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### 8th Standard Science Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 8 Session 2019 - 2020 TN Stateboard [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

#### 8th Standard Science - Reaching the age of Adolescence Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

The period at which an organism attains sexual maturity is called _____________

• 2)

During puberty, the region below the waist become wider in _____________

• 3)

Many adolescent boys and girls get pimples on face, due to the secretions of _________ gland.

• 4)

The sperm is produced by ____________

• 5)

During menstruation, the progesterone level is ___________

#### 8th Standard Science - Movements Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

Which one of the following organisms lack muscles and skeleton for movement?

• 2)

__________ joints are immovable.

• 3)

Why do underwater divers wear fin-like flippers on their feet ?

• 4)

External ear (pinna )is supported by

• 5)

Cockroach moves with the help of its

#### 8th Standard Science - Atomic Structure Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

The same proportion of carbon and oxygen in the carbon dioxide obtained from different sources proves the law of __________

• 2)

Cathode rays are made up of

• 3)

In water, hydrogen and oxygen are combined in the ratio of _______by mass.

• 4)

Which of the following statements made by Dalton has not undergone any change?

• 5)

A negatively charged ion is called ____________, while positively charged ion is called ____________

#### 8th Science - Air Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

Which of the following is true about oxygen?

• 2)

Aerated water contains

• 3)

Solvay process is a method to manufacture

• 4)

Which of the following is known as azote?

• 5)

___________ is called as vital life

#### 8th Science - Term 1 Forces and Pressure 3 Marks and 5 Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

What is called static pressure of the liquid?

• 2)

Why do deep sea divers wear special suits while diving?

• 3)

Cooking in a place located at a higher altitude is difficult why?

• 4)

What is known as atmospheric pressure?

• 5)

What are the changes happen while applying a force?

#### 8th Science - Term 1 Light Three Marks and Five Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Define the refractive index of a medium.

• 2)

State the Snell’s law of refraction

• 3)

Tabulate the images formed by a convex mirror.

• 4)

Name the rays which involved in reflection of light.

• 5)

Why silver metal is used to make mirror?

#### 8th Science - Term 1 Changes Around Us 3 Marks and 5 Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Explain the role of yeast in making cakes?

• 2)

Justify the statement. Burning of fossil fuels is responsible for global warming.

• 3)

Is rusting good for Iron materials? Explain.

• 4)

Do all the fruits and vegetables undergo browning? Explain.

• 5)

Classify the following day to day activities based on chemical reactions by physical contact, solutions of reactants, heat, light, electricity and catalyst.
a ) burning of crackers during festivals
b) addition of water to quicklime to make it slaked lime
c) silver ornaments become black on exposure to air for a long time
d) copper vessel kept in open air for long time

#### 8th Science - Term 1 Micro Organisms 3 Marks and 5 Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Write the four types of bacteria, based on their shape.

• 2)

What are antibiotics?

• 3)

What are pathogens?

• 4)

How diseases causing micro organisms enter into human beings?

• 5)

Why micro organisms are essential for agriculture?

#### 8th Science - Term 1 Organisation of Life 3 Marks and 5 Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

What is respiration?

• 2)

Define basal metabolism?

• 3)

Define organ

• 4)

What is the significance of stem cell?

• 5)

Write down the classification of animal tissues.

#### 8th Science - Term 1 Plant Kingdom 3 Marks and 5 Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Write short notes about natural system of classification.

• 2)

Write any three economic importance of algae.

• 3)

Write the differences between algae and fungi.

• 4)

How many classes are there in Bryophytes? What are they?

• 5)

Write any four characters of pteridophytes.

#### 8th Science - Term 1 Matter 3 Marks and 5 Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

What is a compound? Give example.

• 2)

What are Semi conductorsr-Clve example

• 3)

What are inorganic compounds? Give example.

• 4)

What are organic compounds? Give example.

• 5)

Give some uses of metalloids

#### 8th Science - Term 1 Measurement 3 Marks and 5 Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Define - mole.

• 2)

What are the differences between Plane angle and solid angle?

• 3)

Give any two uses of super conductors

• 4)

When 3 A of current flows through the circuit for 5 seconds, calculate the charge?

• 5)

Convert i) 90° into radian, ii) $\frac { \pi }{ 6 }$ into degrees.

#### 8th Science - Electricity Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

When an ebonite rod is rubbed with fur, the charge acquired by the fur is

• 2)

An electroscope has been charged by induction with the help of charged glassrod. The charge on the electroscope is

• 3)

Fuse is

• 4)

_______takes place by rubbing objects together.

• 5)

The body which has lost electrons becomes ________

#### 8th Standard Science - Heat Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

Heat is a form of ________.

• 2)

If you apply equal amount of heat to a solid, liquid and gas individually, which of the following will have more expansion?

• 3)

Conduction is the heat transfer which takes place in a____________.

• 4)

A calorimeter is a device used to measure the________.

• 5)

_______ is defined as the amount of heat required to raise the temperature of 1kg of a substance by 1°C.

#### 8th Standard Science - Forces and Pressure Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

If we apply a force against the direction of motion of a body, then the body will

• 2)

Pascal’s law is used in

• 3)

The unit of viscosity is

• 4)

Rain drops are spherical in nature because of _________

• 5)

If the area of contact is greater, then the ______ will be greater.

#### 8th Standard Science - Measurements Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

Which one the following system of units is the British System of unit?

• 2)

SI unit of temperature is

• 3)

SI unit stands for

• 4)

Quantities other than base quantities are called as

• 5)

The solid angle is measured in _______.

#### 8th Science - Introduction to the Information Age Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Name the two types of software

• 2)

Write a short note on Data.

• 3)

Name any four input devices.

• 4)

Define Control unit

• 5)

Explain the classification of computer.

#### 8th Science - Organisation of Life Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

What is cell differentiation?

• 2)

State different types of tissues.

• 3)

Mention the function of ‘Alveoli’?

• 4)

Name the processes by which air enters and comes out of our lungs?

• 5)

Define Metabolism?

#### 8th Science Unit 7 Plant Kingdom Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Define Thallus.

• 2)

What is mean by Binomial Nomenclature? give example.

• 3)

Write any two characters of dicotyledons.

• 4)

Seeds of gymnosperm plants are naked. Why?

• 5)

Write any two economic importance of fungi.

#### 8th Science - Micro Organisms Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Write the name of any nitrogen fixing bacteria.

• 2)

Name the bacteria used in the production of vinegar.

• 3)

Write the names of any three protozoans.

• 4)

Who discovered penicillin?

• 5)

Which diseases can be prevented by vaccination?

#### 8th Science Unit 5 Changes Around Us Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Define a chemical reaction.

• 2)

Define catalysis

• 3)

What happens when an iron nail is placed in copper sulphate solution?

• 4)

What is pollution?

• 5)

What is Tarnishing? Give an example.

#### 8th Science - Matter Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

Name two soft metals that can be cut with a knife.

• 2)

Why are bells made of metals?

• 3)

What does a chemical symbol represent?

• 4)

Mention any three compounds that exist in liquid state.

• 5)

Write three properties of metalloids.

#### 8th Science - Term 1 Model Question Paper - by Uma Rajesh - Coimbatore - View & Read

• 1)

SI unit of temperature is

• 2)

Unit of pressure is

• 3)

The distance from the pole to the focus is called

• 4)

Symbol of Mercury is

• 5)

_______ is used to measure electric current.

#### 8th Science Chapter 2 Forces and Pressure Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

A stone weighs 500 N. Calculate the pressure exerted by it if it makes a contact with a surface of area 25 cm2.

• 2)

Give two examples to verify that a force changes the shape of a body.

• 3)

Give two examples to verify that a force tends to change the static condition of a body.

• 4)

Taking out paste from a tooth paste tube is an example to highlight which physical property?

• 5)

What do you feel when you touch a nail immediately after it is hammered into a wooden plank? Why?

#### 8th Science Unit 1 Measurement Two Marks Questions - by Chitra - Rajapalayam - View & Read

• 1)

What is the unit of mass in FPS system?

• 2)

How many base quantities are included in SI system?

• 3)

Mention the types of clocks based on their display.

• 4)

How many times will the ‘minute hand’ rotate in one hour?

• 5)

When 2 coulomb of charge, flows through a circuit for 10 seconds, calculate the current?

#### 8th Science - Term 1 Five Mark Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Write a short note on different types of clocks.

• 2)

Describe an experiment to prove that the pressure in a liquid increases with depth.

• 3)

What is reflection? Write short notes on regular and irregular reflection?

• 4)

Explain the three types of pollution.

• 5)

Write a short note on bacteria and its structure.

#### 8th Science - Introduction to the Information Age Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

Who is the father of computer?

• 2)

Which one of the following is an output device?

• 3)

Which one of the following is an input device?

• 4)

Pen drive is _____device.

• 5)

Fifth generation computer has ___________ Intelligence.

#### 8th Science Chapter 8 Organisation of Life Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

Osmosis is the movement of water molecules from a ___________.

• 2)

The erythrocyte is placed in _________ solution which has lesser concentration of solutes and greater concentration of water than in the cytoplasm.

• 3)

___________ is a good example for anaerobic respiration.

• 4)

_______ nerve is located at the end of the eyes behind the retina.

• 5)

The size of the cells are measured in units of __________.

#### 8th Standard Science - Plant Kingdom Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

Solanum trilobatum is the binomial name of Thoothuvalai. Here the word ‘Solanum’ refers to

• 2)

_________ is an example for colonial form of algae.

• 3)

The well-developed sporophytic plant body is seen in

• 4)

Penicillin is an antibiotic, which is extracted from________

• 5)

The word ‘Taxonomy’ is derived from __________.

#### 8th Standard Science Chapter 6 Micro Organisms Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

Micro organisms are measured in ______.

