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# 24 Dec 2020: UPSC Exam Comprehensive News Analysis

CNA 24 Dec 2020:-

A. GS 1 Related
B. GS 2 Related
C. GS 3 Related
ECONOMY
1. Cabinet nod for 100% FDI in DTH service
2. Beware of illegal digital lending apps: RBI
DEFENCE
1. Maiden test of MRSAM for Army successful
BUDGETING
1. Cairn Energy wins arbitration award
D. GS 4 Related
E. Editorials
INDUSTRIAL GROWTH
1. The tightrope between production and industrial peace
POLITY
1. Key lesson from farmers’ protest is that steamrolling Parliament backfires
F. Prelims Facts
G. Tidbits
H. UPSC Prelims Practice Questions
I. UPSC Mains Practice Questions

Nothing here for today!!!

2. Beware of illegal digital lending apps: RBI

Context:

• A spate of suicides in Telangana following alleged harassment by personnel of digital lending platforms.

Details:

• The proliferation of several unauthorised digital lending platforms/mobile apps has become a cause for concern.
• These platforms have been indulging in high-handed recovery practices that have driven people to take the extreme step.

Modus operandi of loan sharks

• The digital lending platforms resort to excessive rates of interest and additional hidden charges are demanded from borrowers.
• There have been shreds of evidence of adoption of unacceptable and high-handed recovery methods, and misuse of agreements to access data on the mobile phones of the borrowers.
• RBI has pointed out how unauthorised digital lending platforms/mobile apps attracted borrowers with a promise of loans in a quick and hassle-free manner.

Guidelines for public lending

• Legitimate public lending activities can be undertaken by banks, non-banking financial companies (NBFCs) registered with RBI and other entities who are regulated by the State governments under statutory provisions, such as the money lending acts of the States concerned.

Peer to peer lending

• A peer to peer lending or P2P lending platform facilitates borrowing and lending money directly through an online platform like Lendbox, faircent, etc., making it affordable to get loans online compared to banks.

Conclusion:

• The Reserve Bank of India has cautioned the public against falling into the trap set by unauthorized digital lending platforms.
• The people are advised to carry out verification of the antecedents of the company/firm offering loans online or through mobile apps.

1. Maiden test of MRSAM for Army successful

Context:

• The inaugural test of the Medium Range Surface to Air Missile (MRSAM) for the Indian Army was carried out from the test range at Chandipur in Odisha.

Details:

• India successfully conducted the first Army version test of the state-of-the-art Medium-Range Surface-to-Air Missile (MRSAM).
• The missile has been developed by Defence Research and Development Organisation (DRDO) and Israel Aerospace Industries.

Missile characteristics

• Strike range is close to 100 km, the nuclear-capable ballistic missile weighs around 2.7 tonnes and has a length of 4.5 meters and can transport a payload weighing 60 kg.
• The missile can move with a speed of Mach 2 and has high degrees of manoeuvrability.
• Apart from the missile, the launching platform includes a Multi-Functional Surveillance and Threat Alert Radar (MFSTAR) for detection, tracking, and guidance of the missile.

Application

The new generation MRSAM has been developed to subdue airborne threats in the form of jets, missiles and rockets, including projectiles launched simultaneously.

1. Cairn Energy wins arbitration award

Context:

• An international arbitration tribunal has ruled in favour of Cairn Energy PLC of the U.K and has ordered India to return up to $1.4 billion to Cairn Energy PLC, a decision that the Government of India may challenge. Details: • The dispute between Cairn Energy PLC of U.K and the income tax authorities is over an internal transfer of share between the parent company and its subsidiary. • The dispute over capital gains tax was the bone of contention between Cairn Energy and the tax authorities of India. • The tribunal charged India of violating UK-India bilateral investment treaty and international laws. The story so far • The dispute between the Indian government and Cairn has its genesis in an issue arising over the transferred shares from ‘The Cairn UK’ to ‘Cairn India’ in 2006-07. • The income tax authorities alleged that Cairn UK had made capital gains and served a tax notice under retrospective taxation provisions. • The multiple interpretations of capital gains ensured that the company refused to pay the tax, which led to cases being filed at the Income Tax Appellate Tribunal (ITAT) and the High Court. • Cairn lost the case at ITAT. A case on the valuation of capital gains is still unresolved in front of the Delhi High Court. • In 2011, Cairn Energy sold the majority of its India business, Cairn India, to mining conglomerate Vedanta. Cairn UK was however not allowed to sell a minor stake of about 10 per cent by the income tax authorities. Authorities had also seized Cairn India shares as well as dividends that the company paid to its parent UK firm. Conclusion • The ruling of the tribunal ordering India to pay$1.4 billion to Cairn Energy is worrisome, not just because of the amount that is owed but also because it hurts the image of India at the global level as an investment destination and cast aspersions over ease of doing business.

E. Editorials

Category: INDUSTRIAL GROWTH

1. The tightrope between production and industrial peace

Context:

• Workers at Wistron Corporation’s manufacturing facility near Bengaluru went on a rampage over non-payment of their wages.
• The report from the Karnataka state authorities also found the Taiwanese-run firm did not have enough staff to manage its 10,500 workers.

Details:

• Key Apple supplier Wistron, currently at the centre of a controversy after its workers rioted at its iPhone factory outside Bengaluru, has admitted that some of its workers were not paid “correctly” and in some cases “not on time”.
• This embargo may affect all Wistron units, but the trigger was one of the biggest expressions of industrial unrest in India in recent years.

Reasons for such Industrial Disputes in the recent past in India:

1. Serious lapses in labour practices such as non-payment of wages, providing bonus on time; this has time and again brought the management and the workers into a confrontation.
2. Wilful violation of suppliers through supply chains and subcontracting without adhering to labour standards and protocols.
3. Abdication and evasion of responsibilities by either shifting the onus on sub-contracting firms or keeping the grievance in silent mode.
4. Lack of an effective grievance redressal system in the manufacturing units has meant that the issues and concerns expressed by the working class have not been addressed or properly dealt with.
5. Poor working conditions and harsh work environment take a toll on the workers’ physical and mental health.
6. The apathetic attitude of employers towards the workers – the relationship needs to have empathy and compassion and needs to move away from the master-slave equation.

Impact of such Industrial Disputes

1. Affects future FDI prospects; the investment climate gets vitiated with such disputes forcing the potential investors to look elsewhere. The Kearney FDI Confidence Index does not feature India in the top 25.
2. Lowers the image of the country and might impact the ease of doing business ranking and thereby the investment prospects. The Ease of doing business released by the World Bank has India at 63rd position.
3. The increased trust deficit between employers and employees leading to further unrest.
4. Impacts the production of goods and services in the economy leading to demand-supply mismatch and might lead to inflationary tendencies.
5. Lowers the code of conduct and rule of law.

