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# 3.3 Centripetal acceleration  (Page 2/6)

 Page 2 / 6

Recall that the direction of ${a}_{\text{c}}$ is toward the center. You may use whichever expression is more convenient, as illustrated in examples below.

A centrifuge (see [link] b) is a rotating device used to separate specimens of different densities. High centripetal acceleration significantly decreases the time it takes for separation to occur, and makes separation possible with small samples. Centrifuges are used in a variety of applications in science and medicine, including the separation of single cell suspensions such as bacteria, viruses, and blood cells from a liquid medium and the separation of macromolecules, such as DNA and protein, from a solution. Centrifuges are often rated in terms of their centripetal acceleration relative to acceleration due to gravity $\text{(}g\text{)}$ ; maximum centripetal acceleration of several hundred thousand $g$ is possible in a vacuum. Human centrifuges, extremely large centrifuges, have been used to test the tolerance of astronauts to the effects of accelerations larger than that of Earth’s gravity.

## How does the centripetal acceleration of a car around a curve compare with that due to gravity?

What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed. See [link] (a).

Strategy

Because $v$ and $r$ are given, the first expression in is the most convenient to use.

Solution

Entering the given values of $v=\text{25}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{m/s}$ and $r=\text{500 m}$ into the first expression for ${a}_{\text{c}}$ gives

${a}_{\text{c}}=\frac{{v}^{2}}{r}=\frac{\left(\text{25}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{m/s}{\right)}^{2}}{\text{500 m}}=1\text{.}\text{25}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\text{.}$

Discussion

To compare this with the acceleration due to gravity $\left(g=9\text{.}80\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)$ , we take the ratio of ${a}_{\text{c}}/g=\left(1\text{.}\text{25}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)/\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)=0\text{.}\text{128}$ . Thus, ${a}_{\text{c}}=0\text{.}\text{128 g}$ and is noticeable especially if you were not wearing a seat belt.

## How big is the centripetal acceleration in an ultracentrifuge?

Calculate the centripetal acceleration of a point 7.50 cm from the axis of an ultracentrifuge    spinning at ${\text{7.5 × 10}}^{\text{4}}\phantom{\rule{0.25em}{0ex}}\text{rev/min.}$ Determine the ratio of this acceleration to that due to gravity. See [link] (b).

Strategy

The term rev/min stands for revolutions per minute. By converting this to radians per second, we obtain the angular velocity $\omega$ . Because $r$ is given, we can use the second expression in the equation ${a}_{\text{c}}=\frac{{v}^{2}}{r};\phantom{\rule{0.25em}{0ex}}{a}_{\text{c}}={\mathit{r\omega }}^{2}$ to calculate the centripetal acceleration.

Solution

To convert $7\text{.}\text{50}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{rev}/\text{min}$ to radians per second, we use the facts that one revolution is $2\pi \text{rad}$ and one minute is 60.0 s. Thus,

Now the centripetal acceleration is given by the second expression in as

${a}_{\text{c}}={\mathrm{r\omega }}^{2}\text{.}$

Converting 7.50 cm to meters and substituting known values gives

${a}_{\text{c}}=\left(0\text{.}\text{0750 m}\right)\left(\text{7854 rad/s}{\right)}^{2}=4\text{.}\text{63}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}.$

Note that the unitless radians are discarded in order to get the correct units for centripetal acceleration. Taking the ratio of ${a}_{\text{c}}$ to $g$ yields

$\frac{{a}_{\text{c}}}{g}=\frac{4\text{.}\text{63}×{\text{10}}^{6}}{9\text{.}\text{80}}=4\text{.}\text{72}×{\text{10}}^{5}.$

Discussion

This last result means that the centripetal acceleration is 472,000 times as strong as $g$ . It is no wonder that such high $\omega$ centrifuges are called ultracentrifuges. The extremely large accelerations involved greatly decrease the time needed to cause the sedimentation of blood cells or other materials.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!


text:
# Show that the orthogonal projection onto $Range T$ is equal to $T(T^\ast T)^{-1}T^\ast$ given that $T: V \to W$ is injective

by allonsy676   Last Updated August 14, 2019 09:20 AM - source

Given $$V$$ and $$W$$ as finite-dimensional inner product spaces and an injective linear map $$T: V \to W$$, how can we show that $$P_{Range T} = T(T^\ast T)^{-1}T^* \in \mathcal{L}(W)$$ where $$P_{Range T}$$ is the orthogonal projection onto $$Range T$$ and $$T^\ast$$ is the adjoint of $$T$$? Supposedly this result can be used to derive a useful matrix formula for orthogonal projection, but I'm not sure how to figure out how we can show the equality above. Does $$(T^\ast T)^{-1}$$ even make sense? How do we show that? And what is the intuition of the above formulation?

Among my ideas are trying to show that the right hand side is in the range of $$T$$ (which it seems to be) and trying to utilize the fact that $$P_{Range T}^2 = P_{Range T}$$. But I'm not sure how to proceed from there.

Tags :

format: plain


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## Algebra 1

Published by Prentice Hall

# Chapter 3 - Solving Inequalities - 3-1 Inequalities and Their Graphs - Practice and Problem-Solving Exercises - Page 169: 47

#### Answer

z is greater than or equal to 25.6

#### Work Step by Step

Convert the inequality symbol to words. $z\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underbrace{\geq}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 25.6$ z$\ \ \$ is greater than or equal to$\ \ \$ 25.6

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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## Integrating functions in python

| categories: | tags: | View Comments

Problem statement

find the integral of a function f(x) from a to b i.e.

$$\int_a^b f(x) dx$$

In python we use numerical quadrature to achieve this with the scipy.integrate.quad command.

as a specific example, lets integrate

$$y=x^2$$

from x=0 to x=1. You should be able to work out that the answer is 1/3.

from scipy.integrate import quad

def integrand(x):
return x**2

ans, err = quad(integrand, 0, 1)
print ans

0.333333333333

## 1 double integrals

Integrate $$f(x,y)=y sin(x)+x cos(y)$$ over

$$\pi <= x <= 2\pi$$

$$0 <= y <= \pi$$

i.e.

$$\int_{x=\pi}^{2\pi}\int_{y=0}^{\pi}y sin(x)+x cos(y)dydx$$

The syntax in dblquad is a bit more complicated than in Matlab. We have to provide callable functions for the range of the y-variable. Here they are constants, so we create lambda functions that return the constants. Also, note that the order of arguments in the integrand is different than in Matlab.

from scipy.integrate import dblquad
import numpy as np

def integrand(y, x):
'y must be the first argument, and x the second.'
return y * np.sin(x) + x * np.cos(y)

ans, err = dblquad(integrand, np.pi, 2*np.pi,
lambda x: 0,
lambda x: np.pi)
print ans

-9.86960440109

we use the tplquad command to integrate $$f(x,y,z)=y sin(x)+z cos(x)$$ over the region

$$0 <= x <= \pi$$

$$0 <= y <= 1$$

$$-1 <= z <= 1$$

from scipy.integrate import tplquad
import numpy as np

def integrand(z, y, x):
return y * np.sin(x) + z * np.cos(x)

0, np.pi,  # x limits
lambda x: 0,
lambda x: 1, # y limits
lambda x,y: -1,
lambda x,y: 1) # z limits

print ans

2.0

## 2 Summary

scipy.integrate offers the same basic functionality as Matlab does. The syntax differs significantly for these simple examples, but the use of functions for the limits enables freedom to integrate over non-constant limits.


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I have a question about the instantiation. Like the picture shown below, if my main code is 3.vhd. I want to instantiate entity aaa and bbb in entity MAIN. Is the rule that I should write the "component" in "package", like 1.vhd shows? (My understanding is, all the entity should have its package, if it'll be instantiated. And the component just list the port of this entity.) After that, add "use package.all", and then we can instantiate aaa and bbb in MAIN's architecture. Is there anything wrong?

I'm not familiar with VHDL, but seems verilog didn't have this "package" thing. A module can be instantiated in another modules.

Thanks! :)

For simple setups, you can get away with directly instantiating entities:

entity aaa is
port( ... );
end entity;

architecture foo of aaa is
begin
...
end architecture;

And then in the other source file:

architecture foo of main is
begin
AAA : entity work.aaa
port map( ... );
end architecture;

That is the quickest way to not repeat yourself too much.

Separate component declarations inside a package become useful if you have exchangeable parts and multiple different configurations that combine them in different ways. Unless you need that, go with direct entity instantiation.

• Thanks! That looks like verilog module instantiation now..... :) – Nobody Nov 24 '16 at 13:47


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# UPSC Exam Comprehensive News Analysis Nov16

A. GS1 Related
B. GS2 Related
GOVERNANCE
1. SC pulls up States for not recruiting judges
2. There can’t be a ban on use of word ‘Dalit’ in media: PCI
INTERNATIONAL RELATIONS
1. PM favours inclusive Indo-Pacific region
2. Vietnam opposes military alliances in region: envoy
3. India, China agree to expand military ties
C. GS3 Related
ECONOMY
1. Fitch retains rating for India at ‘BBB-’
SCIENCE AND TECHNOLOGY
1. ‘Super-Earth’ found orbiting Sun’s nearest single star
2. Ice age crater discovered beneath Greenland glacier
D. GS4 Related
E. Editorials
INTERNATIONAL RELATIONS
1. Searching for an elusive peace
SCIENCE AND TECHNOLOGY
1. ‘Super-Earth’ found orbiting Sun’s nearest single star
POLITY AND GOVERNANCE
1. When judges legislate
F. Tidbits
1. Himachal CM flags off 'Startup Yatra'
2. 4 Indian authors shortlisted for DSC Prize
G. Prelims Fact
1. FAME India Scheme
H. UPSC Prelims Practice Questions
I. UPSC Mains Practice Questions

A. GS1 Related

Nothing here for today!!!