• 2)

_______ shows both living and nonliving characteristics.

• 3)

______ is a prokaryotic micro organisms.

• 4)

__________ Vaccine is used to cure foot and mouth disease

• 5)

Causative organism for rabies is ___________

#### 8th Standard Science - Changes Around Us Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

Burning of paper is a______ change.

• 2)

______ metal undergoes rusting.

• 3)

Which of the following factor induces electrolysis?

• 4)

Dissolved gases like sulphur dioxide, nitrogen oxides in rain water causes______

• 5)

______ is the basic material to manufacture urea.

#### 8th Standard Science Unit 4 Matter Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

Matter is composed of

• 2)

Which one of metal possess low tensile strength?

• 3)

The property which allows metals to be hammered into their sheets is ___________

• 4)

The element which possess character of both metals and non metals are called_______.

• 5)

Material which has a definite volume but no definite shape and has one free surface is called as ______

#### 8th Standard Science - Light Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

Mirrors having a curved reflecting surface are called as

• 2)

The centre of a sphere of which the reflecting surface of a spherical mirror is a part is called

• 3)

Focal length is equal to half of the

• 4)

Nature of the images formed by a convex mirror is _________.

• 5)

It the angle of incidence is 45°, then the angle of reflection is ______.

#### 8th Standard Science Unit 2 Forces and Pressure Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

If we apply a force against the direction of motion of a body, then the body will

• 2)

Pressure exerted by a liquid is increased by

• 3)

The unit of viscosity is

• 4)

The pressure of a liquid column _____ with the depth of the column.

• 5)

The property of _____ of a liquid surface enables the water droplets to move upward in plants.

#### 8th Science Unit 1 Measurement Book Back Questions - by Chitra - Rajapalayam - View & Read

• 1)

SI unit of temperature is

• 2)

SI unit stands for

• 3)

Quantities other than base quantities are called as

• 4)

_______ of substance, contains 6.023 × 10+23 atoms or molecules.

• 5)

The uncertainty in measurement is called as _______.

#### 8th Standard Science - Organisation of Life One Mark Question with Answer Key - by Chitra - Rajapalayam - View & Read

• 1)

__________ is tough and thick white sheath that protect the inner parts of the eye.

• 2)

Maintenance of constant internal environment of the body is known as _________

• 3)

In the absence of oxygen, glucose is broken down in to ________.

• 4)

_____is a thin transparent membrane that is spread across the sclera

• 5)

_________million alveoli located at the end of branchial tubes

#### 8th Standard Science - Introduction to the Information Age One Mark Question with Answer - by Chitra - Rajapalayam - View & Read

• 1)

Who is the father of computer?

• 2)

Which one of the following is an output device?

• 3)

Which one of the following is an input device?

• 4)

Example of Application program

• 5)

Which of the following component are used in fourth generation?

#### 8th Standard Science - Plant Kingdom One Mark Question and Answer - by Chitra - Rajapalayam - View & Read

• 1)

The first vascular cryptogams in land plants are ________.

• 2)

The well-developed sporophytic plant body is seen in

• 3)

Binominal Nomenclature was first introduced in the year of _______

• 4)

______ is used as a food for domestic animals

• 5)

Cercospora personata causes _________

#### 8th Science Chapter 6 Micro Organisms One Mark Question and Answer - by Chitra - Rajapalayam - View & Read

• 1)

Micro organisms are measured in ______.

• 2)

_______ shows both living and nonliving characteristics.

• 3)

______ is a prokaryotic micro organisms.

• 4)

Plasmodium belongs to _________ type of protozoan.

• 5)

__________ is an acid - loving bacteria

#### 8th Science Unit 5 Changes Around Us One Mark Question and Answer - by Chitra - Rajapalayam - View & Read

• 1)

Burning of paper is a______ change.

• 2)

The burning of matchstick is an example for chemical reaction based on______

• 3)

______ metal undergoes rusting.

• 4)

Rusting of iron is a _________ change.

• 5)

Decomposition of limestone is an example for chemical reaction based on __________

#### 8th Standard Science Chapter 4 Matter One Mark Question and Answer - by Chitra - Rajapalayam - View & Read

• 1)

Symbol of Mercury is

• 2)

A form of non-metal which has high ductility is

• 3)

Which one of metal possess low tensile strength?

• 4)

The property which allows metals to be hammered into their sheets is ___________

• 5)

The non-metal which conduct current is

#### 8th Standard Science - Light One Mark Question with Answer Key - by Chitra - Rajapalayam - View & Read

• 1)

Mirrors having a curved reflecting surface are called as

• 2)

The distance from the pole to the focus is called

• 3)

Focal length is equal to half of the

• 4)

If the focal length of a spherical mirror is 10 cm, what is the value of its radius of curvature?

• 5)

The refractive index of water is

#### 8th Standard Science - Forces and Pressure One Mark Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Which of the following liquids has more viscosity?

• 2)

The unit of viscosity is

• 3)

Even if we tilt the barometric tube at various angles, the level of mercury will______

• 4)

Rain drops are spherical in nature because of _________

• 5)

The unit for surface tension is _________

#### 8th Science Chapter 1 Measurement One Mark Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Which one the following system of units is the British System of unit?

• 2)

Luminous intensity is the intensity of

• 3)

Quantities other than base quantities are called as

• 4)

__________ is the measure of the perceived power of light.

• 5)

Electric current (I) = ____________

#### 8th Science Term 1 Model Question Paper 3 - by Chitra - Rajapalayam - View & Read

• 1)

Quantities other than base quantities are called as

• 2)

Which of the following statements about approximation is wrong?

• 3)

Pressure exerted by a liquid is increased by

• 4)

The refractive index of water is

• 5)

An imaginary line perpendicular to the reflecting surface is called

#### 8th Standard Science Term 1 Model Question Paper 2 - by Chitra - Rajapalayam - View & Read

• 1)

SI unit stands for

• 2)

The unit for surface tension is _________

• 3)

The liquid metal used in thermometers is

• 4)

Burning of paper is a______ change.

• 5)

Limestone contains ______ mainly.

#### 8th Standard Science Term 1 Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Which one the following system of units is the British System of unit?

• 2)

SI unit stands for

• 3)

Unit of pressure is

• 4)

Matter is composed of

• 5)

#### 8th Standard Science Term 1 Five Marks Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

List out the base quantities with their units.

• 2)

Give the different types of friction and explain each with an example.

• 3)

Explain how friction can be minimised.

• 4)

Explain the images formed by a concave mirror?

• 5)

Speed of light in air is 3 × 108 m s–1 and the refractive index of a medium is 1.5. Find the speed of light in the medium.

#### 8th Standard Science Term 1 Two Marks Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Assertion: The SI system of units is the suitable system for measurements.
Reason: The SI unit of temperature is Kelvin.
a. If both assertion and reason are true and reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. Assertion is true, but reason is false.
d. Assertion is false, but reason is true.

• 2)

Assertion: Avogadro’s number is the number of atoms in one mole of substance.
Reason: Avogadro’s number is a constant
a. If both assertion and reason are true and reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. Assertion is true, but reason is false.
d. Assertion is false, but reason is true.

• 3)

Assertion: Broad straps are used in bags.
Reason: Broad straps last for long life.
a. If both assertion and reason are true and the reason is the correct explanation of the assertion.
b. If both assertion and reason are true, but the reason is not the correct explanation of the assertion.
c. If the assertion is true, but the reason is false.
d. If the assertion is false, but the reason is true.

• 4)

Assertion: Algae are heterotrophic.
Reason: They don’t have chlorophyll.
(a) If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
(c) If Assertion is true but Reason is false.
(d) If both Assertion and Reason are false.

• 5)

Assertion (A): Some algae are living as colonial form.
Reason (R): Some of the algae are Symbionts.
a. Both are correct
b. Both are wrong
c. A is correct R is wrong
d. A is wrong R is correct

#### 8th Standard Science Term 1 Model One Marks Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Which one the following system of units is the British System of unit?

• 2)

Luminous intensity is the intensity of

• 3)

SI unit stands for

• 4)

Unit of pressure is

• 5)

The unit of viscosity is

#### 8th Standard Science Chapter 9 Introduction to the Information Age Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Who is the father of computer?

• 2)

Which one of the following is an input device?

• 3)

Fifth generation computer has ___________ Intelligence.

• 4)

First generation computer has_________

• 5)

Example of Application program

#### 8th Standard Science Chapter 8 Organisation of Life Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

__________ is tough and thick white sheath that protect the inner parts of the eye.

• 2)

The process of air passing in and out the lungs is called ___________.

• 3)

_______tissues for conduction of nerve impalses

• 4)

_________million alveoli located at the end of branchial tubes

• 5)

__________ is the structural and functional unit of living organisms.

#### 8th Standard Science Chapter 7 Plant Kingdom Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Solanum trilobatum is the binomial name of Thoothuvalai. Here the word ‘Solanum’ refers to

• 2)

The first vascular cryptogams in land plants are ________.

• 3)

Binominal Nomenclature was first introduced in the year of _______

• 4)

Penicillin is an antibiotic, which is extracted from________

• 5)

______ is the earliest system of classification in plants.

#### 8th Standard Science Chapter 6 Micro Organisms Model Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Micro organisms are measured in ______.

• 2)

______ is a prokaryotic micro organisms.

• 3)

Based on shape, the bacteria are classified into _______ types.

• 4)

_________is a ball-shaped bacteria.

• 5)

Yeast reproduces by __________

#### 8th Standard Science Chapter 5 Changes Around Us Important Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Burning of paper is a______ change.

• 2)

The burning of matchstick is an example for chemical reaction based on______

• 3)

Brine is a concentrated solution of ______.

• 4)

In Haber’s process of producing ammonia ______ is used as a catalyst.

