for getting highest marks in M.Sc. (Mathematics) and also obtained best teacher
award in 2012 from the Government of Andhra Pradesh. He is co-authored more than 12 mathematics books (Intermediate and B.Sc.) which were published by Telugu Academy, Govt. of Andhra Pradesh. Further
45 research papers of his have been published in many national and international journals. His recent publications of books are “Numerical Methods”, “Applications of derivatives” and “A detailed
study on limits and continuity”.
Dr. E. Rama is working as Associate Professor in the department of Mathematics, Osmania University, Hyderabad, Telangana, India. She obtained her M.Sc. and Ph.D. in Mathematics from Kakatiya
University, Warangal, Telangana, India. She is a gold medalist in both UG and PG. She has 20 years of teaching experience in private and government institutions. She published more than 20
publications in national and international journals.
• Paperback: 616 pages
• Publisher: White Falcon Publishing; 1 edition (2022)
• Author: K. Sambaiah, E. Rama
• ISBN-13: 9781636406466
• Product Dimensions: 7 x 1 x 10 Inch
Indian Edition available on:
We Also Recommend
|
{"url":"https://store.whitefalconpublishing.com/products/real-analysis-volume-1","timestamp":"2024-11-03T18:35:49Z","content_type":"text/html","content_length":"99375","record_id":"<urn:uuid:88873965-9806-4cf3-ab7b-26060871e675>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00247.warc.gz"}
|
Hi, I was hoping for some clarification from Professor Maitzen about his comments on infinite sets (on March 7). The fact that every natural number has a successor is only true for the natural
numbers so far encountered (and imagined, I suppose). Granted, I can't conceive of how it could be that we couldn't just add 1 to any natural number to get another one, but that doesn't mean it's
impossible. It seems quite strange, but there are some professional mathematicians who claim that the existence of a largest natural number (probably so large that we would never come close to
dealing with it) is much less strange and problematic than many of the conclusions that result from the acceptance of infinities. If we want to define natural numbers such that each natural number by
definition has a successor, then mathematical induction tells us there are infinitely many of them. But mathematical induction itself only proves things given certain mathematical definitions.
Whether those definitions indeed correspond to reality is another question. Am I missing something here? Thanks so much!!
|
{"url":"https://www.askphilosophers.org/question/5084","timestamp":"2024-11-09T04:16:43Z","content_type":"text/html","content_length":"33215","record_id":"<urn:uuid:28979738-9e2a-4407-ae9f-77b2cb159aa3>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00447.warc.gz"}
|
Vedic Astrology: Charakhandas and Rasinamas (Duration of sign)
We are starting a series on mathematical aspect of astrology and today's post is about calculating the duration of signs at any place. In this post we are going to study the meaning of Rasinamas,
Charakhandas, calculation of charakhandas, rashimanas and ayanamsha.
Astrology is the science which is based on mathematics and for the purpose of making accurate predictions it is absolutely essential that the student is conversant with the mathematical aspects. In
fact, it is said that 'Suryasiddhanta' and 'Brihat Jataka' are two wheels of chariot on which it runs. From this it can concluded that the equal importance should be given to the mathematical aspect
of the science.
Rasimanas means the rising period of the sign or rasi. The duration of each sign is a function of latitude of a place. The average duration of any ascendant is 120 minutes. It is important to know
exact duration, because without it the ascendant cannot be ascertained.
The earth rotates round its axis. During its rotation, the twelve signs rise and set in their respective order. However, the rising time of each sign varies. This is because the ecliptic is angular
to the equator. For this , the duration of rasis at the equator are first identified. This is called as "Lankodaya". (the reason for naming this as Lankodaya is due to the fact that Sri Lanka is near
to the equator). The duration of rasis at the equator is as follows-
Aries, Virgo, Libra, Pisces 111 min. 36sec
Taurus, Leo, Scorpio, Aquarius 119 min 40sec
Gemini, Cancer, Sagittarius, Capricorn 128 min 44 sec
It means that the ascensional differences. It is the function of latitude and declination. The ascensional difference is deducted or added from the rashimanas at equator to arrive at the rasimanas of
the defined place. The rasimanas are further used to calculate the ascendant - one of the important mathematical point for studying horoscope.
Determination of rashimanas at the given place
The formula for determining charakhandas for the signs Aries Virgo Libra Pisces is
[19335312*sin(30)*sin( latitudes of the place ) ]
cos( latitudes of the place )*60*3365.3581
The formula for the signs Taurus Leo, Scorpio, Aquarius is
[19335312*sin(60)*sin( latitudes of the place ) ]
cos( latitudes of the place )*60*7270.1068
For the rest of the signs
[19335312*sin(90)*sin( latitudes of the place ) ]
cos( latitudes of the place )*60*20151.243
The answer for the above formula is in minutes.
Let us calculate the charakhandas for the place at 45N00 latitude(Longitude is not required since it is the function of latitudes only).