B. GS2 Related

1. SC pulls up States for not recruiting judges

Context:

CJI-led Bench took note of over 5,000 vacancies in subordinate judiciary

Details:

• The SC pulled up various State governments and the administrative side of the High Courts for delay in filling vacancies in subordinate judicial services.
• A bench headed by Chief Justice Ranjan Gogoi reprimanded particularly Uttar Pradesh, West Bengal and Delhi for their inefficiency and inordinate delay in filling up vacancies of judges in high courts and subordinate courts.

Issue:

• It found that the source of the problem lay in poor infrastructure, from courtrooms to residences for judges.
• Sheer lackadaisical approach to conducting the appointment process on time is another reason.
• Systemic defects in the appointment process most certainly contributed to vacancies in the lower judiciary.

Concerns:

• A first-of-its-kind study by Delhi-based Vidhi Centre for Legal Policy has found that most States and their High Courts do not adhere to the schedule laid down by the Supreme Court for filling up judicial vacancies.
• Shortage of Judicial institutions and Judges ultimately increases the time of trial.
• Existence of a large number of pending cases hampers the ability of judges to deal with fresh cases.
• Existing strength of judges in the lower judiciary is wholly inadequate for the kind of workload that is constantly flowing in for disposal by the courts.

Way Forward:

• There is a pressing need to analyse the systemic challenges that prevent vacancies in the lower judiciary from being filled. This would involve asking questions about the fairness of recruitment processes, adequacy of incentive structures, and the culture of legal education and profession in the country.
• Efforts should be laid on strengthening the infrastructure.
• There has to be a centralised selection mechanism for appointment of judicial officers in subordinate judiciary. It would make recruitment more efficient and transparent.
• The average time taken for appointment of judges to the subordinate judiciary to fill in the vacancies must reduce.

2. There can’t be a ban on use of word ‘Dalit’ in media: PCI

Context:

The Press Council of India has ruled that there cannot be a complete ban on the use of word ‘Dalit’.

Background:

• The debate over the appropriateness of using the term ‘Dalit’ to refer to members of the Scheduled Castes is far from new.
• A decade ago, the National Commission for Scheduled Castes disfavoured the use of ‘Dalit’, which it felt was unconstitutional.
• This is because belonging to a ‘Scheduled Caste’ is a legal status conferred on members of castes named in a list notified by the President under Article 341 of the Constitution. And arguably must be used in official documents and communications.
• The Information and Broadcasting Ministry had issued an advisory to all media outlets to not use the word “Dalit” to refer to members belonging to the Scheduled Castes.
• In its advisory, the I&B Ministry said: “It is accordingly advised that media may refrain from using the nomenclature “Dalit” while referring to members belonging to the Scheduled Caste in compliance with Bombay High Court..”
• In an earlier order this year, the Ministry of Social Justice too had issued a similar advisory to all the State governments and Union Territories that in all official transactions, the constitutional term “Scheduled Caste” should be used instead of the word “Dalit”.

Details:

• The PCI chairman said that “Our reading of the Bombay High Court order is that it did not seek a ban on the word ‘Dalit’. We deliberated on the order and have come to the conclusion that it is advisable not to issue directions/orders prohibiting the use of word ‘Dalit’,”

Conclusion:

• Arguably, ‘Scheduled Caste’ is the appropriate way to refer to this class of people in official communications and documents.
• However, it is strange to oppose the use of the term ‘Dalit’ in the media and in non-official contexts — a nomenclature chosen and used by the community itself.
• Doing so lends itself to the charge that there is an attempt to deny the powerful and emotive meaning of the word Dalit.
• ‘Dalit’ must be recognised as an expression of self-empowerment. In the absence of a better word, Dalit has been the preferred word in the movements for justice for Dalits till now.
• Nevertheless, it has to be adjudicated on case-to-case basis.

1. PM favours inclusive Indo-Pacific region

Context:

East Asia Summit 2018 is being held in Singapore. It is Prime Minister Modi’s 5th East Asia Summit (EAS). India has been participating in the EAS since its very inception in 2005.

Details:

• Thoughts on enhancing multilateral cooperation, economic and cultural ties among member nations were shared at the EAS.
• The PM also reiterated India’s vision of a peaceful, open and inclusive Indo-Pacific region, strengthening maritime cooperation and commitment to a balanced Regional Comprehensive Economic Partnership (RCEP) pact

East Asia Summit:

The EAS consists of 10 ASEAN nations (Indonesia, Thailand, Singapore, Malaysia, the Philippines, Vietnam, Myanmar, Cambodia, Brunei and Laos), Australia, China, India, Japan, New Zealand, South Korea, Russia and the U.S. It was formed to further the objectives of regional peace, security and prosperity.

RCEP:

The RCEP, involving 10 ASEAN members as well as China, Japan, Australia, India, New Zealand and South Korea, would cover about half the world’s population and a third of its GDP.

2. Vietnam opposes military alliances in region: envoy

Context:

• Vietnam has an “ambivalent” position on the Quad grouping comprising India, Australia, Japan, and the U.S., Ambassador Pham Sanh Chau said.
• It was expressed that, while Vietnam welcomed any country’s initiative to preserve freedom of navigation and overflight in the region, it was opposed to any military alliance that could undermine regional peace and security.
• It was asserted that Vietnam will not join any alliance in order to fight any third country.

Background:

• In November last year, India, the US, Australia and Japan gave shape to the long-pending “Quad” Coalition to develop a new strategy to keep the critical sea routes in the Indo-Pacific free of any influence.
• The four countries agreed to partner with other countries and forums in the region to promote a free, open, rules-based and inclusive order in the Indo-Pacific that fosters trust and confidence.
• They committed to strengthening connectivity and quality infrastructure based on sovereignty, equality and territorial integrity of all nations, as well as transparency, economic viability and financial responsibility.
• The discussions focused on cooperation in areas such as connectivity, sustainable development, counter-terrorism, non-proliferation and maritime and cybersecurity.
• The move was seen as an effort to contain China’s growing influence in the Indo-Pacific region.
• The US has been pushing for a greater role for India in the Indo-Pacific which is seen by many countries as an effort to contain China’s growing clout in the region.
• India is known to be reluctant in giving military shape to “Quad”

Details:

• India’s Stand:
• According to a release from the Ministry of External Affairs (MEA) in Delhi, the Quad countries agreed to “strengthening connectivity and quality infrastructure” in the region according to principles of sovereignty and economic viability.
• While India and Japan are already cooperating on a number of projects in South Asia, which are seen as a counter to projects China is planning under the Belt and Road Initiative, there are as yet no ‘Quad’ level projects.
• “They agreed to partner with other countries and forums in the region to promote a free, open, rules-based and inclusive order in the Indo-Pacific that fosters trust and confidence,” the MEA said in the statement. That suggests that the Quadrilateral would not be an exclusive grouping on maritime security in the region
• Differences in Singapore:
• The Quad grouping met in Singapore. In a sign that the four countries continued to have differences on the objectives of the grouping, each of the four sides issued separate statements.
• Priorities:
• Vietnam’s major priorities in India would include helping establish a direct flight between the two countries.
• Bringing Vietnam’s national television service to New Delhi
• Clearing hurdles to improved bilateral trade especially in certain fruits.

3. India, China agree to expand military ties

Context:

India and China are set to expand their military ties, in tune with the spirit of the Wuhan informal summit between Chinese President Xi Jinping and Prime Minister Narendra Modi in April.

Details:

• For the first time, cadets from Indian and Chinese military academies, as well mid-level officers, will meet each other regularly.
• There would be continued visits at the level of military commands and civilian officers of the Ministry of Defence.
• The talks reflected the visible and gradual easing of tensions following the Doklam crisis and the Wuhan informal summit.
• A decision also has been taken to add new confidence-building measures to maintain peace and tranquillity on the borders
• The two sides stressed the need to “further strengthen military-to-military ties in order to strengthen political and strategic mutual trust between the two countries
• The statement pointed out that the two delegations forked a timetable on “specific defence exchanges for 2019”.
• The sources confirmed that the regular hand-in-hand joint military exercise between India and China will be held before the year-end.

How will this move impact India-China relations?

• The move is a bid to strengthen communication between both the armies.
• Reciprocal high-level visits and joint training exercises for the military – two of the world’s largest – will also be enhanced.
• It will help strengthen political and strategic mutual trust.
• It is the first step to maintaining peace and tranquillity in the India-China border areas. And also in improving bilateral defence ties post the Doklam standoff.

In order to continue to strengthen the ties, both the countries should establish a regular border meeting mechanism for the generals of the respective theatre commands.

C. GS3 Related

1. Fitch retains rating for India at ‘BBB-’

Context:

Fitch Ratings has retained India’s sovereign rating at ‘BBB-‘

Details:

• ‘BBB-‘ is the lowest investment grade rating with a stable outlook.
• Fitch has Refused to upgrade India’s credit rating for the 12th year in a row.
• Stating a weak fiscal position continues to constrain the ratings and there were significant risks to macroeconomic outlook.

What does the rating say?