• 5)

______ is responsible for Global warming.

#### 8th Standard Science Chapter 4 Matter Important Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Matter is composed of

• 2)

The Pictorial symbol for water given by the alchemists was

• 3)

Symbol of Mercury is

• 4)

Which one of metal possess low tensile strength?

• 5)

The non-metal which conduct current is

#### 8th Standard Science Chapter 3 Light Important Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

Mirrors having a curved reflecting surface are called as

• 2)

The centre of a sphere of which the reflecting surface of a spherical mirror is a part is called

• 3)

The distance from the pole to the focus is called

• 4)

If the focal length of a spherical mirror is 10 cm, what is the value of its radius of curvature?

• 5)

The refractive index of water is

#### 8th Standard Science Chapter 2 Forces and Pressure Important Question Paper - by Chitra - Rajapalayam - View & Read

• 1)

If we apply a force against the direction of motion of a body, then the body will

• 2)

The unit of viscosity is

• 3)

_______is the force acting perpendicularly on any given surface area of a body

• 4)

The unit for surface tension is _________

• 5)

If the area of contact is greater, then the ______ will be greater.

#### 8th Science Measurement Important Questions - by Chitra - Rajapalayam - View & Read

• 1)

Electric current belongs to ______quantities

• 2)

SI unit of temperature is

• 3)

_______ can be used as memory or storage element in the computers.

• 4)

__________ is the measure of the perceived power of light.

• 5)

The unit of charge is ______

#### Class 8th Standard New Syllabus Creative Question In Chapter Forces And Pressure - by Samitha - View & Read

• 1)

If we apply a force against the direction of motion of a body, then the body will

• 2)

Which of the following liquids has more viscosity?

• 3)

The unit of viscosity is

• 4)

Name two instruments, which help to measure the pressure of a fluid.

• 5)

Define one atmosphere.

#### 8th Standard New Syllabus Chapter Five Important Question - by Samitha - View & Read

• 1)

Burning of paper is a______ change.

• 2)

The burning of matchstick is an example for chemical reaction based on______

• 3)

______ metal undergoes rusting.

• 4)

The pigment responsible for browning of apples is______.

• 5)

Which of the following factor induces electrolysis?

#### Creative Questions For 8th standard Science For Second Chapter - by Samitha - View & Read

• 1)

Electric current belongs to ______quantities

• 2)

SI unit of temperature is

• 3)

Amount of substance is

• 4)

Luminous intensity is the intensity of

• 5)

Which one of the following devices is used to measure electric current

### TN Stateboard Updated Class 8th Science Syllabus

#### T1 - Measurement

Introduction - System of Units - Temperature - Electric Current ( I ) - Amount of substance - Luminous Intensity - Plane angle - Solid Angle - Clocks - Accuracy in Measurements - Approximation - Rounding off - Numerical Problems

#### T1 - Forces and Pressure

Introduction - Force - Pressure Exerted By Air - Atmospheric Pressure - Forces In Liquids - Surface Tension - Friction - Viscous Force or Viscosity

#### T1 - Light

Introduction - Types of Mirrors - Terms Related to Spherical Mirrors - Images Formed By Spherical Mirrors - Applications of Curved Mirrors - Laws of Reflection - Types of Reflection - Multiple Reflections - Refraction of Light - Dispersion

#### T1 - Matter

Introduction - Why Symbols? - Metals and Non-Metals - Compound

#### T1 - Changes Around Us

Introduction - Chemical Reactions Based On Physical Contact - Chemical Reactions Based On Solution of Reactants - Chemical Reaction Based On Electricity - Chemical Reactions Based On Heat - Chemical Reactions Based On Light - Chemical Reaction Based On Catalyst - Effects of Chemical Reactions

#### T1 - Micro Organisms

Introduction - Virus - Bacteria - Fungi - Algae - Protozoa - Uses of Microorganisms In Medicine, Agriculture, Industry and Daily Life - Harmful Microorganisms - Microbes In Food Process - Relationship Between Man and Microbes-Balances, Imbalances and Uses - Prions - Virions

#### T1 - Plant Kingdom

Introduction - Taxonomy - Outline of Bentham and Hooker’s System of Classification - Binomial Nomenclature - Salient Features of Algae - Fungi - Bryophytes - Pteridophytes - Differences between Bryophytes and Pteridophytes - Gymnosperms - Angiosperms (Closed seeded plants) - Uses of Medicinal plants

#### T1 - Organisation of Life

Introduction - Organization of Cells and Tissues - Homeostasis - Diffusion - Osmosis - Osmoregulation - Cellular respiration - Metabolism

#### T1 - Introduction to the Information Age

Generation of Computers - Parts of a Computer - Input Unit - Mouse - Keyboard - Central Processing Unit (CPU) - Control Unit - Arithmetic Logic Unit - Memory Unit - Output Unit - Classification of Computer - Personal computer and its types - Hardware - Software - Types of Software - System Software - Application Software

#### TN StateboardStudy Material - Sample Question Papers with Solutions for Class 8 Session 2019 - 2020

Latest Sample Question Papers & Study Material for class 8 session 2019 - 2020 for Subjects Maths, Social Science in PDF form to free download [ available question papers ] for practice. Download QB365 Free Mobile app & get practice question papers.

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Tag Info

8

While there is some interesting research into order-independent transparency rendering, it's extremely complex to implement. And even sorting individual leaves can still cause artifacts where one leaf overlaps itself. So your safest bet is probably Alpha Testing. This is where you specify a threshold opacity value; anything above that value is rendered 100% ...

6

The best way to sort your scene is actually to do it in at least two stages/buckets. It is true that you need back-to-front sorting for translucent geometry for proper alpha-blending, but you want front-to-back sorting for best Z-buffer performance on opaque geometry. You can often get away with not bothering to sort opaque objects at all, leaving them ...

6

Use a file format that supports alpha (png), an editor that can save it with a transparent background (gimp2, photoshop, basically not paint) and make sure you load the sprite correctly

5

In your first example (glBlendFunc( GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA)), you're telling it to blend colors based on the alpha of the image which gets drawn on top (the "Foreground" one). So when you're blending 50% between the foreground color (38,50,168) and the background color (38,50,168) in the bottom left corner of the image, you unsurprisingly get ...

5

Alpha blending in 3D is tricky, simply due to the fact that you're (usually) still rendering the quad (or polygon) to the depth buffer using the depth buffer, even if your visible texture is just a tiny part of that. To achieve proper rendering you'll have to render everything in the correct order, essentially from back to front. If you don't use the ...

5

With the introduction of programmable blending units, the intuitive meaning of alpha being a measure of opaqueness doesn't always hold. In the two-operand blend you have two contributing fragments: the source (what you're blending, the new fragment), the destination (what already exists in the spot you're blending to). You have two independent blending ...

4

You need to write: return float4(1.0f, 0.0f, 0.0f, 1.0f); The float4 is necessary to construct a vector. The way you've written it currently, the compiler is interpreting it as the comma operator. The result is that you only return the last element (the alpha component), which then gets replicated to all four components of the result.

3

Using premultiplied alpha everywhere is a fine choice for composition. It allows you to include both additive and alpha-blended elements, as well as anything in between, and you can composite premultiplied-alpha images together using GPU hardware blend modes. In cases where alpha has the usual interpretation (opacity) I'm not aware of any reason not to use ...

3

Wrapping the SKEmitterNode in an SKEffectNode allows the EmitterNode to be rendered into a framebuffer which is subsequently rendered onto the screen. I tested this out (after much push and pull of different nodes and scenes and views) and this results in the exact effect you want, where the Add blend mode is applied to a background that is not rendered ...

2

BlendState.ColorWriteChannels is a bitfield with a bit for each of the four channels. You can make it write to RGB only by setting blendState.ColorWriteChannels = ColorWriteChannels.Red | ColorWriteChannels.Green | ColorWriteChannels.Blue;

2

With shaders and ordinary alpha blending I don't think this is possible. If you wanted to replace all the alpha values in the scene by a global constant, you could use D3DBLEND_BLENDFACTOR and D3DBLEND_INVBLENDFACTOR. But it sounds to me like you want to multiply each pixel's alpha value by a global constant. This is best done in the pixel shader. That ...

2

You can try drawing on a texture in memory without alpha and then draws the result with the desired value of alpha. This link tells you how to draw texture memory: http://www.riemers.net/eng/Tutorials/XNA/Csharp/Series3/Render_to_texture.php

2

Unfortunately, the problem is hopeless as it stands. You cannot get acceptable filtering at boundaries without each tile being somehow more aware of its neighbours. I recommend changing the way you draw tiles. Here is what you should do. First, render your tiles to an offscreen framebuffer at ratio 1:1 (using GL_NEAREST, which already works for you). Then, ...

2

Ok I figured this stuff out, was not obvious. The reference MSDN page i talked about does state that "Blend type" "Alpha Blending" uses the following formula in XNA 4: (source × Blend.SourceAlpha) + (destination × Blend.InvSourceAlpha) But despite this, BlendState.AlphaBlend field has the following pre-set parameters: ColorSourceBlend Blend.One ...

2

You basically put a one alpha value in each channel. For example you have Alpha0 = 0.5, Alpha1 = 0.2, Alpha2 = 0.7, Alpha3 = 1.0. The "packed" texture would be R = 0.5, G = 0.2, B = 0.7, A = 1.0.

2

If I have understood your approach, instead of drawing let's say a grid on nxn quads, you are building a mesh from all that quads and trying to render it with a single draw call, right? Storing sprite colors into vertex color attributes it's fine, and that's a rather common approach. For what concern blending (and not considering gl_LastFragData), you can'...

2

This issue happens with some MSAA or CSAA implementations. Try disabling anti-aliasing and see if it goes away. If that is the case you might need to force multi-sampling resolve before rendering your transparency. The other solution would be to force some overlap of your tiles.