Solutions

1. Enforcement of labour laws for employees’ benefit will make India an even more attractive and contrasting alternative to China where labour exploitation is widely prevalent.
2. With global firms under pressure to exhibit higher standards in environmental compliance, social and corporate governance, India also needs to up its game on enforcing compliance with the laws of the land and treating labour-employer disputes in a fair and equitable manner.
3. It may be a good time for the government to rekindle a tripartite dialogue mechanism with trade unions and employers like the erstwhile Indian Labour Conference, not held since 2015.
4. Improve the avenues for workers to channelize their grievances.
5. Industries to bring in ethical ‘code of conduct’ in tune with the welfare of workers and keep a strong monitoring system for the same.

Conclusion

• With the country on the cusp of a new labour law regime being marketed as a business-friendly regimen, misgivings about their provisions or unresponsive systems for employees’ grievances can only foment more such unrest.
• Inequitable labour-capital relations could hit India’s investment destination credo and thus India should move towards a more holistic approach through dialogue and new labour laws to protect the rights of workers to avoid any such incidents in the future.

Category: POLITY

1. Key lesson from farmers’ protest is that steamrolling Parliament backfires

[This editorial is taken from the Indian Express.]

Context:

• The recent protests by farmers with regards to the farm acts passed has raised concerns over a lack of engagement between the ruling party and the opposition while passing the law.

Details:

• The farm acts were passed by the Union Government with very little deliberation in the parliament and without any consultation with the farmers.
• The farm protests that have followed and continued for close to three weeks now have caused immense hardship to the farming community.

Reforms objective

• It appears that the new legislation is needed and will usher in required market reforms in the overregulated farm sector.
• So far there is no concrete piece of evidence to show that the new proposals will negatively impact farmers in the long run.
• The Minimum Support Price has no economic justification regardless of demand and supply. Linking MSP to the manufacture of essential medicines will give a better picture, there are no mechanisms that guarantee a pharmaceutical company a minimum price for essential medicines that it produces, irrespective of whether the quantity produced far exceeds the demand.

Farm liberalization

• The benefits of liberalizing the non-agricultural sector of the economy in 1991 established that, in the end, market forces cannot be ignored and a tight state control can be counterproductive.
• The fallouts of the enforcement of the Essential Commodities Act.
• Initial experiences under the Essential Commodities Act, 1955, were not as desired.
• Numerous control orders were passed on products such as cement and steel, and these were intended to ensure their availability at fair prices.
• The consequence was not what was expected, it could be witnessed:
• Severe shortages,
• Huge black market and
• Massive corruption.

Debate, discussion, deliberation

• The farm laws, however ennobling in its intentions, ought to have been passed after engaging with the relevant stakeholders.
• The farm laws would not have encountered as much opposition as they have if it was demonstrated through empirical data, objective analysis and impassionate reasoning, but passing it through a voice vote, was an injustice.
• As the farm bills marked a radical departure from the existing system of selling agricultural produce, the least that could have been done was to refer them to a Select Committee. The haste with which the new legislation was pushed through was not justifiable.

Parliamentary setup in India

• The core theme behind democracy is to give “voice to the voiceless”, where every individual matters as one and none more than one.
• India has adopted representative democracy, wherein the elected representatives represent the will of the people and the parliament stands for the institutionalisation of people’s will.
• Parliament is at the heart of the Indian democratic setup, it is supposed to be a chamber where policies, laws that are fundamental to the governance of the country are to be discussed, debated and deliberated.
• The demand by the Opposition for discussion was also turned down. The ruling party undoubtedly commands a majority and has the right to implement the promises it has made in its manifesto, but as it was once said, the opposition must have its say before the government has its way.

Parliament committees

• Many legal experts suggested that the government must have referred the bills before it became acts to the select committees, it is because of the following reasons listed below.
• The functions of the Parliament are varied, complex and voluminous. Time and expertise are required to make a detailed scrutiny of all legislative measures and other matters.
• Parliamentary committees assist in the discharge of duties of parliament.
• The Standing and Select committees help the lawmakers to source expertise, diverse opinions from outside of the parliament.
• It also provides a platform to overcome rigid party stance and adopt a more flexible, acceptable way going forward.
• Parliamentary committees work away from the public gaze, hence there are no incentives in ‘playing to the gallery’.
• It is a matter of concern that fewer and fewer bills are being referred to Select Committees or even deliberated upon.
• The recent data show that while 71 per cent of the bills were referred to a Select Committee in the 15th Lok Sabha (2009-14), only 25 per cent were so referred in the 16th Lok Sabha (2014-19).
• In 2019, 17 bills were referred and none in 2020, a statistic that does not bode well to our democracy. The standing committees will refine the policies and add value to the policies, it’s a platform that needs to be engaged more.

Laboratory federalism

• It is no surprise that farm legislation which has such wide-ranging implications is met with resistance. Thus the best way to demonstrate their beneficial effects is to implement the laws in select states or districts for a year; implementation in pilot mode can help build confidence and ensure greater acceptance.
• The feedback can illustrate if the new law can achieve its objects and prove beneficial to the nation, it can also reveal flaws in the new law.
• Indeed, if GST had been implemented on a trial basis for select products, it would have revealed the serious technological deficiencies and the nation would have benefitted by delaying its implementation.
• However, it is still not too late to implement the new farm laws in select states and demonstrate their salutary effect, this is similar to how a company undergoes several iterations before launching the product in the market.

Conclusion

• The wisdom that all ruling parties can derive is that abiding by the constitutional conventions pays dividends — it benefits the nation and preserves the dignity of Parliament.
• The delay that arises by following parliamentary procedures and constitutional conventions can actually provide the proof that the new law is really the right choice and those opposing it have placed their short-term vested interests ahead of the national interest.
• Parliament is sometimes referred to as the “Temple of Democracy”, its role as the highest deliberative organ in the country must not be forgotten. Deliberation is at the centre of any representative democracy, therefore Parliament and its committees should be made full use of for arriving at legislations that contribute to the welfare of people.

F. Prelims Facts

Nothing here for today!!!

G. Tidbits

Nothing here for today!!!

H. UPSC Prelims Practice Questions

Q1. Consider the following statements:

1. Article 43-A was added to the Constitution by the 42nd Constitutional Amendment Act, 1976.
2. A-43-A belongs to Gandhian directive principles.

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

Explanation:

Article -43-A belongs to Socialistic DPSP and was added by the 42nd Constitutional Amendment Act.

Q2. Consider the following statements:
1. The International Labour Organisation (ILO) was formed in 1945 at the end of the Second World War.
2. India is a founding member of the International Labour Organisation.
3. The World Employment and Social Outlook (WESO) is released by ILO.

Choose the correct option:

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. All of the above

Explanation:

ILO was formed in 1919 as a part of the Treaty of Versailles.

Q3. Consider the following statements:
1. National Commission for Minorities (NCM) is a constitutional body.
2. 5 communities are notified as religious minorities.
3. The tenure of the members of the National Commission for Minorities is 3 years.