• The rating, said, “it balances a strong medium-term growth outlook and favourable external balances relative to peers with weak fiscal finances, a fragile financial sector and some lagging structural factors
• Risks to the macroeconomic outlook are significant, and include a drop in credit growth, resulting from further problems in the banking or shadow-banking sector.
• Risks to the macroeconomic outlook are significant, and include a drop in credit growth, resulting from further problems in the banking or shadow-banking sector.
• A weak fiscal position continues to constrain India’s sovereign ratings.
• Government debt at close to 70 per cent of GDP, a difficulty to meet deficit target of 3.3 per cent of GDP in the current financial year (2018-19) due to lower revenues including from GST in first half, and expenditures being difficult to control in the run-up to general elections were main reasons for the weak fiscal position.
• The Indian economy continues to exhibit some structural weaknesses relative to peers and is less developed on a number of metrics.
• Governance standards continue to be weak, as illustrated by a low score for the World Bank governance indicator (47th percentile versus the ‘BBB’ median of 59th percentile). India’s ranking on the United Nations Human Development Index (31st percentile versus the ‘BBB’ median of 68th percentile) also indicates relatively low basic human development
• It listed recent defaults by Infrastructure Leasing & Financial Services and some public-sector banks to highlight risks in a sector that in recent years supplied around a third of total credit growth.

1. ‘Super-Earth’ found orbiting Sun’s nearest single star

Context:

Astronomers have discovered a frozen planet with a mass over three times that of the Earth, orbiting the closest solitary star to the Sun.

Details:

• The potentially rocky planet, known as Barnard’s star b, is a ‘super-Earth’ and orbits around its host star once every 233 days.
• The planet lies at a distant region from the star known as the ‘snow line’ This is well beyond the habitable zone in which liquid water, and possibly life, could exist, researchers said.
• The planet’s surface temperature is estimated to be around -170°C. However, if the planet has a substantial atmosphere the temperature could be higher and conditions potentially more hospitable.

Barnard’s star:

• Barnard’s star is an infamous object among astronomers and exoplanet scientists, as it was one of the first stars where planets were initially claimed but later proven to be incorrect.
• At nearly six light-years away Barnard’s star is the next closest star to the Sun after the Alpha Centauri triple system.
• It is a type of faint, low-mass star called a red dwarf. Red dwarfs are considered to be the best places to look for exoplanet candidates, which are planets outside our solar system.
• Barnard’s star b is the second closest known exoplanet to our Sun. The closest lies just over four light-years from Earth. That exoplanet, Proxima b, orbits around the red dwarf Proxima Centauri.
• The researchers used the radial velocity method during the observations that led to the discovery of Barnard’s star b. This technique detects wobbles in a star which are likely to be caused by the gravitational pull of an orbiting planet. These wobbles affect the light coming from the star.

2. Ice age crater discovered beneath Greenland glacier

Context:

Scientists have uncovered an asteroid impact crater, bigger than the area of Paris, buried beneath a kilometre of snow and ice in northern Greenland.

Details:

• This is the first time that a crater of any size has been found under one of Earth’s continental ice sheets.
• The crater measures more than 31 km in diameter, placing it among the 25 largest impact craters on Earth
• It was formed when a kilometre-wide iron meteorite smashed into northern Greenland.
• The finding suggests that a giant iron asteroid smashed into what is today a glacier during the last ice age, an era known as the Pleistocene Epoch that started 2.6 million years ago.
• The discovery could lead to insights into the ice age climate, and the effects on it from the eruption of debris that would have resulted from such a cataclysmic collision.

D. GS4 Related

Nothing here for today!!!

E. Editorials

1. Searching for an elusive peace

(India and the Neighbourhood; India- Afghanistan Relations)

The News:

• Last week, Russia had hosted a regional conference on Afghanistan to nudge the reconciliation process between the Taliban and the Afghan authorities.
• In this regional conference, the Taliban were represented by the political council chief, Sher Mohammad Stanikzai.
• Representatives from Afghanistan, China, Pakistan, Iran, Kyrgyzstan, Tajikistan, Uzbekistan, Kazakhstan, Turkmenistan, the U.S. and India were also present at the meeting, making it the first time that all stakeholders were present in the same room.

Editorial Analysis:

Background of the Meeting:

• It is important to note that considerable political manoeuvring preceded the meeting.
It was earlier planned for September, 2018 but failed to materialise.
The Taliban were initially opposed to attending since the Afghan government insisted on co-chairing the meeting.
• The diplomatic solution was to have Afghanistan represented by the High Peace Council (HPC), set up and supported by the government with the specific aim of furthering peace talks, though formally not part of government.
• India sent two seasoned former diplomats, with the Ministry of External Affairs describing its participation as “non-official”.
• The U.S. was represented by its Moscow embassy officials.
• Aware of the differences, the Russians refrained from attempting a final statement or even a group photograph. Nevertheless, with this meeting, Russia has sent a clear signal that it is back in the game in Afghanistan.

A Historical Note on the involvement of the Taliban:

• The idea of reconciliation with the Taliban has been around for over a decade.
• From a historical perspective, as the Taliban insurgency grew 2005 onwards, the British, deployed in Helmand, soon found merit in doing side deals with local Taliban commanders by turning a blind eye to opium production in the area.
• Further, with the help of the Germans and the Norwegians, they began to persuade the U.S. to work for a political outcome.
• After being elected in 2008, President Barack Obama ordered a full-scale review of the U.S.’s Afghanistan policy.
• After extracting an assurance from the generals that the insurgency would be defeated in 18 months, Mr. Obama announced a shift to counter-insurgency mode with a surge of over 40,000 troops, but added that phased drawdown of troops would begin in end-2011.
• Operation Enduring Freedom formally ended in December 2014, handing over primary responsibility for combat operations to the Afghan security forces even as the insurgency gained ground.

A Note on Operation Enduring Freedom:

1. Operation Enduring Freedom (OEF) was the official name used by the U.S. government for the Global War on Terrorism. On October 7, 2001, in response to the September 11 attacks, President George W. Bush announced that airstrikes targeting Al Qaeda and the Taliban had begun in Afghanistan.
2. Operation Enduring Freedom primarily refers to the War in Afghanistan, but it is also affiliated with counterterrorism operations in other countries, such as OEF-Philippines and OEF-Trans Sahara.
3. After 13 years, on December 28, 2014, President Barack Obama announced the end of Operation Enduring Freedom in Afghanistan. Continued operations in Afghanistan by the United States’ military forces, both non-combat and combat, now occur under the name Operation Freedom’s Sentinel.
• Later, the U.S. soon realised that insurgency could not be contained as long as sanctuaries existed in Pakistan. They also realised that its carrot and stick policy with Pakistan had cost the U.S. $33 billion but failed to change Pakistan’s policy. • A total cut-off was not possible as long as U.S. troops in Afghanistan depended on supply lines through Pakistan. • Crucially, in 12 years, the U.S. had lost 2,300 soldiers and spent$105 billion in rebuilding Afghanistan, more than $103 billion (in inflation-adjusted terms) spent under the Marshall Plan on rebuilding West Europe after World War II. • Finally, war weariness demanded an exit and a political solution was unavoidable. Growing Visibility of the Taliban: A Look at the sequence of events: 1. It is important to note that after prolonged negotiations, a Taliban office opened in Doha in June 2013 to promote talks and a peace process. 2. However, when the office started flying the Taliban flag, calling itself the political bureau of the Islamic Emirate of Afghanistan, it angered both the U.S. and Afghan governments. 3. The office was closed down though the Qatar authorities continue to host Taliban leaders. • Further, coming to power in 2014 after a bitterly contested election, Afghan President Ashraf Ghani moved to improve relations with Pakistan. • He had even called on the then Army Chief, Gen. Raheel Sharif, at the GHQ, to push for reconciliation. Preliminary talks were held in Murree but derailed in July 2015 when Mr. Ghani asked for a supportive audio/video (instead of a written statement) by Taliban leader Mullah Omar and learnt that he had died over two years earlier. • It is also important to note that an internal power struggle within the Taliban erupted with Mullah Akhtar Mansour emerging as the leader. • Insurgency grew with the Taliban briefly taking over Kunduz and Ghormach districts and threatening Ghazni. Mr. Ghani felt betrayed and lashed out, accusing Pakistan of “waging war”. Quadrilateral Coordination Group: • The Quadrilateral Coordination Group is a new initiative involving the U.S., China, Pakistan and Afghanistan. This was launched in January 2016. • After a couple of meetings, there was a roadmap; Pakistan was to use its influence to get the Taliban to the negotiating table. • Hopes were dashed when the Taliban demanded exit of foreign troops, release of detainees from Guantanamo, and removal of its leaders from international blacklists. Frustrated with Pakistan’s inability to get Mullah Mansour to fall in line, the U.S. eliminated him in a drone strike in May 2016 in Balochistan. Maulvi Haibatullah was appointed as his successor. Concluding Remarks • Mr. Ghani launched the Kabul Process for Peace and Security Cooperation, and in February, 2018 made an unconditional dialogue offer to the Taliban. • The Taliban rejected his overture, declaring that they were ready to engage in direct talks only with the Americans. • Mr. Ghani persisted, resulting in a three-day ceasefire during Eid. • In conclusion, it is important to note that today, the Afghan government controls barely half the country, with one-sixth under Taliban control and the rest contested. • However, most significant is the ongoing depletion in the Afghan security forces because of casualties, desertions and a growing reluctance to join. • U.S. President Donald Trump’s South Asia policy announced last August aimed at breaking the military stalemate by expanding the U.S. and NATO presence, putting Pakistan on notice and strengthening Afghan capabilities has clearly failed. Experts believe that it is because of this failure that multiple processes are underway. • Finally, everyone agrees that the war has to end; the question for the U.S. is how to manage the optics of the exit while not conceding victory to the Taliban. • Lastly, since, July 2011, when the former President and Chair of the HPC, Burhanuddin Rabbani, visited Delhi, India has supported an ‘Afghan-led and Afghan-owned’ peace process. Last month, during Russian President Vladimir Putin’s India visit, both countries expressed their commitment to the Moscow Format. • India doesn’t have the leverage to play spoiler but its presence is recognition that its economic cooperation programmes make it the most widely accepted development partner. • It is important to note that pragmatism dictates that India remains engaged with the multiple processes underway. Peace remains elusive but India’s engagement demonstrates commitment to the idea of a stable, independent and peaceful Afghanistan. 1. Another orbit(ISRO, GSAT29) The News: • In a recent development, the Indian Space Research Organisation has marked a big milestone by successfully testing its heavy-lift launcher while launching an advanced communication satellite. • It plans to use this for the Chandrayaan-II moon mission in the early months of 2019. Editorial Analysis: A Look at Some Specifics: • From a historical perspective, the first successful experimental flight of the GSLV MkIII was in 2014 when it carried a dummy crew module as a payload. This proved its capacity in the atmospheric flight regime. Its first developmental flight was on June 5, 2017, when it launched GSAT19, weighing 3,136 kg. • On 14th November, 2018, the Geosynchronous Satellite Launch Vehicle MarkIII (GSLV MkIII) launched GSAT29, which is an advanced communications satellite, into a geosynchronous transfer orbit where the satellite’s closest approach to earth would be 190 km and the farthest 35,975 km. • The launcher bearing the 3,423 kg satellite took off from a launchpad at the Satish Dhawan Space Centre at Sriharikota. • Seventeen minutes after the launch, after various stages, the vehicle injected the satellite into the transfer orbit. • Taking over smoothly, ISRO’s master control facility at Hassan assumed the command and control of the satellite, and it will be manoeuvred into a geostationary orbit, its final destination, in days. Once placed, the satellite’s solar panels and antennae will unfold and work will begin. • With a liftoff mass of 640 tonnes, the GSLV MkIII is the heaviest launch vehicle made in India, and GSAT29 is the heaviest satellite to take off from Indian soil. Both launcher and satellite have other characteristics that make them stand out. The launcher can carry payloads up to 4 tonnes to the geosynchronous transfer orbit and up to 10 tonnes to a low-earth orbit. The multi-band, multi-beam satellite can cater to the communication needs of people in Jammu and Kashmir and the Northeast. • GSLV Mk III is a three-stage heavy lift launch vehicle developed by the Indian Space Research Organisation (ISRO). • Two massive boosters with solid propellant constitute the first stage, the core with liquid propellant form the second stage and the cryogenic engine completes the final stage. • GSAT-29 is a multiband, multi-beam communication satellite, intended to serve as test bed for several new and critical technologies. Its Ku-band and Ka-band payloads are configured to cater to the communication requirements of users including those from remote areas especially from Jammu & Kashmir and North-Eastern regions of India. • In addition, the Q/V-Band communication payload onboard is intended to demonstrate the future high throughput satellite system technologies. Geo High Resolution Camera will carry out high resolution imaging. Optical Communication Payload will demonstrate data transmission at a very high rate through optical communication link. • After the successful launch, ISRO Chairman Dr K Sivan said: “India has achieved significant milestone with our heaviest launcher lifting off the heaviest satellite from the Indian soil. The launch vehicle has precisely placed the satellite in its intended orbit. I congratulate entire ISRO team for this achievement.” • Declaring GSLV MKIII operational, Dr Sivan announced that Chandrayaan-2 and Gaganyaan missions will be launched by this heavy-lifter. • Experts believe that the GSAT-29 will help to bridge the digital divide. • Lastly, it is important to note that the success of GSLV MkIII-D2 marks an important milestone in Indian space programme towards achieving self-reliance in launching heavier satellites. The success of this flight also signifies the completion of the experimental phase of GSLV Mark III. Concluding Remarks • In conclusion, the present launch marked the second developmental flight of the MkIII. • With these two successes, the launcher is declared ‘operational’ and joins the ranks of the working vehicles, the PSLV and the GSLV. • It is important to note that this is far fewer than the number of developmental flights the older launch vehicles were subjected to. This is because the solid and liquid propellant stages had been tested before. The third cryogenic stage could establish its performance in just two developmental flights. • Obviously these were preceded by numerous experimental flights and ground-based tests. • Lastly, this success sets the stage for trying out variations such as other types of engines, different fuel combinations and higher launch capacity. The GSLV MkIII has not just boosted the satellite into its orbit, but also restored morale at ISRO, which had been dented by the GSAT 6A setback. 1. When judges legislate The News: There have been many recent judgments, where the Supreme Court has become hyper-activist in making laws. However, having said this, an important question that arises is: can judges legislate? Editorial Analysis: A Look at Some Specifics: • Experts point out that this question has already been answered in the past by the court. • As a matter of fact, in the Ram Jawaya v. The State of Punjab (1955) case, the court observed: “Our Constitution does not contemplate assumption, by one organ or part of the state, of functions that essentially belong to another.” • This implies that there should be a broad separation of powers in the Constitution of the three organs of the state, and that one organ should not encroach into the domain of another. • If one organ encroaches into the domain of another, the delicate balance in the Constitution will be upset and there will be chaos. • It is important to note that making laws is the function of the legislature. • As observed in Union of India v. Deoki Nandan Aggarwal (1991), “The power to legislate has not been conferred on the courts.” In Suresh Seth v. Commissioner, Indore Municipal Corporation (2005), the court observed: “Under our Constitutional scheme, Parliament and Legislative Assemblies exercise sovereign power to enact laws.” • Experts ask an important question: Is judicial discipline being observed? The following section will examine some recent decisions of the court: 1. Firstly, in Arun Gopal v. Union of India (2017), the Supreme Court fixed timings for bursting Diwali fireworks and prohibited the use of non-green fireworks, although there are no laws to that effect. 2. Secondly, in M.C. Mehta v. Union of India (2018), the court annulled the statutory Rule 115(21) of the Central Motor Vehicle Rules, 1989, when it directed that no BS-4 vehicle should be sold after March 30, 2020, and that only BS-6 vehicles can be sold after that date. 3. Thirdly, in Subhash Kashinath Mahajan v. State of Maharashtra (2018), the court amended the Scheduled Castes and the Scheduled Tribes (Prevention of Atrocities) Act, 1989, by annulling Section 18 which said that no anticipatory bail will be granted to persons accused under the Act; by requiring a preliminary enquiry; and by prohibiting arrest under the Act except with permission in writing by the appropriate authority. 4. Fourthly, in Rajesh Sharma v. The State of Uttar Pradesh (2017), the court felt that Section 498A of the Indian Penal Code was being misused. So it amended that Section by requiring complaints under that provision to be sent to a Family Welfare Committee constituted by the District Legal Services Authority, although there is no such requirement in Section 498A. 5. Lastly, the National Green Tribunal (NGT) ordered that no 15-year-old petrol-driven or 10-year-old diesel-driven vehicle will ply in Delhi, and the Supreme Court has directed impounding such vehicles, though neither the NGT nor the Supreme Court are legislative bodies. In conclusion, it is important to note that if judges are free to make laws of their choices, not only would that go against the principle of separation of powers, it could also lead to uncertainty in the law and chaos as every judge will start drafting his own laws according to his whims and fancies. F. Tidbits 1. Himachal CM flags off ‘Startup Yatra’ • Himachal Pradesh Chief Minister Jai Ram Thakur flagged off a “Startup Yatra”. • The programme is aimed at turning the State’s educated youth into job providers from jobseekers. • The State government, under Startup Yatra would provide all possible help to the youth to develop entrepreneurship under the scheme. 2. 4 Indian authors shortlisted for DSC Prize • Four Indian authors and two authors of Pakistani origin have made it to the shortlist of the$25,000 DSC Prize for South Asian Literature 2018.
• Founded in 2010 by Surina Narula and Manhad Narula, the DSC Prize has helped raise the profile of South Asian writing.
• Now in its eighth year, the DSC Prize is an international literary award focussed on South Asian fiction writing.
• The prize received submissions also from publishers based in the U.K., the U.S., Canada, and Australia, highlighting the growing interest in South Asian writing.

G. Prelims Fact

1. FAME India Scheme

• FAME (Faster Adoption and Manufacture of Hybrid and Electric Vehicles) subsidy.
• The subsidy is given to electric scooters, three-wheelers and electric and hybrid cars.
• The FAME India Scheme was implemented with effect from 1st of April 2015.
• The objective of the scheme is to support hybrid/electric vehicles market development and Manufacturing eco-system. The scheme has 4 focus areas i.e. Technology development, Demand Creation, Pilot Projects and Charging Infrastructure.
• The FAME India Scheme is aimed at incentivising all vehicle segments i.e. 2 Wheeler, 3 Wheeler Auto, Passenger 4 Wheeler Vehicle, Light Commercial Vehicles and Buses.
• The scheme covers Hybrid & Electric technologies like Mild Hybrid, Strong Hybrid, Plug in Hybrid & Battery Electric Vehicles.