2

To get rid of the lines, you need to set Pixmap.setBlending(Blending.NONE); before you draw the circle.

2

One way of doing this is using min blending. With Unity this can be set up in ShaderLab using the BlendOp command. If your objects are all monochrome as seen here, you may simply be able to use min blending directly on the objects as they're rendered and avoid having an alpha channel at all. (White is transparent when using min blending.) Min blending ...

2

If you calculate the final result as final.red = bitmap.red + viewport.red and divide by 255, then you are simply averaging them out, without taking alpha into account. The way I learned to calculate transparency is a formula that is also present in the top of the page you linked: res.r = dst.r * (1 - src.a) + src.r * src.a res.g = dst.g * (1 -src.a) ...

2

Here is how I would have done it (I've reworked your script, tell me if you don't understand something) using UnityEngine; using UnityStandardAssets.Characters.FirstPerson; public class FadeScript : MonoBehaviour { public FirstPersonController fpc; private Material material ; private float targetAlpha = 1 ; private float fadeDuration = 1 ; ...

2

You're drawing the sprite the wrong way: Gdx.gl.glClearColor(0, 0, 0, 1); // Clear the screen with black Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT); // Clear the screen batch.enableBlending(); // Enable alpha batch.begin(); sprite.setAlpha(0); sprite.draw(batch); // This is how you should draw a sprite. batch.end(); batch.disableBlending(); This works ...

2

Change this: float3 rgb = overlying.rgb * overlying.a + (1 - overlying.a) * underlying.a * underlying.rgb; float alpha = underlying.a + (1 - underlying.a) * overlying.a; return float4(rgb, alpha); To this: return underlying + (1 - underlying.a) * overlying; Formula for alpha blending is: $$pixelColour=src\_pixel+(1−src_α).dest\_pixel$$ Taken from here, ...

2

The usual way is: Render opaque objects first Blending disabled (this does not save memory — the render target still has just as many pixels with just as many bits of colour information — but it does save time spent doing the blending calculation) Sorted front to back (so earlier objects tend to occlude later objects, and you can skip drawing some of the ...

1

This portion of your code is not technically blend state, but could be affecting the behavior here: glDepthMask(FALSE) glDepthFunc(GL_EQUAL) D3D11 does have corresponding state to this, and you can set it by creating and binding a ID3D11DepthStencilState object, in a similar way to what you're doing with the ID3D11BlendState. See https://msdn.microsoft....

1

What do you mean by "wrong"? Your first step could be to say clearly (to yourself, or in a unit test, or in this question) "I expected alphaBlend(something,something) to produce (something, preferably a number), but what I got was (something else)." Like, blended red and blue, expected purple, got mauve. Or whatever. Hex values would be clearer... At a ...

1

This is just a guess, but I notice that the edges of your image(s) are anti-aliased. When you scale the images down using Linear filtering, the semi-transparent edges might be set to black, because the filter cannot handle semi-transparent pixels. This is just an idea, but it might be worth a try to remove the semi-transparent pixels which surround the image(...

1

A quote from the document you pasted: 15.070 If I draw a translucent primitive and draw another primitive behind it, I expect the second primitive to show through the first, but it's not there? Is depth buffering enabled? If you're drawing a polygon that's behind another polygon, and depth test is enabled, then the new polygon will typically ...

1

It took quite a while but I've found the solution and am posting it here for anyone else who has the same issue. The draw code remains the same. Pixel Shader: // Texture sprite sheet. uniform extern texture ScreenTexture; sampler screen : register(s0) = sampler_state { Texture = <ScreenTexture>; MinFilter = POINT; // Stops pixels bleeding ...

1

I think you may be interested in glDepthRange (...). That affects the mapping from NDC [-1.0,1.0] to window-space Z (the depth buffer stores window-space Z) during the viewport transformation. Effectively the nearplane becomes nearVal and the farplane becomes farVal. You can fool with this to bias and/or rescale your assigned depth values, but GL clamps ...

Only top voted, non community-wiki answers of a minimum length are eligible

format: plain


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## WeBWorK Main Forum

### Webwork warning

by Siman Wong -
Number of replies: 4

Our IT staff just updated our webwork server to v 2.15.  While creating new courses for the fall semester I made a mistake, so I deleted that course using the web interface and tried again.  But in the second time I got, besides the message "Successfully created the course ***", the following WeBWork Warnings:

• Replacing old data for [coursename] status: D at /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator/CourseAdmin.pm line 843.
In the past I had difficulty deleting courses using the web interface and I had to ssh into the webwork server to manually delete certain files.  But being away from campus I couldn't find my notes, and when I ssh into the server after I deleted the course (and before I recreated it) I couldn't find file/directory for that course (but I didn't check for hidden/dot files).  What should I do to resolve this issue?

THANKS!

In reply to Siman Wong

### Re: Webwork warning

by Sean Fitzpatrick -

You can safely ignore that, I think. I've had the same warning in this situation.

All it means is that you created the course using the same course ID as the previous attempt, so there was an existing database entry for that course ID.

Making the new course will overwrite the existing data. But you don't care, because (a) there wasn't really any data to begin with, and (b) you deleted the course containing that data.

In reply to Sean Fitzpatrick

### Re: Webwork warning

by Siman Wong -
Thanks! Being a paranoid person, I will sleep better if I could get rid of this error message. Based on your reply, sounds like that we should clear the database entry after the initial delete before I recreate the course. Is there a safe way to do that?

I remember running into this issue in earlier versions of WW, and I had to use delcourse to clean up leave over stuffs. But I couldn't remember how to do that...
In reply to Siman Wong

### Re: Webwork warning

by Sean Fitzpatrick -

I never touch the database and probably should not be trusted to do so even if I had a good reason to.

I'm pretty sure the warning is just that new course data is going to overwrite old course data you don't care about.

I've never done anything about it and I think it's been fine?

The alternative is to make a slight change to the course name the second time around.

In reply to Sean Fitzpatrick

### Re: Webwork warning

by Andras Balogh -

I am recreating annually previously archived and deleted courses, and in about 10% of the time (10 out of 100) I receive this warning. So far I have not seen anything else wrong, but I do wander if archiving/deleting some courses did not work completely.


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ct6b00650_si_002.txt (63.51 kB)

# Relativistic Prolapse-Free Gaussian Basis Sets of Quadruple‑ζ Quality: (aug-)RPF-4Z. III. The f‑Block Elements

dataset
posted on 22.12.2016, 00:00 by Tiago Quevedo Teodoro, Lucas Visscher, Albérico Borges Ferreira da Silva, Roberto Luiz Andrade Haiduke
The f-block elements are addressed in this third part of a series of prolapse-free basis sets of quadruple-ζ quality (RPF-4Z). Relativistic adapted Gaussian basis sets (RAGBSs) are used as primitive sets of functions while correlating/polarization (C/P) functions are chosen by analyzing energy lowerings upon basis set increments in Dirac–Coulomb multireference configuration interaction calculations with single and double excitations of the valence spinors. These function exponents are obtained by applying the RAGBS parameters in a polynomial expression. Moreover, through the choice of C/P characteristic exponents from functions of lower angular momentum spaces, a reduction in the computational demand is attained in relativistic calculations based on the kinetic balance condition. The present study thus complements the RPF-4Z sets for the whole periodic table (Z ≤ 118). The sets are available as Supporting Information and can also be found at http://basis-sets.iqsc.usp.br.

## Exports

figshare. credit for all your research.


text:
## Unit vectors transformation from cartesian to elliptic coordinates [closed]

I'm going to find a relation between cartesian and elliptic unit vectors.

For ellipse with major a and minor semiaxes $a$ and $b$ cartesian coordinates are:
$x=f \text{cosh}(\xi)\text{cos}(\eta)$;
$y=f \text{sinh}(\xi)\text{sin}(\eta)$,
where $f = \sqrt{a^2-b^2}$.

Elliptic coordinates are:
$\xi = Re(\text{acosh}( {{x + iy} \over {f}} ))$;
$\eta = Im(\text{acosh}( {{x + iy} \over {f}} ))$,
(this equations are taken from [1, 9.11 p.170]).

According to [2, (6) p.481] elliptic unit vectors are related to cartesian by this matrix equation:
${\begin{pmatrix} \mathbf{\vec{e_x}} \\ \mathbf{\vec{e_y}} \end{pmatrix}} = { \frac{1}{\sqrt{D}} } {\begin{pmatrix} \text{sinh}(\xi)\text{cos}(\eta) & -\text{cosh}(\xi)\text{sin}(\eta) \\ \text{cosh}(\xi)\text{sin}(\eta) & \text{sinh}(\xi)\text{sin}(\eta) \end{pmatrix}} {\begin{pmatrix} \mathbf{\vec{e_\xi}} \\ \mathbf{\vec{e_\eta}} \end{pmatrix}}$,
where $D = { 1 \over 2 } (\text{cosh}(2\xi) - \text{cos}(2\eta))$ is a determinant of a matrix (see above). This matrix is build from a partial derivatives $\begin{pmatrix} \frac{\partial x}{\partial \xi} & \frac{\partial x}{\partial \eta} \\ \frac{\partial y}{\partial \xi} & \frac{\partial y}{\partial \eta} \end{pmatrix}$ (AFAIU, Jacobian, see [3])..

I need to find the matrix $M$ of inverse transformation:
${\begin{pmatrix} \mathbf{\vec{e_\xi}} \\ \mathbf{\vec{e_\eta}} \end{pmatrix}} = M {\begin{pmatrix} \mathbf{\vec{e_x}} \\ \mathbf{\vec{e_y}} \end{pmatrix}}$.

Any ideas?