1. 1 only
2. 1 and 3 only
3. 3 only
4. All of the above

Explanation:

• NCM is a statutory body created by the National Commission for Minorities Act, 1992.
• 6 communities, they are Muslims, Christians, Sikhs, Buddhists, Jains, Parsis.
Q4. Which of the following countries border the Central African Republic?
1. Tanzania
2. Sudan
3. Democratic Republic of Congo
4. Senegal

1. 1 and 4 only
2. 2 and 3 only
3. 1, 2 and 3 only
4. 3 and 4 only


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Just an A.P.

Algebra Level 2

$$a{ b }^{ 2 }{ c }^{ 3 },{ a }^{ 2 }{ b }^{ 3 }{ c }^{ 4 },{ a }^{ 3 }{ b }^{ 4 }{ c }^{ 5 }$$ are in A.P find the least value of a+b+c (where a,b,c are real and positive numbers)

×

format: plain


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Bouncing Robots: Graphical Puzzle [closed]

Robots are indicated by the arrowhead shapes and the labels "r", "y", "b", "g". The label obviously corresponds to their color. The aim of the puzzle is to pick up the shapes and put them down in the grey circle located on the north side of the board.

Rules

• Robots can only move in a straight line. Along the light blue paths they start on.
• Robots keep moving until they hit either a Wall or another Robot.
• Robots can only pick up a shape that is of their own color (red Robot can only pick up red shapes).
• Robots will automatically pickup a shape when they land on it.
• Robots can only carry up to 7 sides, going over this limit destroys the Robot, rendering it unavailable for use. Example: Red Robot has picked up a Red Hexagon and a Red Circle. This gives him 7 sides (6 + 1). If Red Robot picked up a Red Triangle, he would be destroyed. To avoid this you need to put shapes down in the grey circle.
• Robots can only move one at a time.

The aim of the game is to places all of the shapes into the grey circle which is a puzzle in itself. I posted it here because I want to see how well people can optimize their paths.

Post your solutions in the format "r s" for Red Robot move South.

Just to clarify One Move ("r s") = One Turn.

• Robots can only move in a straight line? Also, they "keep moving until they hit either another wall or robot" and then what? they stop? they change direction? which direction? – JLee Mar 18 '15 at 18:35
• Circles don't have vertices... – Aify Mar 18 '15 at 18:38
• What kind of shape has only one corner, then? ... A teardrop? – Kevin Mar 18 '15 at 19:01
• So at the grey circle the rule that says that robots block other robots is not applicable? – Ivo Beckers Mar 19 '15 at 4:33
• Do the robots move in parallel or concurrently? e.g. If green moves towards red and vice versa on a straight line without obstacles, will they hit each other in the middle of their path? Or is it that only one robot moves at a time? – CygnusX1 Mar 19 '15 at 13:45

Here is a solution of 137 moves utilizing the idea of getting a robot to the eighth column of the first row to create paths to the grey circle. Although this is unlikely to be optimal, it is a major improvement on PuzzleEater's 191 moves. The format is "[robot] [sequence of moves]".

r esen                         + r circle
y en
r e
y s
r sesw nwsw                    + r hexagon, - circle hexagon, + square
g wnws e                       + g circle
b sene nwn                     + b hexagon
g wnws wnwn ene                + g hexagon
r news enen eswn               + r triangle, - square triangle (finished)
b ws                           + b circle
y n
g nwnw enes enw                - g circle hexagon, + triangle square
y s
r w
g eswn                         - g triangle square (finished)
y wnws esen s                  + y circle triangle
r e
g e
b nwsn esws eses wsen e        - b hexagon circle, + b square triangle
g wses
b swne sws                     - b square triangle (finished)
y nwse nesw nesn wsne swne s   - y circle triangle, + square, - square, + hexagon
r e
b ne
y nes                          - y hexagon (finished)


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THE SUPPLY AND DEMAND FOR MONEY AND OVERALL PRICES - The Mystery of Banking

When economics students read text books, they learn, in the “micro” sections, how prices of specific goods are determined by supply and demand. But when they get to the “macro” chapters, lo and behold! supply and demand built on individual persons and their choices disappear, and they hear instead of such mysterious and ill-defined concepts as velocity of circulation, total transactions, and gross national product. Where are the supply-and-demand concepts when it comes to overall prices?

In truth, overall prices are determined by similar supply-and demand forces that determine the prices of individual products.

Let us reconsider the concept of price. If the price of bread is 70 cents a loaf, this means also that the purchasing power of a loaf of bread is 70 cents. A loaf of bread can command 70 cents in exchange on the market. The price and purchasing power of the unit of a product are one and the same. Therefore, we can construct a diagram for the determination of overall prices, with the price or the purchasing power of the money unit on the Y axis.

While recognizing the extreme difficulty of arriving at a measure, it should be clear conceptually that the price or the purchasing power of the dollar is the inverse of whatever we can construct as the price level, or the level of overall prices. In mathematical terms,

where PPM is the purchasing power of the dollar, and P is the price level.

To take a highly simplified example, suppose that there are four commodities in the society and that their prices are as follows:
eggs $.50 dozen butter$ 1 pound
shoes $20 pair TV set$ 200 set

In this society, the PPM, or the purchasing power of the dollar, is an array of alternatives inverse to the above prices. In short, the purchasing power of the dollar is:

either 2 dozen eggs
or 1 pound butter
or 1/20 pair shoes
or 1/200 TV set

Suppose now that the price level doubles, in the easy sense that all prices double. Prices are now:
eggs $1 dozen butter$ 2 pound
shoes $40 pair TV set$ 400 set

In this case, PPM has been cut in half across the board. The purchasing power of the dollar is now:

either 1 dozen eggs
or 1/2 pound butter
or 1/40 pair shoes
or 1/400 TV set

Purchasing power of the dollar is therefore the inverse of the price level.

SUPPLY OF AND DEMAND FOR MONEY

Let us now put PPM on the Y-axis and quantity of dollars on the X-axis. We contend that, on a complete analogy with supply,demand, and price above, the intersection of the vertical line indicating the supply of money in the country at any given time, with the falling demand curve for money, will yield the market equilibrium PPM and hence the equilibrium height of overall prices, at any given time.

Let us examine the diagram in Figure above. The supply of money, M, is conceptually easy to figure: the total quantity of dollars at any given time.

We contend that there is a falling demand curve for money in relation to hypothetical PPMs, just as there is one in relation to hypothetical individual prices. At first, the idea of a demand curve for money seems odd. Isn’t the demand for money unlimited? Won’t people take as much money as they can get? But this confuses what people would be willing to accept as a gift (which is indeed unlimited) with their demand in the sense of how much they would be willing to give up for the money. Or: how much money they would be willing to keep in their cash balances rather than spend. In this sense their demand for money is scarcely unlimited. If someone acquires money, he can do two things with it: either spend it on consumer goods or investments, or else hold on to it, and increase his individual money stock, his total cash balances. How much he wishes to hold on to is his demand for money.