H. Practice Questions for UPSC Prelims Exam

Question 1. With reference to the Anti-microbial resistance, consider the following statements:
1. Antimicrobial resistance, which is also referred to as drug resistance, results in formation of Super bugs.
2. It happens when microorganisms change when they are exposed to antimicrobial drugs used to treat the infections they cause.
3. India is home to several drug-resistant bugs which are spreading fast and have been noticed even in the operation theatres and intensive care units (ICUs) of several well-regarded hospitals

Select the correct answer using the code given below:

1. Only 1 and 2
2. Only 2 and 3
3. Only 1 and 3
4. 1, 2 and 3

See

Question 2. Consider the following statements:
1. Devaluation and Depreciation refer to reduction in the value of domestic currency.
2. Both are performed by the Government or Central Bank.

Select the correct answer using the codes given below:

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

See

Question 3. Consider the following statements with regard to Biosphere:
1. Biosphere includes both biotic and abiotic components that are present in the lithosphere, hydrosphere and the atmosphere.
2. In a biosphere there are established pathways for movement of energy and matter.

Select the correct answer using the codes given below:

1. 1 only
2. 2 only
3. Both 1 and 2
4. None of the above

See

Question 4. According to the wetland distribution map of India, which of the following regions is
considered as the largest wetland system in India?
1. Himalayan wetlands
2. Indo-Gangetic wetlands
3. Coastal wetlands
4. Deccan wetlands

See

I. Practice Questions for UPSC Mains Exam

1. The existence of a large number of pending cases hampers the ability of judges to deal with fresh cases. Suggest some measures to deal with the pendency of cases in the judiciary.
2. Discuss the role played by India in the peace process of Afghanistan. How different is India’s contribution from other countries involved in the peace process?

Also, check previous Daily News Analysis

“Proper Current Affairs preparation is the key to success in the UPSC- Civil Services Examination. We have now launched a comprehensive ‘Current Affairs Webinar’. Limited seats available. Click here to Know More.”

Enroll for India’s Largest All-India Test Series


text:
# Question

The target population is all stocks in the S&P 500 index. Is each of the following a parameter or a statistic?
a. The average price/earnings ratio for all 500 stocks in the S&P index.
b. The proportion of all stocks in the S&P 500 index that had negative earnings last year.
c. The proportion of energy-related stocks in a random sample of 50 stocks.
d. The average rate of return for 20 stocks recommended by a broker.

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text:
# Time-propagation TDDFT¶

Optical photoabsorption spectrum as well as nonlinear effects can be studied using time propagation TDDFT. This approach scales better than linear response, but the prefactor is so large that for small and moderate systems linear response is significantly faster.

## Ground state¶

To obtain the ground state for TDDFT, one has to just do a standard ground state with a larger simulation box. A proper distance from any atom to edge of the simulation box is problem dependent, but a minimum reasonable value is around 6 Ångströms and recommended between 8-10 Ång. In TDDFT, one can use larger grid spacing than for geometry optimization. For example, if you use h=0.25 for geometry optimization, try h=0.3 for TDDFT. This saves a lot of time.

A good way to start is to use too small box (vacuum=6.0), too large grid spacing (h=0.35), and too large time step (dt=16.0). Then repeat the simulation with better parameter values and compare. Probably lowest peaks are already pretty good, and far beyond the ionization limit, in the continuum, the spectrum is not going to converge anyway. The first run takes only fraction of the time of the second run.

For a parallel-over-states TDDFT calculation, you must choose the number of states so, that these can be distributed equally to processors. For example, if you have 79 occupied states and you want to use 8 processes in parallelization over states, add one unoccupied state to get 80 states in total.

Ground state example:

# Standard magic
from ase import Atoms
from gpaw import GPAW

# Beryllium atom
atoms = Atoms(symbols='Be',
positions=[(0, 0, 0)],
pbc=False)

# Add 6.0 ang vacuum around the atom
atoms.center(vacuum=6.0)

# Create GPAW calculator
calc = GPAW(nbands=1, h=0.3)
# Attach calculator to atoms
atoms.calc = calc

# Calculate the ground state
energy = atoms.get_potential_energy()

# Save the ground state
calc.write('be_gs.gpw', 'all')

Time-propagation TDDFT is also available in LCAO mode.

## Optical photoabsorption spectrum¶

Optical photoabsorption spectrum can be obtained by applying a weak delta pulse of dipole electric field, and then letting the system evolve freely while recording the dipole moment. A time-step around 4.0-8.0 attoseconds is reasonable. The total simulation time should be few tens of femtoseconds depending on the desired resolution.

Example:

from gpaw.tddft import *

time_step = 8.0                  # 1 attoseconds = 0.041341 autime
iterations = 2500                # 2500 x 8 as => 20 fs
kick_strength = [0.0,0.0,1e-3]   # Kick to z-direction

td_calc = TDDFT('be_gs.gpw')

# Kick with a delta pulse to z-direction
td_calc.absorption_kick(kick_strength=kick_strength)

# Propagate, save the time-dependent dipole moment to 'be_dm.dat',
# and use 'be_td.gpw' as restart file
td_calc.propagate(time_step, iterations, 'be_dm.dat', 'be_td.gpw')

# Calculate photoabsorption spectrum and write it to 'be_spectrum_z.dat'
photoabsorption_spectrum('be_dm.dat', 'be_spectrum_z.dat')

Note

Make sure to number of iterations is divisible by the dump interval such that the last iteration will be stored in the restart file. Otherwise append td_calc.write(‘be_td.gpw’, mode=’all’) to the script.

When propagating after an absorption kick has been applied, it is a good idea to periodically write the time-evolution state to a restart file. This ensures that you can resume adding data to the dipole moment file if you experience artificial oscillations in the spectrum because the total simulation time was too short.

Example:

from gpaw.tddft import *

time_step = 8.0                  # 1 attoseconds = 0.041341 autime
iterations = 2500                # 2500 x 8 as => 20 fs

# Read restart file with result of previous propagation
td_calc = TDDFT('be_td.gpw')

# Propagate more, appending the time-dependent dipole moment to the
# already existing 'be_dm.dat' and use 'be_td2.gpw' as restart file
td_calc.propagate(time_step, iterations, 'be_dm.dat', 'be_td2.gpw')

# Recalculate photoabsorption spectrum and write it to 'be_spectrum_z2.dat'
photoabsorption_spectrum('be_dm.dat', 'be_spectrum_z2.dat')

Typically in experiments, the spherically averaged spectrum is measured. To obtain this, one must repeat the time-propagation to each Cartesian direction and average over the Fourier transformed dipole moments.

## Fourier transformed density and electric near field¶

To analyze the resonances seen in the photoabsorption spectrum, see Induced density oscillations and electric near field from TDDFT.

## Time propagation¶

Since the total CPU time also depends on the number of iterations performed by the linear solvers in each time-step, smaller time-steps around 2.0-4.0 attoseconds might prove to be faster with the ECN and SICN propagators because they have an embedded Euler step in each predictor step:

$\tilde{\psi}_n(t+\Delta t) \approx (1 - i \hat{S}^{\;-1}_\mathrm{approx.}(t) \tilde{H}(t) \Delta t)\tilde{\psi}_n(t)$

, where $$\hat{S}^{\;-1}_\mathrm{approx.}$$ is an inexpensive operation which approximates the inverse of the overlap operator $$\hat{S}$$. See the Developers Guide for details.

Therefore, as a rule-of-thumb, choose a time-step small enough to minimize the number of iterations performed by the linear solvers in each time-step, but large enough to minimize the number of time-steps required to arrive at the desired total simulation time.

## TDDFT reference manual¶

The TDDFT class and keywords:

Keyword

Type

Default

Description

ground_state_file

string

Name of the ground state file

td_potential

TDPotential

None

Time-dependent external potential

propagator

string

'SICN'

Time-propagator ('ECN'/'SICN'/'SITE'/'SIKE')

solver

string

'CSCG'

Linear equation solver ('CSCG'/'BiCGStab')

tolerance

float

1e-8

Tolerance for linear solver

Keywords for absorption_kick():

Keyword

Type

Default

Description

kick_strength

float[3]

[0,0,1e-3]

Kick strength

Keywords for propagate():

Keyword

Type

Default

Description

time_step

float

Time step in attoseconds (1 autime = 24.188 as)

iterations

integer

Iterations

dipole_moment_file

string

None

Name of the dipole moment file

restart_file

string

None

Name of the restart file

dump_interal

integer

500

How often restart file is written

Keywords for gpaw.tddft.photoabsorption_spectrum():

Keyword

Type

Default

Description

dipole_moment_file

string

Name of the dipole moment file

spectrum_file

string

Name of the spectrum file

folding

string

Gauss

Gaussian folding (or Lorentzian in future)

width

float

0.2123

Width of the Gaussian/Lorentzian (in eV)

e_min

float

0.0

Lowest energy shown in spectrum (in eV)

e_max

float

30.0

Highest energy shown in spectrum (in eV)

delta_e

float

0.05

Resolution of energy in spectrum (in eV)

class gpaw.tddft.TDDFT(filename, td_potential=None, propagator='SICN', calculate_energy=True, propagator_kwargs=None, solver='CSCG', tolerance=1e-08, **kwargs)[source]

Time-dependent density functional theory calculation based on GPAW.

This class is the core class of the time-dependent density functional theory implementation and is the only class which a user has to use.

Create TDDFT-object.