The value of 45N00 latitude charakhandas for the signs Aries Virgo Libra Pisces is
Sin (45) = 0.707106
Cos (45) = 0.707106
[19335312*0.5*sin( 45 ) ]
____________________________ = 47.88 minutes or 47 minutes 53 seconds
The value of 45N00 latitude charakhandas for the signs Taurus Leo scorpio aquarius is
Cos(45) = 0.707106
Sin(45) = 0.707106
[19335312 * 0.866025 * 0.707106 ]
______________________________ = 38.39 minutes or 38 minutes 23 seconds
The value of 45N00 latitude charakhandas for the signs Gemini Cancer Sagittarius capricorn is
Sin(90)= 1
Cos(45) = 0.707106
Sin(45) = 0.707106
________________________________________ = 16.00 minutes (approximately).
Thus the charakhandas for 45N00 latitudes are 47.88 minutes for Aries, Virgo, Libra and Pisces signs, 38.39 minutes for Taurus, Leo, scorpio, aquarius signs and 15.99 minutes for Gemini Cancer
Sagittarius capricorn signs.
If the birth is in northern latitude then the charakhandas thus obtained by the above formulae be added or subtracted to or from rasimanas at the equator. If the birth is in northern hemisphere then
deduct the charakhandas thus obtained for the following signs viz. Capricorn, Aquarius, Pisces, Aries, Taurus and Gemini. The charakhandas calculated for the rest of the signs be added. If the birth
is in the southern hemisphere then the reverse holds true. Let us calculate rasimanas at 45N00 latitudes.
│Sr.no│Sign │Rising period at 0 Lat.│+/-│Charakhandas at 45N00│Rasimanas or duration of signs │
│ 1 │Aries │111 min. 36 sec │ - │47 minutes 53 seconds│63 minutes 43 seconds │
│ 2 │Taurus │119 min 40 sec │ - │38 minutes 23 seconds│81 minutes 17 seconds │
│ 3 │Gemini │128 min 44 sec │ - │16.00 minutes │112 minutes 44 seconds │
│ 4 │Cancer │128 min 44 sec │ + │16.00 minutes │144 minutes 44 seconds │
│ 5 │Leo │119 min 40 sec │ + │38 minutes 23 seconds│158 minutes 03 seconds │
│ 6 │Virgo │111 min. 36 sec │ + │47 minutes 53 seconds│159 minutes 29 seconds │
│ 7 │Libra │111 min. 36 sec │ + │47 minutes 53 seconds│159 minutes 29 seconds │
│ 8 │Scorpio │119 min 40 sec │ + │38 minutes 23 seconds│158 minutes 03 seconds │
│ 9 │Sagittarius│128 min 44 sec │ + │16.00 minutes │144 minutes 44 seconds │
│ 10 │Capricorn │128 min 44 sec │ - │16.00 minutes │112 minutes 44 seconds │
│ 11 │Aquarius │119 min 40 sec │ - │38 minutes 23 seconds│81 minutes 17 seconds │
│ 12 │Pisces │111 min. 36 sec │ - │47 minutes 53 seconds│63 minutes 43 seconds │
Aries Virgo Libra Pisces 111 min. 36 sec
Taurus Leo Scorpio Aquarius 119 min 40 sec
Gemini Cancer Sagittarius Capricorn 128 min 44 sec
During every year, the sun has two movements, one towards north called uttarayana and the other towards south called dakshinayana. During this solar movement the sun crosses the equator twice in the
year; firstly during his northern course and secondly during his southern course.
When the sun reaches his equinoctial point the duration of day and night is equal. The year commence at the time at which the sun reaches this point i.e. 0 degree Aries.
If we consider the commencement of the year when the sun is in conjunction to the fixed star and also at the equinoctial point and calculate the year accordingly, it will be observed that in the
subsequent year the sun intersects the equator before the sun is in conjunction with the fixed star. The difference gets accumulated every year. This difference which gets accumulated every year is
50.33 seconds of an arc. The movement is retrograde i.e. towards west and is called precession of equinox.
The precession of equinox is the most important factor not only for mathematical purpose but also for predictive purpose. It has divided astrology into 2 schools of thought -
a) Sayana System also called as Moving Zodiac (Tropical System)
b) Nirayana System also called as Fixed Zodiac (Sidereal System)
Sayana system includes precession of equinox and horoscope is cast after including the precession.
Nirayana System however considers the precession for casting of horoscope but the accumulated difference of precession calculated with respect to the fixed point of the zodiac, usually a star, is
We follow nirayana system since the Hindus adopted sayana system for mathematical purpose only and it was reduced to niryana system for predictive purpose.
|
{"url":"http://www.prosperitynjoy.com/2015/04/vedic-astrology-charakhandas-and.html","timestamp":"2024-11-01T22:06:25Z","content_type":"application/xhtml+xml","content_length":"249267","record_id":"<urn:uuid:a02d67cf-34a5-478e-862f-d2c2d649bca5>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00070.warc.gz"}
|