Let us look at people’s demand for cash balances. How much money people will keep in their cash balance is a function of the level of prices. Suppose, for example, that prices suddenly dropped to about a third of what they are now. People would need far less in their wallets, purses, and bank accounts to pay for daily transactions or to prepare for emergencies. Everyone need only carry around or have readily available only about a third the money that they keep now. The rest they can spend or invest. Hence, the total amount of money people would hold in their cash balances would be far less if prices were much lower than now. Contrarily, if prices were triple what they are today, people would need about three times as much in their wallets, purses, and bank accounts to handle their daily transactions and their emergency inventory. People would demand far greater cash balances than they do now to do the same “money work” if prices were much higher. The falling demand curve for money is shown in Figure below.

Here we see that when the PPM is very high (i.e., prices overall are very low), the demand for cash balances is low; but when PPM is very low (prices are high), the demand for cash balances is very high.

We will now see how the intersection of the falling demand curve for money or cash balances, and the supply of money, determines the day-to-day equilibrium PPM or price level.

DEMAND FOR MONEY

Suppose that PPM is suddenly very high, that is, prices are very low. M, the money stock, is given, at $100 billion. As we see in Figure below, at a high PPM, the supply of total cash balances, M, is greater than the demand for money. The difference is surplus cash balances—money, in the old phrase, that is burning a hole in people’s pockets. People find that they are suffering from a monetary imbalance: their cash balances are greater than they need at that price level. And so people start trying to get rid of their cash balances by spending money on various goods and services. But while people can get rid of money individually, by buying things with it, they can’t get rid of money in the aggregate, because the$100 billion still exists, and they can’t get rid of it short of burning it up. But as people spend more, this drives up demand curves for most or all goods and services. As the demand curves shift upward and to the right, prices rise. But as prices overall rise further and further, PPM begins to fall, as the downward arrow indicates. And as the PPM begins to fall, the surplus of cash balances begins to disappear until finally, prices have risen so much that the $100 billion no longer burns a hole in anyone’s pocket. At the higher price level, people are now willing to keep the exact amount of$100 billion that is available in the economy. The market is at last cleared, and people now wish to hold no more and no less than the $100 billion available. The demand for money has been brought into equilibrium with the supply of money, and the PPM and price level are in equilibrium. People were not able to get rid of money in the aggregate, but they were able to drive up prices so as to end the surplus of cash balances. Conversely, suppose that prices were suddenly three times as high and PPM therefore much lower. In that case, people would need far more cash balances to finance their daily lives, and there would be a shortage of cash balances compared to the supply of money available. The demand for cash balances would be greaterthan the total supply. People would then try to alleviate this imbalance, this shortage, by adding to their cash balances. They can only do so by spending less of their income and adding the remainder to their cash balance. When they do so, the demand curves for most or all products will shift downward and to the left, and prices will generally fall. As prices fall, PPM ipso factorises, as the upward arrow shows. The process will continue until prices fall enough and PPM rises, so that the$100 billion is no longer less than the total amount of cash balances desired.

Once again, market action works to equilibrate supply and demand for money or cash balances, and demand for money will adjust to the total supply available. Individuals tried to scramble to add to their cash balances by spending less; in the aggregate, they could not add to the money supply, since that is given at $100 billion. But in the process of spending less, prices overall fell until the$100 billion became an adequate total cash balance once again.

The price level, then, and the purchasing power of the dollar, are determined by the same sort of supply-and-demand feedback mechanism that determines individual prices. The price level tends to be at the intersection of the supply of and demand for money, and tends to return to that point when displaced.

As in individual markets, then, the price or purchasing powerof the dollar varies directly with the demand for money and inversely with the supply. Or, to turn it around, the price level varies directly with the supply of money and inversely with the demand.


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# [SOLVED]Problems with Inverter

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##### Junior Member level 3
Hello

I am working on inverter. I have some problems going with it.

Here is the code I am using. I am giving pulses from an ATMEGA162 Micro controller.

I am working on hardware. Final Hardware will be driven by another series of micro controller. So I am not very good with this code. I am applying +DC Bus of 30V

Problems I am having are:

IGBTs are getting very heated up.

a) I think by putting dead time, it will solve the problem. But I am not sure how to put it in this code. Any help

b) or if there is anything else which might be wrong with the inverter. Please do guide

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#define f 400
#define spc 24
#define Phase1L PORTC.0
#define Phase1H PORTC.1
#define Phase2L PORTC.2
#define Phase2H PORTC.3
#define Phase3L PORTC.4
#define Phase3H PORTC.5

flash unsigned char PWMCodes[721]={0,0,4,9,13,18,22,27,31,35,40,44,49,53,57,62,66,70,75,79,83,87,91,96,100,104,108,112,116,120,124,127,131,135,139,143,146,150,153,157,160,164,167,171,174,177,180,183,186,190,192,195,198,201,204,206,209,211,214,216,219,221,223,225,227,229,231,233,235,236,238,240,241,243,244,245,246,247,248,249,250,251,252,253,253,254,254,254,255,255,255,255,255,255,255,254,254,254,253,253,252,251,250,249,248,247,246,245,244,243,241,240,238,236,235,233,231,229,227,225,223,221,219,216,214,211,209,206,204,201,198,195,192,190,186,183,180,177,174,171,167,164,160,157,153,150,146,143,139,135,131,128,124,120,116,112,108,104,100,96,91,87,83,79,75,70,66,62,57,53,49,44,40,35,31,27,22,18,13,9,4,0,4,9,13,18,22,27,31,35,40,44,49,53,57,62,66,70,75,79,83,87,91,96,100,104,108,112,116,120,124,127,131,135,139,143,146,150,153,157,160,164,167,171,174,177,180,183,186,190,192,195,198,201,204,206,209,211,214,216,219,221,223,225,227,229,231,233,235,236,238,240,241,243,244,245,246,247,248,249,250,251,252,253,253,254,254,254,255,255,255,255,255,255,255,254,254,254,253,253,252,251,250,249,248,247,246,245,244,243,241,240,238,236,235,233,231,229,227,225,223,221,219,216,214,211,209,206,204,201,198,195,192,190,186,183,180,177,174,171,167,164,160,157,153,150,146,143,139,135,131,128,124,120,116,112,108,104,100,96,91,87,83,79,75,70,66,62,57,53,49,44,40,35,31,27,22,18,13,9,4,0};

void main(void)
{
unsigned char i=0,j=0,k=0;
DDRA=0x00;
DDRB=0x13;
DDRC=0x3F;
DDRD=0x10;

TCCR0=0x69;
TCCR1A=0x81;
TCCR1B=0x09;
TCCR2=0x69;
TCCR3A=0x81;
TCCR3B=0x09;