Parameters:

filename: string

File containing ground state or time-dependent state to propagate

td_potential: class, optional

Function class for the time-dependent potential. Must have a method ‘strength(time)’ which returns the strength of the linear potential to each direction as a vector of three floats.

propagator: {‘SICN’,’ETRSCN’,’ECN’,’SITE’,’SIKE4’,’SIKE5’,’SIKE6’}

Name of the time propagator for the Kohn-Sham wavefunctions

solver: {‘CSCG’,’BiCGStab’}

Name of the iterative linear equations solver for time propagation

tolerance: float

Tolerance for the linear solver

The following parameters can be used: $$txt$$, $$parallel$$, $$communicator$$ $$mixer$$ and $$dtype$$. The internal parameters $$mixer$$ and $$dtype$$ are strictly used to specify a dummy mixer and complex type respectively.

absorption_kick(kick_strength)[source]

Delta absorption kick for photoabsorption spectrum.

Parameters:

kick_strength: [float, float, float]

Strength of the kick, e.g., [0.0, 0.0, 1e-3]

get_td_energy()[source]

Calculate the time-dependent total energy

initialize(reading=False)[source]

Inexpensive initialization.

propagate(time_step, iterations, dipole_moment_file=None, restart_file=None, dump_interval=100)[source]

Propagates wavefunctions.

Parameters:

time_step: float

Time step in attoseconds (10^-18 s), e.g., 4.0 or 8.0

iterations: integer

Iterations, e.g., 20 000 as / 4.0 as = 5000

dipole_moment_file: string, optional

Name of the data file where to the time-dependent dipole moment is saved

restart_file: string, optional

Name of the restart file

dump_interval: integer

After how many iterations restart data is dumped

read(filename)[source]

Read atoms, parameters and calculated properties from output file.

Read result from self.label file. Raise ReadError if the file is not there. If the file is corrupted or contains an error message from the calculation, a ReadError should also be raised. In case of succes, these attributes must set:

atoms: Atoms object

The state of the atoms from last calculation.

parameters: Parameters object

The parameter dictionary.

results: dict

Calculated properties like energy and forces.

The FileIOCalculator.read() method will typically read atoms and parameters and get the results dict by calling the read_results() method.

gpaw.tddft.photoabsorption_spectrum(dipole_moment_file, spectrum_file, folding='Gauss', width=0.2123, e_min=0.0, e_max=30.0, delta_e=0.05)[source]

Calculates photoabsorption spectrum from the time-dependent dipole moment.

Parameters:

dipole_moment_file: string

Name of the time-dependent dipole moment file from which the spectrum is calculated

spectrum_file: string

Name of the spectrum file

folding: ‘Gauss’ or ‘Lorentz’

Whether to use Gaussian or Lorentzian folding

width: float

Width of the Gaussian (sigma) or Lorentzian (Gamma) Gaussian = 1/(sigma sqrt(2pi)) exp(-(1/2)(omega/sigma)^2) Lorentzian = (1/pi) (1/2) Gamma / [omega^2 + ((1/2) Gamma)^2]

e_min: float

Minimum energy shown in the spectrum (eV)

e_max: float

Maximum energy shown in the spectrum (eV)

delta_e: float

Energy resolution (eV)


text:
# Regular Expression Limitation with Paragraph Replacement

I got into a situation where it seems like there is no way forward.

After : there is paragraph break which I want to remove but when I search using :$, it searches just fine but no matter what I put in replace box, it doesn't remove the paragraph break. I found that When I search :$ then it will search a paragraph break after : but won't remove the paragraph mark. Tabs, newlines, paragraphs \t \n $So any alternative to this. I tried with Alt Search as well but it won't let me do the thing either. edit retag close merge delete ## 2 Answers Sort by » oldest newest most voted I do not write in Hindi or anything in 'Complex Text Layot' but I tested a bit just now with AltSerach V1.4.1 in LibO V5.2.2. (The previos AS V1.4 does not list LibO V5.) You know that AltSearch is using a slightly extended and different coding?$ is a "zero-width-lookahead-assertion" functionally while \p is denoting the next-paragraph-mark itself. Found groups (parentheses used in the search string) are denoted \1, \2 and so on in AltSearch.

Seraching for (:)\p the correct substrings were found - also if the text was inside a right to left sequence. Using \1 as replace string then replaced the combined finding with the colon allone and the next-paragraph-mark was deleted.

more

You my friend, are a lifesaver. :-)

( 2016-11-30 14:22:48 +0100 )edit

Indeed, you cannot cross paragraph borders with the build-in regular expressions engine. That is: you can search for a paragraph break alone or for something that's at the en of a paragraph, but not both at the same time.

Try with the AltSearch extension instead that provides more options (maybe you need to use the [::BigBlock::] tag provided by the extension)

more


text:
# zbMATH — the first resource for mathematics

Weighted spaces of harmonic and holomorphic functions: Sequence space representations and projective descriptions. (English) Zbl 0898.46022
Summary: We study the structure of inductive limits of weighted spaces of harmonic and holomorphic functions defined on the open unit disk of $$\mathbb{C}$$, and of the associated weighted locally convex spaces. Using a result of Lusky we prove, for certain radial weights on the open unit disk $$D$$ of $$\mathbb{C}$$, that the spaces of harmonic and holomorphic functions are isomorphic to complemented subspaces of the corresponding Köthe sequence spaces. We also study the spaces of harmonic functions for certain non-radial weights on $$D$$. We show, under a natural sufficient condition for the weights, that the spaces of harmonic functions on $$D$$ are isomorphic to corresponding spaces of continuous or bounded functions on $$\partial D$$.

##### MSC:
 46E10 Topological linear spaces of continuous, differentiable or analytic functions 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) 46E15 Banach spaces of continuous, differentiable or analytic functions
Full Text:
##### References:
 [1] DOI: 10.1215/S0012-7094-71-03847-6 · Zbl 0214.37802 [2] DOI: 10.1007/BF01180688 · Zbl 0661.46008 [3] Rudin, Real and complex analysis, second edition (1974) · Zbl 0278.26001 [4] Bierstedt, Doga Mat. 10 pp 54– (1986) [5] Bierstedt, Advances in the theory of Fréchet spaces pp 181– (1989) [6] Bierstedt, Bull. Soc. Roy. Sci. Liége 57 pp 567– (1988) [7] Bierstedt, Resultate Math. 14 pp 242– (1988) · Zbl 0688.46002 [8] DOI: 10.1002/mana.19881350115 · Zbl 0688.46001 [9] DOI: 10.1007/BF01195220 · Zbl 0693.46022 [10] Ahlfors, Complex analysis (1979) [11] Köthe, Topological vector spaces. Vol. 1 (1983) [12] Koosis, Introduction to H (1980) [13] Horváth, Topological Vector Spaces and Distributions (1966) [14] Ehrenpreis, Fourier Analysis in Several Complex Variables 17 (1970) [15] Bonet, Reports of the Department of Mathematics, University of Helsinki 51 (1994) [16] Bierstedt, Functional Analysis, Holomorphy and Approximation Theory 71 pp 27– (1982) [17] DOI: 10.2307/1998953 · Zbl 0599.46026 [18] Bierstedt, Aspects of Mathematics and its Applications pp 169– (1986) [19] Shields, J. Reine Angew. Math. 299/300 pp 259– (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# A note on LERF groups and generic group actions Academic Article

•
• Overview
•

### abstract

• Let $G$ be a finitely generated group, $\mathrm {Sub}(G)$ the (compact, metric) space of all subgroups of $G$ with the Chaubuty topology and $X!$ the (Polish) group of all permutations of a countable set $X$. We show that the following properties are equivalent:(i) Every finitely generated subgroup is closed in the profinite topology,(ii) the finite index subgroups are dense in $\mathrm {Sub}(G)$,(iii) A Baire generic homomorphism $\phi: G\rightarrow X!$ admits only finite orbits. Property (i) is known as the LERF property. We introduce a new family of groups which we call {\it {A-separable}} groups. These are defined by replacing, in (ii) above, the word" finite index" by the word" co-amenalbe". The class of A-separable groups contains all LERF groups, all amenable groups and more. We investigate some properties of these groups.

### publication date

• January 1, 2014


text:
How they got this unit?

1. Nov 16, 2016

Dineshkarthi

I am in a study of sizing air compressor for a new manufacturing plant ,I googled for some calculation and i got the problem shown in the attachment .i have one doubt how they got the unit bar in the final answer ...?

Attached Files:

• Unit conversion.JPG
File size:
57.7 KB
Views:
42
2. Nov 16, 2016

Staff: Mentor

That's the kind of equation that only works with a given set of units. The book must mention somewhere what these units are (like $l$ must be in meters).

3. Nov 16, 2016

JBA

What is not defined is the units for the "450" constant value in the equation. Many times this type of constant includes in its value some type of units conversion ratio.

4. Nov 16, 2016


text:
# Does the extension of the absorption line of $\text{CO}_2$ with temperature play a role in the climate change?

I've read not long ago that the absorption line of the $$\text{CO}_2$$ becomes larger with temperature thanks to Doppler effect (if it's false it would be great to tell me). My question is the following: Does this imply, like I think, that more energy is "stored" on Earth (thanks to greenhouse effect) and so play a role in climate change?

If the answer is yes, how big is this role?

• Your are asking about a very tiny (third-order?) feedback effect. If the absolute temperature rise is 1%, the doppler broadening will increase 0.5%. I think you will find that collision broadening is greater than doppler broadening throughout the troposphere. For example, the effective width of oxygen's microwave absorption lines due to collisions is about 0.3 GHz at sea level. – Bert Barrois Jun 4 '18 at 12:34

No. Not in a significant way.