References:
1. J. C. Gutiérrez-Vega and S. Chávez-Cerda, "Probability distributions in classical and quantum elliptic billiards," Revista Mexicana de Física, Vol. 47, no. 5, pp. 480-488, Oct. 2001.
2. N. W. McLachlan, "Theory and applications of Mathieu functions," Oxford University Press, 1937. 3. http://en.wikipedia.org/wiki/Curvilinear_coordinates

-
This looks to me the sort of question that would work better on maths.stackexchance.com; I recommend that you try there (or one of the other sites mentioned in the FAQ). – Andrew Stacey Dec 1 2011 at 12:41
Thank you. I reposted the question to math.stackexchange.com/questions/87391/…. – N0rbert Dec 1 2011 at 14:21


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# Detection of signals in Noise - PowerPoint PPT Presentation

Detection of signals in Noise. 指導老師 : 黃文傑 姓名 : 吳政修. outline. Review Bayes’ formula Decision rules Maximum a posteriori probability (MAP) ML detection in AWGN channel. Review Bayes’ formula. Conditional probability: Total probability: Bayes’ formula:.

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## PowerPoint Slideshow about ' Detection of signals in Noise' - anais

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### Detection of signals in Noise

• Review Bayes’ formula

• Decision rules

• Maximum a posteriori probability (MAP)

• ML detection in AWGN channel

• Conditional probability:

• Total probability:

• Bayes’ formula:

Decision rules observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• The optimum detector chooses to minimize

or equivalently, to maximize

• The corresponding probability of being correct is

Maximum a posteriori probability (MAP) observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• The probability of the decision be correct, given that observing vector x, is

• The probability of error is as follows

• Thus the optimum decision observes the particular received vector X=x and the output chooses to maximize the .

MAP detection rule observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• MAP

if for all

Thus if all transmitted symbols occur equally likely, i.e.

Then the decision is equivalent to the maximum likelihood decision rule.

if for all

In an AWGN channel observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• In an AWGN channel

• AWGN ML detection

if for all

The decision is to choose a message point closest to the received signal point, which is intuitively.

Optimum receiver observation vector x can take on a finite number of values, then given x, the probability that the symbol was transmitted.

• For a correlator receiver, we consider that

1.equally likely source symbols

2.AWGN channel


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# What is the difference Cross-entropy and KL divergence?

Both of Cross-entropy and KL divergence are tools to measure the distance between two probability distribution. What is the difference? $$H(P,Q) = -\sum_x P(x)\log Q(x)$$ $$KL(P | Q) = \sum_{x} P(x)\log {\frac{P(x)}{Q(x)}}$$ Moreover, minimization of KL is equivalent to minimization of Cross-Entropy.

I want to know them instinctively.

Thank you very much in advance.

• You're missing a $\ln$ in the KL definition. I will add it in, but noted here so other can identify a source of confusion. – conjectures Jul 19 '18 at 13:18

You will need some conditions for claiming the equivalence of minimizing cross entropy to minimizing KL divergence. I will put your question under the context of classification problems using cross entropy as loss functions.

Let us first recall that entropy is used to measure the uncertainty of a system, which is defined as $$S(v)=-\sum_ip(v_i)\log p(v_i)\label{eq:entropy},$$ for $p(v_i)$ as the probabilities of different states $v_i$ of the system. From an information theory point of view, $S(v)$ is the amount of information is needed for removing the uncertainty.

For instance, the event A I will die eventually is almost certain (maybe we can solving the aging problem for word almost), therefore it has low entropy which requires only the information of the aging problem cannot be solved to make it certain. However, the event B The president will die in 50 years is much more uncertain than A, thus it needs more information to remove the uncertainties.

Now look at the definition of KL divergence between events A and B $$D_{KL}(A\parallel B) = \sum_ip_A(v_i)\log p_A(v_i) - p_A(v_i)\log p_B(v_i)\label{eq:kld},$$ where the first term of the right hand side is the entropy of event A, the second term can be interpreted as the expectation of event B in terms of event A. And the $D_{KL}$ describes how different B is from A from the perspective of A.

To relate cross entropy to entropy and KL divergence, we formalize the cross entropy in terms of events A and B as $$H(A, B) = -\sum_ip_A(v_i)\log p_B(v_i)\label{eq:crossentropy}.$$ From the definitions, we can easily see $$H(A, B) = D_{KL}(A\parallel B)+S_A\label{eq:entropyrelation}.$$ If $S_A$ is a constant, then minimizing $H(A, B)$ is equivalent to minimizing $D_{KL}(A\parallel B)$.

A further question follows naturally as how the entropy can be a constant. In a machine learning task, we start with a dataset (denoted as $P(\mathcal D)$) which represent the problem to be solved, and the learning purpose is to make the model estimated distribution (denoted as $P(model)$) as close as possible to true distribution of the problem (denoted as $P(truth)$). $P(truth)$ is unknown and represented by $P(\mathcal D)$. Therefore in an ideal world, we expect $$P(model)\approx P(\mathcal D) \approx P(truth)$$ and minimize $D_{KL}(P(\mathcal D)\parallel P(model))$. And luckily, in practice $\mathcal D$ is given, which means its entropy $S(D)$ is fixed as a constant.

• Thank you for your answer. It deepened my understanding. So when we have a dataset, it is more effective to minimize cross- entropy rather than KL, right? However, I cannot understand the proper use of them. In other words, when should I minimize KL or cross entropy? – Jourd Jul 19 '18 at 14:00
• After reading your answer, I think it is no use to minimize KL because we always have a dataset, P(D). – Jourd Jul 19 '18 at 14:03
• Ideally, one would choose KL divergence to measure the distance between two distributions. In the context of classification, the cross-entropy loss usually arises from the negative log likelihood, for example, when you choose Bernoulli distribution to model your data. – doubllle Jul 19 '18 at 14:14
• You might want to look at this great post. The symmetry is not problem in classification as the goal of machine learning models is to make predicted distribution as close as possible to the fixed P(D), though regularizations are usually added to avoid overfitting. – doubllle Jul 19 '18 at 14:35
• I understood the asymmetry of KL. However, I haven't understood how to use minimization of KL or Cross-Entropy differently yet. It means that when should I minimize KL and when should I minimize Cross-Entropy. I think $S_A$ is always a constant, isn't it? – Jourd Jul 19 '18 at 22:15

I suppose it is because the model usually working with the samples packed in mini-batches. For KL divergence, it can be written as $$H(q, p) = D_{KL}(p, q)+H(p) = -\sum_i{p_ilog(q_i)}$$ From the equation, we could see that KL divergence can depart into a Cross-Entropy of p and q (the first part), and a global entropy of ground truth p (the second part).

In may machine learning projects, minibatich is involved to expedite training, where the $$p'$$ of a minibatch may be different from the global $$p$$. In such a case, Cross-Entropy is relatively more robust in practical when KL divergence needs a stabler H(p) to finish her job.

• This is being automatically flagged as low quality, probably because it is so short. At present it is more of a comment than an answer by our standards. Can you expand on it? We can also turn it into a comment. – gung May 20 at 17:49
• The answer has been updated. – zewen liu May 20 at 18:11


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## Display Custom Taxonomy Associated to Post ACF

Question

I tried different solutions I found here, but can’t make it work. I have a custom post type “Properties” and each of the properties has custom taxonomy (diff. multiple categories) which tie-up to advanced custom fields select field (For Sale, For Lease, OffMarket).

I wanted to display all custom taxonomy to a specific page like For Sale and display associated custom taxonomy to the landing page of For Sale. However, I have still displays the custom category which belongs to “For Lease” instead of “For Sale”.

<?php
$taxonomy = 'property_category';$tax_terms = get_terms($taxonomy, [ 'order' => 'ASC', 'hide_empty' => true, 'exclude' => [ 18 ] ]); ?>
<button data-filter="*" class="is-checked">ALL</button>
 <?php foreach ($tax_terms as $tax_term) { echo '
' . '<button data-filter=".' .$tax_term->slug . '" ' . '>' . \$tax_term->name.'</button>
';
}
?>

Example:

Under the For-Sale landing page, I have “Warehouse”, “For Sale” and “Retail” categories. And for the For-Lease landing page, I have “Ground Lease”, “For Lease”, and “Office”. However, using the code above, it displays all categories even if you are viewing the “For-Sale” or “For-Lease” landing page.

0
3 years 2019-10-21T14:59:16-05:00 0 Answers 79 views 0


text:
#### 12th Standard English Medium Maths Reduced Syllabus Creative Two Mark Questions with Answer key - 2021(Public Exam )

12th Standard

Reg.No. :
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Maths

Time : 02:45:00 Hrs
Total Marks : 100

2 Marks

50 x 2 = 100
1. For the matrix A, if A3 = I, then find A-1.

2. Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

3. Find the rank of the matrix A =$\left[ \begin{matrix} 4 \\ 7 \end{matrix}\begin{matrix} 5 \\ -3 \end{matrix}\begin{matrix} -6 \\ 0 \end{matrix}\begin{matrix} 1 \\ 8 \end{matrix} \right]$.