OCR0=0x00;
OCR1A=0x00;
OCR1B=0x00;
OCR2=0x00;
OCR3AH=0x00;
OCR3AL=0x00;
OCR3BH=0x00;
OCR3BL=0x00;

while (1)
{

for (i=0;i<spc;i++)
{
j=i+8;
k=i+16;
if(i<12)
{
Phase1L=0;
Phase1H=1;
}
else
{
Phase1H=0;
Phase1L=1;
}

if((j>11)&&(j<24))
{
Phase2H=0;
Phase2L=1;
}
else
{
Phase2L=0;
Phase2H=1;
}

if((k>23)&&(k<36))
{
Phase3L=0;
Phase3H=1;
}
else
{
Phase3H=0;
Phase3L=1;
}
OCR0=PWMCodes[(i+1)*(360/spc)];     // Output Phase#1 (OCR0)
OCR3AL=PWMCodes[(j+1)*(360/spc)]; // Output Phase#2 (OCR3A)
OCR2=PWMCodes[(k+1)*(360/spc)];   // Output Phase#3 (OCR2)
};

};
}

Last edited by a moderator:

#### Vbase

##### Full Member level 6
Hello

b) or if there is anything else which might be wrong with the inverter. Please do guide
If the microcontroller outputs are giving delays for on and no delay for off (most PWM do), these delays will cause overlapping by reversing the polarity of the signals by the optocouplers. Overlapping of the gates drives will cause the IGBTs to conduct together and overheat.
Try adding logic inverters or connecting the microcontroller outputs directly to the IR2112.I've illustrated the drive signals to show what I mean. The left shows signals that are never high together to avoid IGBT conducting together. This is normal signals from M/C.
On the right the signals are inverted as your optocoupler does. I marked the area that the IGBTs will conduct together.

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text:
What length of the wire of specific resistance $48×{10}^{-8}\text{\hspace{0.17em}}\Omega \text{\hspace{0.17em}\hspace{0.17em}}m$is needed to make the resistance of 4.2 Ω (diameter of wire = 0.4 mm

(1) 4.1 m

(2) 3.1 m

(3) 2.1 m

(4) 1.1 m

Concept Questions :-

Derivation of Ohm's law
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A strip of copper and another of germanium are cooled from room temperature to 80 K. The resistance of

(1) Each of these increases

(2) Each of these decreases

(3) Copper strip increases and that of germanium decreases

(4) Copper strip decreases and that of germanium increases

Concept Questions :-

Derivation of Ohm's law
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter, the change in the resistance of the wire will be :

(1) 300%

(2) 200%

(3) 100%

(4) 50%

Concept Questions :-

Derivation of Ohm's law
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Express which of the following setups can be used to verify Ohm’s law

 (1) (2) (3) (4)

Concept Questions :-

Derivation of Ohm's law
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

In a hydrogen discharge tube, it is observed that through a given cross-section 3.13 × 1015 electrons are moving from right to left and 3.12 × 1015 protons are moving from left to right. What is the electric current in the discharge tube and what is its direction :

(1) 1 mA towards the right

(2) 1 mA towards left

(3) 2 mA towards left

(4) 2 mA towards the right

Concept Questions :-

Current and current density
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Difficulty Level:

A resistance R is stretched to four times its length. Its new resistance will be

(1) 4 R

(2) 64 R

(3) R/4

(4) 16 R

Concept Questions :-

Derivation of Ohm's law
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High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

What is the resistance of a carbon resistance which has bands of colours brown, black and brown

(1) 100 Ω

(2) 1000 Ω

(3) 10 Ω

(4) 1 Ω

Concept Questions :-

Colour coding of resistors
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Difficulty Level:

The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then :

(1) The resistance will be doubled and the specific resistance will be halved

(2) The resistance will be halved and the specific resistance will remain unchanged

(3) The resistance will be halved and the specific resistance will be doubled

(4) The resistance and the specific resistance, will both remain unchanged

Concept Questions :-

Derivation of Ohm's law
To view Explanation, Please buy any of the course from below.
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Difficulty Level:

The following four wires are made of the same material and are at the same temperature. Which one of them has highest electrical resistance :

(1) Length = 50 cm, diameter = 0.5 mm

(2) Length = 100 cm, diameter = 1 mm

(3) Length = 200 cm, diameter = 2 mm

(4) Length = 300 cm, diameter = 3 mm

Concept Questions :-

Derivation of Ohm's law
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Difficulty Level:

The potential difference between points A and B of the adjoining figure is

(1) $\frac{2}{3}V$

(2) $\frac{8}{9}V$

(3) $\frac{4}{3}V$

(4) 2 V

Concept Questions :-

Combination of resistors
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Difficulty Level:


text:
Lesson plan

# Lesson 1: What are Scaled Copies?

teaches Alabama State Standards 7-17.
teaches Arizona State Standards 7.G.A.1
teaches Common Core State Standards MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards 7.G.A.1 http://corestandards.org/Math/Content/7/G/A/1
teaches Georgia State Standards MGSE7.G.1.
teaches Kansas State Standards 7.G.1.
teaches Minnesota State Standards 7.3.2.3.
teaches Minnesota State Standards 7.3.2.2.
teaches Minnesota State Standards 7.3.2.1.
teaches New York State Standards NY-7.G.1.
teaches Ohio State Standards 7.G.1.b.
teaches Ohio State Standards 7.G.1.
teaches Pennsylvania State Standards CC.2.3.7.A.2.

# Lesson 1: What are Scaled Copies?

This lesson introduces students to the idea of a scaled copy of a picture or a figure. Students learn to distinguish scaled copies from those that are not—first informally, and later, with increasing precision. They may start by saying that scaled copies have the same shape as the original figure, or that they do not appear to be distorted in any way, though they may have a different size. Next, they notice that the lengths of segments in a scaled copy vary from the lengths in the original figure in a uniform way. For instance, if a segment in a scaled copy is half the length of its counterpart in the original, then all other segments in the copy are also half the length of their original counterparts. Students work toward articulating the characteristics of scaled copies quantitatively (e.g., “all the segments are twice as long,” “all the lengths have shrunk by one third,” or “all the segments are one-fourth the size of the segments in the original”), articulating the relationships carefully (MP6) along the way.

The lesson is designed to be accessible to all students regardless of prior knowledge, and to encourage students to make sense of problems and persevere in solving them (MP1) from the very beginning of the course.

Lesson overview

• 1.1 Warm-up: Printing Portraits (10 minutes)
• There is a digital applet in this activity.
• 1.2 Activity: Scaling F (10 minutes)
• There is a digital applet in this activity.
• 1.3 Activity: Pairs of Scaled Polygons (15 minutes)
• Includes "Are you Ready for More?" extension problem
• There is a digital applet in this activity.
• Lesson Synthesis
• 1.4 Cool-down: Scaling L (5 minutes)

Learning goals:

• Describe (orally) characteristics of scaled and non-scaled copies.
• Identify scaled copies of a figure and justify (orally and in writing) that the copy is a scaled copy.

Learning goals (student facing):

• Let’s explore scaled copies.