The full width at half maximum (FWHM) of a spectral line widened by thermal Doppler broadening is

$$\Delta f_{\text{FWHM}}={\sqrt{\frac{8kT\ln(2)}{mc^{2}}}}f_{0}$$

where $$m$$ is the mass of the emitting particle, $$T$$ is the temperature, $$f_{0}$$ is the frequency of the spectral line, and $$k$$ is the Boltzmann constant.

Let's look at the CO$$_2$$ absorption lines:

(Image from Wikipedia commons, source)

Let's take for example the band roughly between 12 and 20 $$\mu m$$. That corresponds to frequencies from 15 to 25 THz, with a mean of 20 THz.

If we solve the above equation for the mass of a CO$$_2$$ molecule ($$44.01/6.02\times 10^{23}$$ g), a frequency of 20 THz and an Earth's mean temperature of let's say 15°C (288.15 K) we get 1158 kHz broadening, and for an scenario 2°C warmer it would be 1162 kHz.

Therefore, the width of the absorption band would grow 8 kHz (4 kHz on either side). Which considering the original width of 10 THz corresponds to a 0.00008% increase. This could be roughly equated to an analogous increase in absorbed energy, which is absolutely negligible for all practical effects.


text:
# Mining Large Graphs and Streams using Matrix and Tensor Tools (extended abstract)

### Abstract

Coevolving streams of numerical measurements, as well astime evolving graphs, can well be represented as tensors. Here we review the fundamental matrix and tensors tools forthe analysis and mining of large scale streams and graphs.

Type
Publication
In SIGMOD ‘07: Proceedings of the 2007 ACM SIGMOD international conference on Management of data
Date
Tags
Citation
C. Faloutsos, T. G. Kolda, J. Sun. Mining Large Graphs and Streams using Matrix and Tensor Tools (extended abstract). In SIGMOD ‘07: Proceedings of the 2007 ACM SIGMOD international conference on Management of data, Beijing, China (2007-06-11 to 2007-06-14), ACM, pp. 1174, 2007. https://doi.org/10.1145/1247480.1247647

### BibTeX

@inproceedings{FaKoSu07,
author = {Christos Faloutsos and Tamara G. Kolda and Jimeng Sun},
title = {Mining Large Graphs and Streams using Matrix and Tensor Tools (extended abstract)},
booktitle = {SIGMOD '07: Proceedings of the 2007 ACM SIGMOD international conference on Management of data},
venue = {Beijing, China},
eventdate = {2007-06-11/2007-06-14},
publisher = {ACM},
pages = {1174},
year = {2007},
doi = {10.1145/1247480.1247647},
}


text:
Transmission Lines Books

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General Transmission-Line Theory. The Characteristic Impedance of Transmission Lines. The Schwarz-Christoffel Transformation. Characteristic Impedance by Variational Methods. Characteristic Impedance of a Strip Line Determined by Variational Methods.

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A length less than 80km (50 miles) Voltage level less than 69 kV; Capacitance effect is negligible; Only resistance and inductance are taken in calculation capacitance is neglected.; Medium Transmission Line. A medium transmission line is classified as a transmission line with. A length more than 80 km (50 miles) but.

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text:
Welcome to mathimatikoi.org forum; Enjoy your visit here.

## It is a straight line!

Differential Geometry
Tsakanikas Nickos
Community Team
Articles: 0
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

### It is a straight line!

Let $c \ \colon \left[ 0,1 \right] \longrightarrow \mathbb{R}^{n}$ be a regular parametrized curve with the property that all its tangents pass through a fixed point. Show that the image of $c$ lies in a straight line. What can be said if the condition of regularity is dropped?


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# $3 + 4 = 7$!!

Find the number of pairs $(x,y) \in \mathbb{Z}$ such that

$x^3+y^4=7$

For more problems try the sets My Problems and THRILLER.

×

Problem Loading...

Note Loading...

Set Loading...


text:
# readworthy

T H E M A N U A L (HOW TO HAVE A NUMBER ONE THE EASY WAY)

“Firstly, you must be skint and on the dole. Anybody with a proper job or tied up with full time education will not have the time to devote to see it through.” – the Timelords (AKA the KLF)

# existential crisis playlist

the soundtrack, played seperately or all together:

# grid paper using Stata

I just wrote a program to make grids using Stata! Not much use for many people, but if you have a friend who is a knitter and needs a grid template, well this may come in handy 🙂

This is an ado file, so just: 1) copy the text below the image into a text editor; 2) save it with the extension “.ado”; 3) put it in your Stata personal directory

The following grid was generated using the command:
mkgrid 60 80 "44 162 95" vthin label alt

 /** Program to produce a y by x grid Carl Higgs 16 April 2016

 Input parameters (arguments): y number of vertical spaces x number of horizontal spaces colour line colour width line width labels whether numbered axes are desired (if so, write "label" here, or leave blank) alt if you have specified having labels, you might want them to alternate: type "alt" e.g. mkgrid 60 80 mkgrid 60 80 black mkgrid 60 80 black vthin label mkgrid 60 80 black vthin label alt **/ * capture program drop mkgrid program mkgrid, rclass version 13.1 args y x colour width labels alt di "y is y' and x is x'" drop _all loc obs = max(y',x') set obs obs' if y'==obs' { egen y = fill(1(1)y') gen x = x' } else { gen y = y' egen x = fill(1(1)x') } loc aspect = y'/x' if "labels'"=="label" { tw sc y x, ms(i) /// graphregion(fcolor(white) lcolor(white)) scheme(s2color) /// xlab(0(1)x',grid nogextend gmin glc("colour'") alt' labsize(vsmall) glwidth("width'")) /// ylab(0(1)y',grid nogextend gmin glc("colour'") alt' angle(h) labsize(vsmall) glwidth("width'")) /// ytitle("") /// xtitle("") /// aspect(aspect') /// xsca(noextend) ysca(noextend) /// name(grid_y'xx',replace) } else { tw sc y x, ms(i) /// graphregion(fcolor(white) lcolor(white)) scheme(s2color) /// xlab(0(1)x',grid nogextend gmin glc("colour'") glwidth("width'")) /// ylab(0(1)y',grid nogextend gmin glc("colour'") glwidth("width'")) /// ytitle("") /// xtitle("") /// aspect(aspect') /// xsca(off) ysca(off) /// name(grid_y'xx',replace) }

end

A 5×5 grid:

A 2496×738 grid, towards the limits of what this code can do, the artifacts of electrical glitch spirits start to surface:

# bird mites

In late November 2015 we had a bit of a bird mite infestation (we think).  First awareness of it as an insect issue was after going to the doctor with what I thought was a strange rash; the doctor advised that this was urticaria (a new word for me  – ie. hives) resulting from an allergic reaction most likely to some type of insect…. The worst case scenario for us was bed bugs…

Traumatic bed bugs: years ago a friend was house-sitting for us and she has the unlucky superpower of being super-sensitive to bed bug bites – massive allergic reaction.  We (in 2009) were sceptical at first having never knowingly come across these, and that we didn’t have any such reaction – however once we started looking we found all the evidence – blood spotting on the sheets, mattress and furniture near the bed, shed skins and little white eggs in the joins of the wooden bed frame and nearby wooden bookshelf – and laid there as test bait with a torch at the ready and saw them crawling on us.    Well we learnt a few lessons in dealing with this issue over the next few months – the biggest help was the ‘Code of Practice For the Control of Bed Bug Infestations in Australia‘ by Stephen Doggett of the Department of Medical Entomology at Westmead Hospital in Sydney.

So returning to late 2015, we were cautiously aware that unlike this previous experience and later encounters with ‘chinches’ while travelling in Latin America in 2013 that our current allergic reaction suggested something different.  Nevertheless we isolated all sheets and clothing in the bed room, bagging these up and systematically hot washed and freezing these while we looked for BB evidence (bloodspots, eggs, cascas, certain sweet smell) – nothing; and this was a relief.  But we still didn’t know what this issue was – and it’s not much fun to be covered in painfully itchy bites!

To cut the ramble short – there were two possibilities that we saw as being plausible: bird mites or rate mites.  We had heard scurrying in the roof above our bed recently, and we had noticed a lot of birds around.  Our landlord came around and found bird droppings in the roof cavity and some small holes in the ceiling tiles.

We did some more research and found an article in the Australian Department of Health’s Communicable Diseases Intelligence journal describing a bird mite infestation in Wollongong at a similar time of year: apparently young starlings are known to leave their nests at this time of year, and their opportunistic bird mites hungrily seek out an alternate meal.  Humans, although not satisfactory, make a decent second best in the short term.  Inspired by this author’s detective work, we purchased a USB microscope from JayCar and got our clear tape at the ready – and when Caroline felt something crawling on her torso we were able to get it on the sticky tape:

A tiny thing (it was fun playing entomologist)! And it really did match up to the profile of either a rat mite or bird mite.  Doing a bit of investigation, I found an empty nest in a cluster of branches of an overgrown vine-extending tree which had over the past few months grown to extend brushing up against the mesh screen of our bedroom window and which had also pushed their way into the roof eaves above our bedroom.  Well I did some severe pruning to this tree, and a pest inspector sent by the landlord also suggested he thought bird mites were the likely source of the bites and he sprayed some pyrethrum  in the guttering  (a step I wasn’t sure about as I thought this might send things scurrying into our house!  But he was the expert so we went with it).  It is now a couple of months later and things seem fine, so the idea of bird mites having a last ditech attempt at a meal after their little bird hosts had skipped the nest seems like the likely explanation for the bites and the  allergic reaction I had.