4. Find k if the equations x + 2y + 2z = 0, x - 3y - 3z = 0, 2x + y + kz = 0 have only the trivial solution.

5. Find Re (z) and im (z) if z = 5i11 + 7i3

6. If z=$\left( \frac { \sqrt { 3 } }{ 2 } +\frac { i }{ 2 } \right) ^{ 107 }+\left( \frac { \sqrt { 3 } }{ 2 } -\frac { i }{ 2 } \right) ^{ 107 }$ , then show that Im (z) =0

7. Find the argument of -2

8. Find value of a for which the sum of the squares of the equation x2 - (a- 2) x - a-1=0 assumes the least value.

9. Find the number of positive and negative roots of the equation x7 - 6x6 + 7x5 + 5x2+2x+2

10. If ${ cot }^{ -1 }\left( \cfrac { 1 }{ 7 } \right) =\theta$ find the value of cos $\theta$

11. Ecalute $sin\left( { cos }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) \right)$

12. Find the equation of tangent to the circle x2 +y2 + 2x - 3y - 8 = 0 at (2, 3).

13. If the line y = 3x + 1, touches the parabola y2 = 4ax, find the length of the latus rectum?

14. For the ellipse x2 + 3y2 = a2, find the length of major and minor axis.

15. Find the Cartesian equation of a.line passing through the pointsA(2, -1, 3) and B(4, 2, 1)

()

-1

16. Find the parametric form of vector equation of the plane passing through the point (1, -1, 2) having 2, 3, 3.as direction ratios of normal to the plane.

()

2

17. Flnd the equation of the plane containing the line of intersection of the planes x + y + Z - 6 = 0 and
2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1)

()

x = -1 is one root

18. Find the equation of the tangent to the curve y2=4x+5 and which is parallel to y=2x+7

19. Verify Rolle ’s Theorem for $f(x)=\left| x-1 \right| ,O\le x\le 2$

20. Obtain Maclaurin’s Series expansion for e2x.

21. Evaluate the following limits, if necessary using L’Hopitalrule
(i) $\underset { x\rightarrow 2 }{ lim } \cfrac { sin\pi x }{ 2-x }$
(ii) $\cfrac { lim }{ x\rightarrow 2 } \cfrac { { x }^{ n }-{ a }^{ n } }{ x-2 }$
(iii) $\underset { x\rightarrow \infty }{ lim } \cfrac { sin\frac { 2 }{ x } }{ \frac { 1 }{ x } }$
(iv) $\underset { x\rightarrow \infty }{ lim } \cfrac { { x }^{ 2 } }{ { e }^{ x } }$

22. Find the absolute extreme of the function f(x)=x2-2x+2 on the closed interval [0,3]

23. Prove that the function f(x)=2x2+3x is strictly increasing on $\left[ -\cfrac { 1 }{ 2 } ,\cfrac { 1 }{ 2 } \right]$

24. Determine the domain of convexity of the function y=ex

25. IF u(x, y) = x2 + 3xy + y2, x, y, ∈ R, find tha linear appraoximation for u at (2, 1)

26. If w=log(x2+y2),x=cosθ,y=sinθ, find $\cfrac { dw }{ d\theta }$

27. Without using any kind of computational aid use linear approximation to find the value of e0.1

28. Find the area of the region enclosed by the curve y = $\sqrt x$ + 1, the axis of x and the lines x=0, x=4.

29. Find the volume of the solid obtained by revolving the area of the triangle whose sides are x = 4, y = 0 and 3x - 4y = 0 about x - axis

30. If $\int _{ 0 }^{ \infty }{ \cfrac { { x }^{ 2 }dx }{ \left( { x }^{ 2 }+{ a }^{ 2 } \right) \left( { x }^{ 2 }+{ b }^{ 2 } \right) \left( { x }^{ 2 }+{ c }^{ 2 } \right) } } =\cfrac { \pi }{ 2(a+b)(b+c)(c+a) }$ then find $\int _{ 0 }^{ \infty }{ \cfrac { dx }{ \left( { x }^{ 2 }+4 \right) \left( { x }^{ 2 }+9 \right) } }$

31. Find the area bounded by y=x2+2, x-axis, x=1 and x=2.

32. Find the area of the region bounded by the curve y=sin x and the ordinate x=0.$x=\cfrac { \pi }{ 3 }$

33. Find the area bounded by y=cosx,y=x+1,y=0.

34. Determine the order and degree of $\cfrac { \left[ 1+\left( \frac { dy }{ dx } \right) ^{ 2 } \right] ^{ \frac { 3 }{ 2 } } }{ \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =k$

35. Find the order and degree of $\left( \cfrac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }+cos\left( \cfrac { dy }{ dx } \right) =0$

36. Form the Differential Equation representing the family of curves y=Acos(x+B) where A and B are parameters.

37. Solve : $\cfrac { dy }{ dx } =\cfrac { { e }^{ x }-{ e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } }$

38. How many types of random variables are there? What are they?

39. Define Probability Mass Function.

40. Define Variance of a random variable X?

41. What is the Probability Mass function of a binomial random variable?

42. The probability distribution of a random variable X is given under :

Find (i) k
(ii) E(X)

43. The p.d.f of a continuous random variable X is
$f(x)=\begin{cases} k,0\le x\le 4 \\ 0,otherwise \end{cases}$ Find k.

44. Consider the binary operation ∗ defined on the set A = {a,b,c, d} by the following table:

 * a b c d a a c b d b c d a a d d b a c

Is it commutative and associative?

45. In the set of integers under the operation * defined by a * b = a + b - 1. Find the identity element.

46. In a non empty set S on which a binary operation * is defined and for an element a∈S.a✳a✳a=e,where e is the identity element. Find the inverses of a and a✳a.

47. If a☰b(mod n) and C☰d(mod n),check whether a+c☰(b+d) (mod n).

48. Form the truth table of (~q)^p.


text:
# Alternating sum of square roots of binomial coefficients

Let $$c_n = \sum_{r=0}^n (-1)^r \sqrt{\binom{n}{r}}.$$ It is clear that $c_n = 0$ if $n$ is odd. Remarkably, it appears that despite the huge positive and negative contributions in the sum defining $c_{2m}$, the sequence $(c_{2m})$ may be very well behaved.

Is $c_n > 0$ for all even $n$?

An affirmative answer will imply that the function $F(x) = \sum_{n=0}^\infty x^n/\sqrt{n!}$ is always strictly positive, thereby answering this earlier question.

Numerical computation using Magma shows that $c_n > 0$ if $n$ is even and $n \le 2000$. To give some illustrative values, $c_{100} = 0.077737 \ldots$, $c_{1000} = 0.019880 \ldots$ and $c_{2000} = 0.013317 \ldots$.

A comment by Mark Sapir on the earlier question suggests a stronger result might hold.

Is $c_{n} > c_{n+2} > 0$ for all even $n$?

I have checked that this is the case for all even $n \le 2000$.

It is very natural to ask what happens if we replace $\sqrt{\binom{n}{r}}$ with $\binom{n}{r}^\alpha$ for $\alpha \in (0,1)$. For $n\le 250$ the generalized version of the conjecture continues to hold if $\alpha = k/10$ where $k \in \mathbf{N}$ and $k \le 9$. Of course when $\alpha = 1$ we have $c_n = 0$ for all $n$, so, as David Speyer remarked in a comment on the earlier question, there is a good reason for the cancellation in this case.

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If you denote $\sum_{r=0}^n (-1)^r \binom{n}{r}^\alpha$ by $f(n,\alpha)$, then $f(2n,1)=0, f(2n,0)=1$, and $f(2n,\alpha)$ seems to be decreasing with $\alpha$ for every $n$. That fact (which is stronger than both conjectures you mentioned) may be more feasible. – Mark Sapir Jan 6 '12 at 0:51
Mark, yes, the positivity of this infinite set of finite sums feels to me quite similar to (and, as you point out, implies) the positivity of the infinite series I asked about earlier in the question you reference, and suffers from the same delicate cancellation of huge quantities. I sort of suspect that if you could crack the infinite series, you could crack this, too. – J Russell Jan 6 '12 at 2:06
Indeed $c_n>0$, read my response below. In a similar fashion $c_n>c_{n+2}$ should follow, too. – GH from MO Jan 6 '12 at 6:18
A related (and fairly easy) fact is $\lim_{n\rightarrow\infty}\sum_{k=0}^{2n}(-1)^k{2n\choose k}^{1/{2n\choose k}}=1$. – Roland Bacher Jan 6 '12 at 10:21
$n\longmapsto \sum_{r=0}^{2n}(-1)^r{2n\choose r}^\alpha$ seems to be bounded for all real $\alpha\leq 3/2$ and seems to be unbounded for $\alpha>3/2$. – Roland Bacher Jan 6 '12 at 18:12

Here's a proof of the positivity of $$c_n(\alpha) := \sum_{r=0}^n (-1)^r {n\choose r}^\alpha$$ for all even $n$ and real $\alpha < 1$. It follows (via M.Wildon's clever $F(x) F(-x)$ trick at mo.84958) that $\sum_{n=0}^\infty \phantom. x^n / n!^{\alpha} > 0$ for all $x \in\bf R$. [EDIT fedja has meanwhile provided a very nice direct proof of the positivity of $\sum_{n=0}^\infty \phantom. x^n / n!^{\alpha}$.]

The key is to write $c_n(\alpha)$ as a finite difference $$\sum_{r=0}^n \phantom. (-1)^r {n\choose r} \cdot {n\choose r}^{\alpha - 1}$$ and show that the Gamma interpolation $$\bigl(\Gamma(r+1)\Gamma(n-r+1) / n!\bigr)^{1-\alpha} = n!^{\alpha-1} \exp\bigl((1-\alpha) (\log\Gamma(r+1) + \Gamma(n-r+1)\bigr)$$ of ${n\choose r}^{\alpha - 1}$ has a positive $n$-th derivative for all $r \in [0,n]$.