Learning targets (student facing):

• I can describe some characteristics of a scaled copy.
• I can tell whether or not a figure is a scaled copy of another figure.

Required materials:

• pre-printed slips, cut from copies of the blackline master

Required preparation:

• You will need the Pairs of Scaled Polygons blackline master for this lesson. (See Additional Materials section of this lesson)
• Print and cut slips A–J for the Pairs of Scaled Polygons activity.
• Prepare 1 copy for every 2 students.
• If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.

Glossary:

• scaled copy - A scaled copy is a copy of a figure where every length in the original figure is multiplied by the same number. For example, triangle $$DEF$$ is a scaled copy of triangle $$ABC$$. Each side length on triangle $$ABC$$  was multiplied by 1.5 to get the corresponding side length on triangle $$DEF$$.

• Access the complete Grade 7 glossary.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.


text:
1. ## Implicit Differentiaton

Could somebody please clarify for me what does it mean exactly, in simple terms?

Then i have the following problem i have some questions about:

$y^5 + 3x^2 = sin x - 4y^3$

Then we differentiate...

$(5y^4 . y') + (6x) = (cos x) - (12y^2 . y')$

Ok, now where did that y' come from and what exactly does it mean?

2. Originally Posted by janvdl

Could somebody please clarify for me what does it mean exactly, in simple terms?

Then i have the following problem i have some questions about:

$y^5 + 3x^2 = sin x - 4y^3$

Then we differentiate...

$(5y^4 . y') + (6x) = (cos x) - (12y^2 . y')$

Ok, now where did that y' come from and what exactly does it mean?
the y' is actually short for dy/dx

i think i told you what this notation meant before, dy/dx means "the derivative of y with respect to x"

in implicit differentiation we have to take account of what variable we are differentiating, and what variable we are differentiating with respect to. in the question you posted, you wanted to take the derivative with respect to x. so when we take the derivative of an x term, we attach dx/dx (we took "the derivative of x with respect to x"), however, since derivative notations can function as fractions, the dx's cancel and it becomes 1, so you don't see it, since it's like multiplying by one. however, when we take the derivative of a y term, we attach dy/dx (since we took "the derivative of y with respect to x"), and that doesn't cancel, so it stays. we write y' when it's understood what we are differentiating with respect to.

we need implicit differentiation to differentiate when we have mixed terms that we can't really separate. it would be hard to solve for y and then find y' that way, so we do it implicitly

3. Originally Posted by Jhevon
the y' is actually short for dy/dx

i think i told you what this notation meant before, dy/dx means "the derivative of y with respect to x"

in implicit differentiation we have to take account of what variable we are differentiating, and what variable we are differentiating with respect to. in the question you posted, you wanted to take the derivative with respect to x. so when we take the derivative of an x term, we attach dx/dx (we took "the derivative of x with respect to x"), however, since derivative notations can function as fractions, the dx's cancel and it becomes 1, so you don't see it, since it's like multiplying by one. however, when we take the derivative of a y term, we attach dy/dx (since we took "the derivative of y with respect to x"), and that doesn't cancel, so it stays. we write y' when it's understood what we are differentiating with respect to.

we need implicit differentiation to differentiate when we have mixed terms that we can't really separate. it would be hard to solve for y and then find y' that way, so we do it implicitly
Ok, so every y in the term has to be multiplied with y' ?

By the way Jhevon, u gota be online on msn before i can send you a message. Im using my phone for msn.

4. Originally Posted by janvdl
Ok, so every y in the term has to be multiplied with y' ?

By the way Jhevon, u gota be online on msn before i can send you a message. Im using my phone for msn.
yes. and if you were differentiating with respect to another variable besides x (which you will do when you start related rates) you would have to add x' to all the x terms as well

5. Originally Posted by Jhevon
which you will do when you start related rates...
Thats next years worries Jhevon.
Thanks for the help guys.

6. Originally Posted by janvdl
Thats next years worries Jhevon.
Thanks for the help guys.
actually, related rates is usually the topic taught right after (or very soon after) implicit differentiation, so it's closer than you think

7. Originally Posted by Jhevon
actually, related rates is usually the topic taught right after (or very soon after) implicit differentiation, so it's closer than you think
I'm actually not supposed to be doing this kind of stuff already.


text:
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# how to find interquartile range