So here is a little song and video, the latter featuring some microscope footage from the Digitech 5MP USB microscope camera of our bird mite!

Quick little mash up video using some old footage I had lying around (see fox-faced dancing animal in the Ghostlight video), Resolume, the bird mite microscope vid, and a webcam shot of some paper with ‘dear Adversaire’ written on it.

# Latex to Excel

Converting LaTeX tables to Excel is a pain; here are some steps I found useful for reformatting and removing persistent hidden whitespace characters:

• remove the \\ symbols and import the latex text document in Excel with the ampersand symbol (&) set as a delimiter (simple and good idea from this blog post – thank you Ever Barbero!)
• replacing intervening table code (e.g. \multicolumn{5}{c} ) and remaining curly brackets with nothing
• and replacing sub-/super-script (eg. ^2) and other symbol codes (eg. \chi) with their equivalent unicode characters (e.g. χ²)
• using the ‘TRIM(cell reference)’ formula in Excel to remove space characters except for single space between words/values…. However in itself I found this did not work satisfactorily.  Through trial and error I found that the embellishment of the TRIM() function as TRIM(CLEAN(cell reference)) removes hidden characters which trim alone may not. I had hidden spaces screwing up alignment of table items, and expanding this formula —actually, IF(ISBLANK(cell reference,””,TRIM(CLEAN(cell reference))) , so empty cells didnt’ return as errors — to reference the tables contents, and then pasted as values over the top solved this problem.

Whilst writing this post I found a StackOverflow post covering this and a few other tips which would have saved me some trial and error time if I found it sooner.


text:
# Question #fb2aa

Jan 21, 2017

This is what's going on here.

#### Explanation:

The difference between atoms and ions in that context comes from the nature of the chemical substance that you're dealing with.

When you're dealing with a covalent compound, you will refer to its constituent elements as atoms because covalent compounds are formed when atoms share electrons.

On the other hand, when you're dealing with an ionic compounds, you will refer to its constituent elements as ions because ionic compounds are formed when atoms lose or gain electrons.

In other words

• $\text{covalent compounds " -> " NO ions " = " atoms}$
• $\text{ionic compounds " -> " ions}$

For example, calcium chloride is an ionic compound that contains calcium cations, ${\text{Ca}}^{2 +}$, and chloride anions, ${\text{Cl}}^{-}$

${\text{CaCl"_2 -> "Ca"^(2+) + 2"Cl}}^{-}$

Notice that each formula unit of calcium chloride contains a total of $3$ ions, $1$ calcium cation and $2$ chloride anions. This, of course, means that every mole of calcium chloride contains $3$ moles of ions.

You thus have

$\text{2 moles Cl"^(-)/"1 mole CaCl"_2" }$ and ${\text{ " "3 moles ions"/"1 mole CaCl}}_{2}$

as conversion factors to use when converting from moles of calcium chloride to moles of chloride anions or moles of ions (calcium cations and chloride anions).

Since you won't find any calcium and chlorine atoms in this substance, you will refer to them as calcium cations and chloride anions, i.e. as ions.

Nitrogen dioxide, ${\text{NO}}_{2}$, is a covalent compound that contains nitrogen atoms bonded by way of covalent bonds to oxygen atoms.

In this case, you say that each molecule of nitrogen dioxide contains $1$ atom of nitrogen and $2$ atoms of oxygen.

Your conversion factor here will be

${\text{3 moles atoms"/"1 mole NO}}_{2}$

because every mole of nitrogen dioxide contains $3$ moles of atoms.

So remember, the nature of the chemical substance tells you if you should use atoms or ions.


text:
# Deeper understanding of the adjoint of a linear operator

My undergraduate classes in Q.M describes the adjoint of a linear operator purely as a mathematical formality. At this point, I'd like a deeper and heuristic understanding of it.

My questions are based on page 24 and 28 of the text An introduction to quantum computing by P. Kaye.

Page 24 outlines the definition of the dual of a Hilbert space $$\mathcal{H}^{*}$$

Definition: Let $$\mathcal{H}$$ be a Hilbert space. The Hilbert space $$\mathcal{H}^{*}$$ is defined as the set of linear maps $$\mathcal{H} \rightarrow \mathbb{C}$$. We denote elements of $$\mathcal{H}^{*}$$ by $$\langle \mathcal{X} |$$, where the action of $$\langle \mathcal{X} |$$ is $$\langle \mathcal{X} | : | \psi \rangle \mapsto \langle \mathcal{X} | \psi \rangle \in \mathbb{C}$$.

Indeed, the Hilbert space $$\mathcal{H}^{*}$$ is just the space of all linear function - each of which with a corresponding row vector form or dual vector - that maps a vector from $$\mathcal{H}$$ to $$\mathbb{C}$$ by contracting a bra and a ket, or, if you're a mathematician, a row vector with a column vector.

On page 28, Each map in $$\mathcal{H}^{*}$$ corresponds to some vector $$\langle{\phi'} |$$. The adjoint of the operator $$T$$, denoted $$T^{\dagger}$$, is defined as the linear map that sends $$\langle {\phi} |$$ to $$\langle {\phi'} |$$, where $$\langle \phi | (T |\psi \rangle) = \langle \phi ' |\psi \rangle$$.

First, by definition, any linear operator on $$\mathcal{H}^{*}$$ maps dual vectors in $$\mathcal{H}^{*}$$ to $$\mathbb{C}$$ so this appears to contradicts the statement made by the author that the adjoint $$T^{\dagger}$$ maps elements in $$\mathcal{H}$$ to $$\mathcal{H}$$.

Second, if the aforementioned is true, how does this validates the claim that $$\langle \phi | (T |\psi \rangle) = \langle \phi ' |\psi \rangle$$?

• To me, the adjoint story is MUCH more understandable in normal, everyday linear algebra notation instead of bra-ket notation. – Randall Apr 21 at 3:16
• "By definition, any linear operator on $\mathcal{H}^*$ maps dual vectors in $\mathcal{H}^*$ to $\mathbb C$" Absolutely not. The elements of $\mathcal{H}^*$ are linear maps $\mathcal{H}\rightarrow\mathbb C$. Linear operators on $\mathcal{H}^*$, by definition, are linear maps $\mathcal{H}^*\rightarrow\mathcal{H}^*$. – eyeballfrog Apr 21 at 4:38
Let $$f$$ be a continuous linear map $$\mathcal{H}\rightarrow \mathbb C$$, and $$\mathcal{H}^*$$ be the set of all such maps. The Riesz representation theorem shows that for each such $$f$$, there is a unique element $$\left|\phi\right>$$ of $$\mathcal{H}$$ such that $$f(\left|\psi\right>) = \left<\phi\right.\left|\psi\right>$$ for all $$\left|\psi\right> \in \mathcal{H}$$. We then make a small abuse of notation and identify $$f$$ with $$\left<\phi\right|$$. The Riesz theorem also shows that $$\mathcal{H}^*$$ is itself a vector space, and that the map $$\mathcal{H}\rightarrow \mathcal{H}^*$$ defined by $$\left|\phi\right> = \left<\phi\right|$$ is antilinear (it preserves addition and replaces scalar multiplication by scalar multiplication by the complex conjugate).
Now suppose $$T:\mathcal{H}\rightarrow\mathcal{H}$$ is a linear operator on $$\mathcal{H}$$. It can be shown that there is another linear operator $$T^\dagger:\mathcal{H}\rightarrow\mathcal{H}$$ such that $$\left<\phi\right|(T\left|\psi\right>) = \left)$$ for all $$\left|\psi\right> \in \mathcal{H}$$ and $$\left<\phi\right| \in \mathcal{H}^*$$, and that this satisfies $$T^{\dagger\dagger} = T$$ and $$(AB)^\dagger = B^\dagger A^\dagger$$ (Exercise: prove this). We then use this to define a corresponding linear operator on $$\mathcal{H}^*\rightarrow \mathcal{H}^*$$, which we will write in postfix notation: $$\left<\phi\right|T^* = \left.
So why did we do all this? The point is that, with this notation, for every linear operator $$T$$ on $$\mathcal{H}$$ and for all for all $$\left|\psi\right> \in \mathcal{H}$$ and $$\left<\phi\right| \in \mathcal{H}^*$$, we have $$\left<\phi\right|(T\left|\psi\right>) = (\left<\phi\right|T^*)(\left|\psi\right>)$$. This means we can drop the parentheses and the $$^*$$ and have an unambiguous symbol: $$\left<\phi\right|T\left|\psi\right>$$. Whether we interpret this as $$T$$ acting on $$\left|\psi\right>$$ (making it equal to $$\left<\phi|T\psi\right>$$) or $$T^*$$ acting on $$\left<\phi\right|$$ (making it equal to $$\left$$) doesn't matter--we get the same result regardless. And this even works with compound operators: $$\left<\phi\right|AB\left|\psi\right> = \left<\phi\right|A\left|B\psi\right> = \left = \left<\phi|AB\psi\right> = \left< A^\dagger\phi|B\psi\right> = \left< B^\dagger A^\dagger\phi|\psi\right> = \left< (AB)^\dagger \phi|\psi\right>.$$ This completes the analogy to matrix notation in finite-dimensional vector spaces, where we write the inner product of two vectors $$(x,y)$$ as $$x^Ty$$, and for a linear operator $$A$$, we can unambiguously write $$x^TAy$$ to represent both $$(x,Ay)$$ and $$(A^Tx,y)$$.