This in turn follows from the fact that the expansion of $\log\Gamma(r+1) + \log\Gamma(n-r+1)$ in a Taylor series about $r = n/2$ has positive $(r - (n/2))^k$ coefficient for each $k=2,4,6,\ldots$. [The coefficient vanishes for odd $k$ because $\log\Gamma(r+1) + \log\Gamma(n-r+1)$ is an even function of $r-(n/2)$.] Indeed the well-known formula $$\log \Gamma(x) = -\gamma x - \log x + \sum_{j=1}^\infty \left[ \frac{x}{j} - \log \left( 1 + \frac{x}{j} \right) \right]$$ shows that the $k$-th derivative of $\log\Gamma(x)$ is positive for all $x>0$ and $k=2,4,6,\ldots$, because this is true for $-\gamma x - \log x$ and for each term in the sum; explicitly the derivative is $k! \phantom. \sum_{j=0}^\infty (x+j)^{-k}$ which is positive termwise. Therefore in the Taylor expansion $$\log \Gamma(r+1) = \log(n/2)! + \sum_{k=1}^\infty \phantom. g_k (r-(n/2))^k$$ each of $g_2,g_4,g_6,\ldots$ is even. Since $\log\Gamma(r+1) + \log\Gamma(n-r+1)$ is $$2\log(n/2)! + 2 \Bigl( g_2 (r-(n/2))^2 + g_4 (r-(n/2))^4 + g_6 (r-(n/2))^6 + \cdots\Bigr),$$ the claim follows. [EDIT David Speyer notes that the convergence of the Taylor series on $|r-(n/2)| \leq n/2$ requires justification, and that the justification is easy because the $\Gamma(z)$ has no zeros and poles only at $0,-1,-2,\ldots$ so the radius of convergence is $(n/2)+1$.] Multiplying by $1 - \alpha$ and substituting into the exponential series, we deduce that $(\Gamma(r+1) \Gamma(n-r+1))^{1-\alpha}$, too, is a positive combination of even powers of $r-(n/2)$.

Now if a function $g$ has positive $n$-th derivative, then its first finite difference $$g(x+1) - g(x) = \int_x^{x+1} g'(y) dy$$ has positive $(n-1)$-st derivative; repeating this argument $n$ times, we find that the $n$-th finite difference is positive, and we're done.

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Beautiful argument. – GH from MO Jan 6 '12 at 7:51
Personally I find the last sentence a bit confusing. I would say: if a function $g$ has positive derivative, then its first finite difference $g(x)-g(x+1)$ is positive; repeating this argument $n$ times, we find that if the $n$-th derivative is positive then the $n$-th finite difference is also positive. – GH from MO Jan 6 '12 at 8:11
Just to fill in a gap that bothered me, you need to know that the Taylor series converges in the relevant range. That's true because the first pole of the $\Gamma$ function is at $0$ and it has no zeroes, so $\log \Gamma(r+1)+ \log \Gamma(n-r+1)$ is analytic on a disc centered at $n/2$ of radius $n/2+1$, which encloses the region we care about. Other than that, gorgeous argument! – David Speyer Jan 6 '12 at 13:24
Thank you for this beautiful proof. – Mark Wildon Jan 6 '12 at 15:13
@Noam: I meant that you are really arguing by induction on $n$, and it would be cleaner to say it that way. Here is something more fun: your argument also gives $\sum_{r=0}^n {n\choose r}^\alpha a^r b^{n-r}\geq 0$ for any real $a$ and $b$, even $n$, and $\alpha\leq 1$. Indeed, this can be reduced to $\sum_{r=0}^n (-1)^r{n\choose r}^\alpha f(n,r;x,y)\geq 0$ for $x,y>0$, where $f(n,r;x,y):=(x/y)^{r-\frac{n}{2}}+(y/x)^{r-\frac{n}{2}}=\sum_{m=0}^\infty a_m\left(r-\frac{n}{2}\right)^{2m}$ with $a_m:=(\log x-\log y)^{2m}/(2m)!\geq 0$. The statement follows as in your original post. – GH from MO Jan 6 '12 at 18:19

The following proof of $c_n>0$ is based on Gjergji Zaimi's response to this related question. In particular the positive answer follows for that question, too. Moreover, the argument below should also show that $c_n>c_{n+2}$.

Let $n>0$ be even. By Chapter 6 of de Bruijn's "Asymptotic Methods in Analysis" (in particular by (6.4.6), (6.6.2), and the conclusion $P=0$ of Section 6.5), we have the following explicit formula:

$$c_n = 2\pi^{-1/2}\sqrt{n!}\ \sum_{m=0}^\infty \ \int_{4m+1}^{4m+2} G_n(x)\ |\sin\pi x|^{-1/2}dx,$$

where

$$G_n(x) := \sqrt{\frac{\Gamma(x)}{\Gamma(1+x+n)}}- \sqrt{\frac{\Gamma(2+x)}{\Gamma(3+x+n)}}.$$

It remains to verify that $G_n(x)>0$ for $x\geq 1$. This reduces to

$$\Gamma(x)\Gamma(3+x+n)>\Gamma(2+x)\Gamma(1+x+n),$$

i.e. to

$$(1+x+n)(2+x+n)>x(1+x).$$

The last inequality is obvious, hence we are done.

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Thank you very much for this proof. I would accept your answer as well if I could. I was able to read all but the end of Section 6.6 of de Bruijn's book via Google Books. He considers the sum $c_n$ for general $\alpha \in (0,1)$, saying 'It should be admitted that this is not a very natural question, as non-integral powers of binomial coefficients do not frequently occur in mathematics. The main reason for its discussion here is, that it is a difficult problem with various interesting aspects'. – Mark Wildon Jan 6 '12 at 17:55
Mark, thank you. I don't know how to make this argument work for any $\alpha \in (0,1)$ since in general the integral is more wildly oscillating. Well, we can restrict to rational $\alpha$ which makes the oscillation more regular. At any rate, you can find and download de Bruijn's book off the internet (link not given, to avoid charges of 'piracy'). – GH from MO Jan 6 '12 at 18:25


text:
-nologo (C# Compiler Options)

The -nologo option suppresses display of the sign-on banner when the compiler starts up and display of informational messages during compiling.

Syntax

-nologo

Remarks

This option is not available from within the development environment; it is only available when compiling from the command line.

This compiler option is unavailable in Visual Studio and cannot be changed programmatically.


text:
# Spectral Subtraction python implementation error

I am trying to implement Spectral subtraction in python. I am new to DSP. I used this article as reference and below code is what I can come up with. Of course I did not get the expected output. I have tried my best to explain the code. Please help me correct the code. Thank you in advance.

def OnSpecSubstract(data, f_size, n_frames):

"""
data is the complete signal
f_size is the size of frames
n_frames is the number of noisy frames
"""

samples = []
phases = []
out = [];

"""
lps is basically the total number of frames that wiil be created, frames will overlap
by 50%
"""
lps = int(len(data)/f_size)+1;

"""
Hanning Window for windowing function
"""
hn_win = np.hanning(f_size)

for i in range(0, (lps*2)):

"""
The 2 line of codes below extract frames of size f_size and append each frame
in list samples. Each frame overlaps by 50% from pervoius frame.
"""
f_loc = int(i*f_size/2);
samples.append( np.asarray( data[ (f_loc):(f_loc+f_size) ] ) )

"""
l_ele is the index of the last element in list samples ie. that frame that was
just appended above.
We perform windowing function on each frame.
Next comes fft of each frame.
Next we save the phase information spererately of each frame in list phases.
In last line we extract the magnitude information of each frame.
"""
l_ele = len(samples)-1;
samples[l_ele] = samples[l_ele] * hn_win[:len( samples[l_ele] )];
samples[l_ele] = fft(samples[l_ele])
phases.append(np.angle(samples[l_ele]))
samples[l_ele] = abs(samples[l_ele])

"""
We check if the current frame has size less than f_size we know that all the
data in signal has been windowed and we break the loop.
"""
if ( len(samples[len(samples)-1]) < f_size ):
break

"""
We assume that first few frames are only noisy frame. Hence, we first initailize
noise by saving the first frame in noise.
"""
noise = np.asarray(samples[0])

"""
Next we add all the noisy frames together. n_frames denotes the number of noisy
frames.
"""
for i in range(1, n_frames):
noise = list(map(lambda x, y : x + y, noise, samples[i]))

"""
Here we take the mean of all the values in noise. We now have the single value for
noise
"""
noise = list(map(lambda x : x/n_frames, noise))
noise = np.mean(noise)
noise *= 2 #The 2 here is bias

"""
We delete the frames that represent noise form samples and phase as we don't
need them.
"""
del samples[:n_frames]
del phases[:n_frames]

"""
Here, we subtract the average noise from each value in each frame.
"""
samples = [ list(map( lambda x : x - noise, i )) for i in samples ]

"""
In the loop below we
First zero off all the negitive amplitudes.
Second, we multiply with each frame their respective phases that was saved earlier.
Third, we inverse fast fourier transform each frame.
"""
for idx, data in enumerate(samples):
samples[idx] = [ 0 if i < 0 else i for i in data ]
samples[idx] = list(map( lambda x, y: x*y, samples[idx], phases[idx] ))
samples[idx] = ifft(samples[idx])

"""
out will be the final reconstructed signal. We first initialize it by saving the
first frame from samples. We then delete the first frame from samples.
"""
out = samples[0]
del samples[0]

"""
Here I try to reconstruct the orignal signal. This is one section where I think there
is definately an issue.
In the below loop what is done is simply the overlapping parts of the frames are
summed up.
"""
for data in samples:

if len(data) == f_size:

"""
dm_pnt is the mid index of data and om_pnt in the index of put that is
f_size/2 places behind the last element.
"""
dm_pnt = int(f_size/2)
om_pnt = int(len(out)-dm_pnt)

out[om_pnt:] = list(map( lambda x, y: x + y, out[om_pnt:], data[:dm_pnt] ))

out = np.concatenate([out, data[dm_pnt:]])

return out

• "I did not get the expected output" so, ok, what did you expect, what did you get instead, how does it differ? What have you considered so far? – Marcus Müller Jul 26 '18 at 7:24

Alright, I was able to figure out a way. I am now getting expected results. However, there is something strange about the output that I don't understand. The result of any Inverst FFT operation is complex numbers ie. real and imaginary part. When we IFFT any signal after processing, to get the actual audio we use only the real part of the IFFT results(correct me if I am wrong). However, here the processed signal is actually the imaginary part. I use the below code to save the imaginary part of the result to a wav file.