In this guide, I will show you how to calculate the interquartile range (IQR) by using Microsoft Excel. It is frequently calculated as a means of identifying what the range of an average performance should be. Points. Example: You have the numbers 7,5,13,1,3,27,18,2,15,6,19,then find out the IQR of this data set? I will also show you how to find the the first (Q1) and third (Q3) quartiles. This calculator calculates the interquartile range from a data set: To calculate the interquartile range from a set of numerical values, enter the observed values in the box. Finding the Mean from … \end{aligned} $$Example 2. The formula for finding the interquartile range is shown below. We can find the interquartile range or IQR in four simple steps: Order the data from least to greatest Find the median Calculate the median of both the lower and upper half of the data The IQR is the difference between the upper and lower medians; Step 1: Order the data . 3. That’s because the interquartile range doesn’t take outliers into account; it cuts them out of the data set by only focusing on the distance within the middle 50 percent of the data (that is, between the 25th and 75th percentiles). That is, IQR = Q 3 – Q 1. The inter-quartile range is$$ \begin{aligned} IQR & = Q_3 - Q_1\\ &= 5 - 3\\ & = 2. The interquartile range (IQR) is the range from the 25 th percentile to the 75 th percentile, or middle 50 percent, of a set of numbers. The last topic we will discuss is the interquartile range which is a measurement of the difference between the third quartile and the first quartile. Enter all the numbers separated by comma. Sort by: Top Voted. IQR = Q 3 - Q 1; How to Find the Minimum. Solution: Step 1: First of all, you have to put the numbers in ascending order. Inter-quartile range. The “interquartile range”, abbreviated “IQR”, is just the width of the box in the box-and-whisker plot. This is the currently selected item. Values must be numeric and separated by commas, spaces or new-line. Formulas to Find Interquartile Range in Google Sheets. 17. The formula used to find out the IQR is as follow, IQR = Q3 – Q1. To do this, we start by finding the median value. Lets see your results! Explain the following terms: measure of spread, range, quartiles, and interquartile range. Wan X, Wang W, Liu J, Tong T. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. It covers the center of the distribution and contains 50% of the observations. Finding range, quartiles, and IQR with frequency tables (grouped and ungrouped tables. I am trying to understand the way to compute iqr (interquartile range). Semi Interquartile Range. 7 11. In this tutorial, I will explain how to find the interquartile range (IQR) in SPSS. The interquartile range is a much better measure of variation than the regular range (maximum value minus minimum value). Problem. Slider. The first quartile, known as Q1, is the value of the 25 th percentile and the third quartile, Q3, is the 75 th percentile. 13. Finding the Interquartile Range 1. IQR measures the difference between 3rd and 1st quartile. The number of values in Q₁ is 5. InterQuartile Range Calculation. Finding the Mean from Dot Plot Moonie Kim. We apply the IQR function to compute the interquartile range of eruptions. IQR = Q3 – Q1. 29. The IQR is the difference between the first (25th percentile) and third (75th percentile) quartiles. Video on how to find the interquartile range from grouped data. 3. You will notice that the fact there is an outlier in this data (60) which has had no bearing on the calculation of the interquartile range. For manually finding the IQR, you must order your dataset from the smallest to the largest number (ascending order). Interquartile Range Calculator Instructions. The following table gives the amount of time (in minutes) spent on the internet each evening by a group of 56 students. An example of the IQR calculation can be seen below. I will also show you how to how to calculate the first and third quartiles for a dataset. Double Stem-Leaf Plot, Box-Whisker Plot Moonie Kim. The interquartile range (IQR), also called as midspread or middle 50%, or technically H-spread is the difference between the third quartile (Q3) and the first quartile (Q1). Enter your data into the text box below, and then hit the "Calculate Percentile" button. 6. The IQR of this set of data is 14-5=9. For the data set: 7, 3, 1, 7, 6, 9, 3, 8, 5, 8, 6, 3, 7, 1, 9 find the: a) median b) lower quartile c) upper quartile d) interquartile range The ordered data set is: This is strangely fun. The IQR tells how spread out the “middle” values are; it can also be used to tell when some of the other values are “too far” from the central value. In this example, we have a data set with an odd number of data points. From the set of data above we have an interquartile range of 3.5, a range of 9 – 2 = 7 and a standard deviation of 2.34. It is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3). What is the IQR? E.g: 1,3,2,6,8,9,10,5. The minimum is the smallest value in a sample data set. 2014;14:135. The interquartile range will be different depending on which method is used to find the lower quartile and the upper quartile. These are often abbreviated to Q1 and Q3 respectively. Statistics assumes that your values are clustered around some central value. In order to determine the interquartile range of the data set, the following steps should be followed: Arrange the data points from lowest to highest Calculate the first quartile position and value Khan Academy is a 501(c)(3) nonprofit organization. When to use five –number summaries and IQRs What you should be able to do: 1. 23. 5 is an odd number, hence the middle value is 5, i.e Q₁ is 5. Variance and standard deviation of a population. Finding the Median from Frequency Table 1 Moonie Kim. The middle of the second half minus the middle of the first half which is going to be equal to eight. Points. This simple tool works out the interquartile range of a set of numbers by calculating the 25th and 75th percentiles, and then subtracting the former from the latter (i.e., IQR = Q3 - Q1). Ask Question Asked 2 years, 1 month ago. 2. Let's do some more of these. How to Find Interquartile Range (Step-by-Step)? Find the interquartile range for the first ten prime numbers. Remember to reorganize the data so that you can find the median values easier. Statistics and Data Finding the Interquartile Range 1. Surface Area of Triangular Prism 1 Moonie Kim. Finding Interquartile Range Introduction Moonie Kim. Score. The IQR is a metric used to represent the midspread of the data. Before finding the interquartile range in R let us look at a simple way to find the interquartile range manually so that you can better understand what the function is doing. Active 1 year, 2 months ago. 5. Quartiles. How do you calculate interquartile range (IQR) correctly using Python? Lets see your results! The interquartile range is 77 – 64 = 13; the interquartile range is the range of the middle 50% of the data.-----With an Odd Sample Size: When the sample size is odd, the median and quartiles are determined in the same way. This video shows how to compute the interquartile range for a set of data. 2. What is the IQR? The interquartile range (IQR) is therefore 18 - 4 = 14. Compute Inter quartile range for the following frequency distribution. 5 10 12 15 (20) 25 27 30 35. The interquartile range of an observation variable is the difference of its upper and lower quartiles. Solution. The "interquartile range", abbreviated "IQR", is just the width of the box in the box-and-whisker plot. Score. Solutions: The first 10 prime numbers are : 2. To find the interquartile range, simply take the upper quartile and subtract the lower quartile: 7.5 - 2.5 = 5. A cumulative frequency diagram is also a good way to find the interquartile range, which is the difference between the upper quartile. Suppose in the previous example, the lowest value (62) were excluded, and the sample size was n=9. Free InterQuartile range (IQR) calculator to find the Inter-quartile range, first quartile, third quartile and median from the set of observed numerical data. The interquartile range (IQR) can be calculated by subtracting quartile 1 from quartile 3 (Q 3 –Q 1),. Semi interquartile range also is defined as half of the interquartile range. Question 2. Interquartile range = Upper Quartile – Lower Quartile = Q 3 – Q 1. Open the slider in a new tab A Formula to Find the Interquartile Range. Finding range, quartiles, and IQR with data lists 4. 19. Find the interquartile range of eruption duration in the data set faithful. Finding the Interquartile Range. Sample Data: Below I am going to provide two different formulas to find the IQR in Docs Sheets. and lower quartile. Let’s look at the step by step calculation of IQR with the help of an example! The median and quartiles are indicated below. To calculate the interquartile range, I just have to find the difference between these two things. Viewed 7k times 3. If we replace the highest value of 9 with an extreme outlier of 100, then the standard deviation becomes 27.37 and the range is 98. Finding the interquartile range. Finding the Interquartile Range 2. For example, how students will typically perform on an exam or the salary levels of a set of employees working in a given industry. Next lesson. where Q 1 is the first quartile and Q 3 is the third quartile of the series. But in Spreadsheet applications, it’s not necessary to keep the numbers in any particular order. As, the above data is already in ascending order, so we don't need to arrange it. So the interquartile range for this first example is going to be 13 minus five. Comparing range and interquartile range (IQR) Interquartile range review. Statistics and Data Finding the Interquartile Range 2. Finding the Mean from Grouped Frequency Table Moonie Kim. Comparing range and interquartile range (IQR) Our mission is to provide a free, world-class education to anyone, anywhere. Uses : The interquartile range has a breakdown point of 25% due to which it is often preferred over the total range. It is a measure of how far apart the middle portion of data spreads in value. Quartiles are the values that divide a list of numbers into quarters: Put the list of numbers in order; Then cut the list into four equal parts; The Quartiles are at the "cuts" Find the IQR by subtracting Q 1 from Q 3. The interquartile range IQR is the range in values from the first quartile Q 1 to the third quartile Q 3. The interquartile range for this data set is 5. Surface Area of Triangular Prism 2 Moonie Kim. Ignore the Population/Sample selector unless you intend to examine the variance or the standard deviation. The IQR can be used as a measure of how spread-out the values are. Q₁ part is- 2,3, 5, 7, 11. BMC Med Res Methodol. The semi-interquartile range is defined as the measures of dispersion. Finding the Interquartile Range. Five –number summaries and interpretation 5. Q1 and Q3 respectively range in values from the smallest value in a tab... Percentile ( Q3 ) quartiles to find the interquartile range for this first example is to! Smallest value in a sample data: below I am going to be equal eight... 5 10 12 15 ( 20 ) 25 27 30 35 7, 11 tutorial I... Q 1 Lower quartile: 7.5 - 2.5 = 5 - 3\\ =. Half minus the middle of the second half minus the middle of the.. It covers the center of the second half minus the middle of the observations ) were excluded, and sample! The 25th percentile ) and third ( Q3 ) quartiles is 5, q₁! Simply take the upper quartile and subtract the Lower quartile = Q 3 – Q 1 set with an number. Population/Sample selector unless you intend to examine the variance or the standard deviation the width the. So the interquartile range for a set of data points ( Q3 ) quartiles is defined half. % of the series how to find interquartile range Population/Sample selector unless you intend to examine the variance or the deviation... Quartile and Q 3 your values are commas, spaces or new-line do you calculate range. 1 from quartile 3 ( Q 3 –Q 1 ), have a data set is,... First example is going to provide two different formulas to find out the IQR subtracting. We apply the IQR is the range of an average performance should be minus middle! 20 ) 25 27 30 35 calculate interquartile range IQR is the how to find interquartile range... 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# Linearly independent skew symmetric complex matrices having the least eigenvalues