1. x = OnSpecSubstract( data, f_size = 400, n_frames = 12 )
2. out = x.imag.astype(np.int16)
3. wavfile.write( 'Output.wav', rate, out)

The real part of the results are very small. The largest real number in the result was around 1.9e-12. Check out this playlist for output.

• The h_samp is noisy data.
• out_b1 is filtered signal with bias = 1.
• out_b2 is filtered signal with bias = 2, and so on.

The amount of musical note increases with bias. I have edited the above code in question to the one that I am using.


text:
Radio Recombination Lines toward the S140/L1204
Session 82 -- HII Regions
Display presentation, Wednesday, 11, 1995, 9:20am - 6:30pm

## [82.04] Radio Recombination Lines toward the S140/L1204

G.T.Smirnov, R.L.Sorochenko (P.N.Lebedev Physical Institute), C.M.Walmsley (MPIfR) (P.N.Lebedev Physical Institute, Russia)

We have used the Effelsberg 100-m telescope to observe the hydrogen and carbon 165$\alpha$ and 166$\alpha$ radio recombination lines towards the S140/L1204 complex. In addition to the transitions known from earlier observations, we detect a feature due to ionized sulphur in the C\,{\sc ii}~region. On the basis of the observed H line parameters, we conclude that the emission nebula S140 is only a part of a larger partially obscured H\,{\sc ii}~region which has an electron temperature of 6400~K and an electron density of order 10~cm$^{-3}$. The obscured fraction of the H\,{\sc ii}~region appears to be either behind or partially immersed in the molecular and C\,{\sc ii}~regions. We derive parameters for the C\,{\sc ii}~region by combining our results with measurements of the C\,{\sc ii}~158~$\mu$m fine structure line and conclude that the temperature is in the range 75--200~K whereas the electron density is in the range 0.5--9~cm$^{-3}$. If there is pressure equilibrium between H\,{\sc ii} and C\,{\sc ii} gas, then the lower values of the temperature and density are preferable.


text: For our dataset of $$n$$ examples, the MSE is simply $$\frac{RSS}{n}$$. Keep in mind that I’ve only described the optimization process at a fairly rudimentary level. Thus, the dataset is huge and distributed across several computing nodes. To reduce the number of steps required, we could try to optimize the gradient_descent function by making the learning rate adaptive. Gradient descent is the most common model optimization algorithm for minimizing error. Since we are varying two parameters simultaneously in our quest for the best estimates that minimize the RSS, we are searching a 2D parameter space. BFGS is one of the default methods for SciPy’s minimize. But this minimum value should be close to the actual minimum. where $$y$$ represents the actual values from our data (the observed values) and $$\hat{y}$$ represents the predicted values of $$y$$ based on the estimated parameters. To tune the model, we need hyperparameter optimization. Optimization is how learning algorithms minimize their loss function. RMSProp is useful to normalize the gradient itself because it balances out the step size. In fact, since we can multiply by any number, you’ll typically see $$\frac{1}{2n}$$ instead of $$\frac{1}{n}$$ as it makes the ensuing calculus a bit easier. These parameter helps to build a function. And in code. How to explore Neural networks, the black box ? We thus find the partial derivatives with respect to each parameter. It is typical to use OLS for linear models since it is the best linear unbiased estimator (BLUE) so that’s what I’ll use for our upcoming home-grown optimizer. However, classical gradient descent will not work well when there are a couple of local minima. … Next, let’s explore how to train a simple … We start with defining some random initial values for parameters. Here, I generate data according to the formula $$y = 2x + 5$$ with some added noise to simulate measuring data in the real world. Popular Optimization Algorithms In Deep Learning. The data might represent the distance an object has travelled (y) after some time (x), as an example. This is a repeated process. To get started, you need to take a random point on the graph and arbitrarily choose a direction. Note: In gradient descent, you proceed forward with steps of the same size. In machine learning, we do the same thing, but the number of options is usually quite large. Genetic algorithms represent another approach to ML optimization. So if we could dynamically adapt the learning rate, we could conceivably get closer to the minimum with less iterations. After the fourth set of iterations, its near the minimum. Then, you keep only those that worked out best. So, after we calculate this cost, how do we adjust $$\theta_0$$ and $$\theta_1$$ such that the cost goes down? Recognize linear, eigenvalue, convex optimization, and nonconvex optimization problems underlying engineering challenges. As mentioned earlier, you can see that along the $$\theta_0$$ axis (looking across the row values), the rate of change in value is lower than along the $$\theta_1$$ axis (looking up and down the row values), which explains the shape of the surface in the 3D plot. This fraction is called the learning rate. You can specify one of many methods to use for optimization. Substituting $$h_{\theta}(x)$$ (hypothesis function) for $$\hat{y}$$ and multiplying by $$\frac{1}{2}$$ to simplify the math to come, we can write the loss function as, $J(\theta) = \frac{1}{2n} \sum\limits_{i=1}^n (y_i - h_{\theta}(x_i))^2$. Finally, it’s worth noting that the optimization process in artificial neural networks (ANN), while based on the same idea of minimizing a cost function, is a bit more involved. Here we have a model that initially set certain random values for it’s parameter (more popularly known as weights). However, I’ll use a very simple, meaningless dataset so we can focus on the optimization. A learning algorithm is an algorithm that learns the unknown model parameters based on data patterns. R’s optim function is a general-purpose optimization function that implements several methods for numerical optimization. Implementing a rough working version of gradient descent is actually quite easy. A larger learning rate allows for a faster descent but will have the tendency to overshoot the minimum and then have to work its way back down from the other side. many local minima? In many supervised machine learning algorithms, we are trying to describe some set of data mathematically. In machine learning, this is done by numerical optimization. It should be noted that optim can solve this problem without a gradient function but can work more efficiently with it. Imagine you have a bunch of random algorithms. You can see after the first 2000 iterations, its value is just over 4. 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From measured datapoints, as an example that cover these algorithms is an attempt to apply the theory evolution. Optimization algorithm to explain the optimization process 've chosen something that I if. Use of the optimization process at a time and are for illustration only... The 2D parameter space fitting, there are are various kind of optimization problem in which we are seeking minimize. An example when there are a couple of local minima stochastic gradient descent works: looks fine far! Endtoend.Ai ’ s calculate these values for parameters have many layers, each with a k-means,... The objective of your data used  BFGS '' in order to perform gradient descent is the of. Your data of videos about neural network optimization that cover these algorithms on deeplearning.ai and! Model that performs well and gives accurate predictions in a particular set of optimization problems where the majority real-life! 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Tamil Nadu Board of Secondary EducationHSC Science Class 11th

# Calculate the work involved in the expansion and compression process. - Chemistry

Calculate the work involved in the expansion and compression process.

#### Solution

Work involved in expansion and compression processes:
In most thermodynamic calculations we are dealing with the evaluation of work involved in the expansion or compression of gases. The essential condition for expansion or compression of a system; is that there should be a difference between external pressure (Pext) and internal pressure (Pint).

For understanding pressure-volume work, let us consider a cylinder that contains V moles of an ideal gas fitted with a frictionless piston of cross-sectional area A. The total volume of the gas inside is V and the pressure of the gas inside is Pint. If the external pressure Pext is greater than Pint, the piston moves inward till the pressure inside becomes equal to Pext. Let this change be achieved in a single step
and the final volume be Vf. In this case, the work is done on the system (+w). It can be calculated as follows
w = − F.∆x ……….(1)

showing work involved in compression processes

F = PextA ……….(2)

Substituting (2) in (1)

w = – Pext. A. ∆x

A .∆x = change in volume = Vf – Vi

w = − Pext.(Vf – Vi) ……….(3)

w = − Pext. (− ∆V) …………(4)
= Pext.∆V

Since work is done on the system, it is a positive quantity.

If the pressure is not constant, but changes during the process such that it is always infinitesimally greater than the pressure of the gas, then, at each stage of compression, the volume decreases by an infinitesimal amount, dV. In such a case we can calculate the work done on the gas by the relation

Wrev = – ∫_("V"_"i")^("V"_"f") pext dV

In a compression process, Pext the external pressure is always greater than the pressure of the system.

i.e., Pext = (Pint + dP)

In an expansion process, the external pressure is always less than the pressure of the system

i.e., Pext = (Pint – dP)

When pressure is not constant and changes in infinitesimally small steps (reversible conditions) during compression from Vi to Vf. the P-V plot looks like in the figure. Work done on the gas is represented by the shaded area.

In the general case, we can write,

Pext = (Pint ± dP). Such processes are called reversible processes. For a compression process work can be related to internal pressure of the system under reversible conditions by writing equation

Wrev = – ∫_("V"_"i")^("V"_"f") Pint dV

For a given system with an ideal gas

Pint V = nRT

pint = "nRT"/"V"

Wrev = – ∫_("V"_"i")^("V"_"f") "nRT"/"V" dV

Wrev = – nRT ∫_("V"_"i")^("V"_"f") ("dV"/"V")

Wrev= – nRT ln ("V"_"f"/"V"_"i")

Wrev= – 2.303 nRT log ("V"_"f"/"V"_"i") ........(5)

If Vf > Vi (expansion), the sign of work done by the process is negative.

If Vf < Vi (compression) the sign of work done on the process is positive.

Concept: System and Surrounding
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#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Chemistry Volume 1 and 2 Answers Guide
Chapter 7 Thermodynamics
Evaluation | Q II. 24. | Page 225
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