Question: Let $A$, $B$ be two $5 \times 5$ (or $7 \times 7$) skew-symmetric complex matrices (i.e. $A^t = -A$), and suppose that $$\forall t,s \in \mathbb{C}, \quad M(t,s):=(tA+sB)^*(tA+sB) \text{ has at most one non-zero eigenvalue } \lambda > 0.$$ Then, how to prove that $A$ and $B$ must in fact be linearly dependent?

Why $5$ or $7$? The reason for the strange numbers is the following: a complex skew-symmetric $n\times n$ matrix $A$ enjoys the Youla decomposition (see the answer to my previous question here: Inequality of Frobenius norm for skew matrices ), which implies that $A^*A$ has (non-negative) eigenvalues coming in pairs. I am interested in when they are as homogeneous as possible, and for odd $n$ this means $n-1$ copies of $\lambda$ and one of $0$. I have a proof of the above fact for $n \geq 9$: First remark that hypothesis and thesis are invariant under common conjugation by a unitary matrix. Let $V(t,s)$ be the $\lambda(t,s)$-eigenspace of $M(t,s)$, and consider $$W = V(1,0) \cap V(0,1) \cap V(1,1) \cap V(1,i).$$ Take an orthonormal basis of $\mathbb{C}^n$ such that the first $n-4$ vectors form a basis for $W$. In this basis, the first $n-4$ column vectors of $A$ are orthogonal, and the same holds for $B$. Some easy computations with $A+B$ and $A+iB$ allows to show that in fact they are all mutually orthogonal, thus giving $2n-8$ orthogonal vectors. Hence $2n - 8 < n$, that is, $n < 8$, unless some of them vanish.

The reason why $3$ is excluded is that the hypothesis is empty in that case, and in fact taking any two linearly independent matrices gives a counterexample. This line of ideas would give the conclusion if one could prove that $W$ has lower codimension than expected (because diagonalizing $A^*A$ and $B^*B$ somehow diagonalizes also $(A+B)^*(A+B)$ and $(A+iB)^*(A+iB)$), but I wasn't able to do that.

Motivation: These strange matrices arise from studying the subspace of the symmetric space $\mathcal{X}_n$ associated to the Lie group $SO^*(2n)$ maximizing the holomorphic sectional curvature. The above "critical" cases are $SO^*(10)$ and $SO^*(14)$. For higher (or even) $n$, this proves that there is no complex plane in any holomorphic tangent space $T_x^{1,0}\mathcal{X}_n$ maximizing the holomorphic sectional curvature. For $n = 3$, $\mathcal{X}_3 \cong \mathbb{B}^3$, the complex $3$-ball, which has constant holomorphic sectional curvature, hence there is indeed a complex $3$-space doing that (the whole tangent space).


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## An equivalent characterization of semigroup congruences

Let $S$ be a semigroup and let $\sigma$ be an equivalence on $S$. Show that $\sigma$ is a congruence on $S$ if and only if for all $a,b,c,d \in S$, if $a \sigma b$ and $c \sigma d$, then $ac \sigma bd$.

Recall that an equivalence on $S$ is a congruence if for all $a,b,c \in S$, if $a \sigma b$ then $ac \sigma bc$ and $ca \sigma cb$.

Suppose $\sigma$ is a congruence, and suppose $a \sigma b$ and $c \sigma d$. Certainly $c \sigma c$ and $b \sigma b$, so we have $ac \sigma bc$ and $bc \sigma bd$. So $ac \sigma bd$.

Conversely, if $a \sigma b$, then we have $c \sigma c$, so that $ac \sigma bc$ and $ca \sigma cb$.


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# ICHEP2018 SEOUL

Jul 4 – 11, 2018
COEX, SEOUL
Asia/Seoul timezone

## Improved determination of d(x) − u(x) flavor asymmetry in the proton by data from the BONuS experiment at JLAB and using an approach by Brodsky, Hoyer, Peterson, and Sakai

Jul 6, 2018, 6:30 PM
2h
COEX, SEOUL

#### COEX, SEOUL

Poster Strong Interactions and Hadron Physics

### Speaker

Maral Salajegheh (1Physics Department, Yazd University, P.O. Box 89195-741, Yazd, Iran)

### Description

The experimental data taken from both Drell-Yan and deep-inelastic scattering (DIS) experiments
suggest a sign-change in $\bar d(x) - \bar u(x)$ flavor asymmetry in the proton at large values of momentum fraction $x$.
In this work, we present a phenomenological study of $\bar d(x) - \bar u(x)$ flavor asymmetry.
First, we extract the $\bar d(x)-\bar u(x)$ distribution using the more recent data from the BONuS experiment at Jefferson Lab on the ratio of neutron to proton structure functions, $F_2^n/F_2^p$,
and show that it undergoes a sing-change and becomes negative at large values of momentum fraction $x$, as expected.
The stability and reliability of our obtained results have been examined by including target mass corrections (TMCs) as well as higher twist (HT) terms which are particularly important
at the large-$x$ region at low Q$^2$.
Then, we calculate the $\bar d(x) - \bar u(x)$ distribution
using the Brodsky, Hoyer, Peterson, and Sakai (BHPS) model and show that if one chooses a mass for the down quark smaller than the one for the up quark it leads to a better description for the Fermilab E866 data. In order to prove this claim, we determine the masses of down and up sea quarks by fitting to the available and up-to-date experimental data for the $\bar d(x)-\bar u(x)$ distribution. In this respect, unlike the previous performed theoretical studies, we have shown that this distribution has a sign-change at $x>0.3$ after evolution to the scale of available experimental data.

### Primary author

Maral Salajegheh (1Physics Department, Yazd University, P.O. Box 89195-741, Yazd, Iran)

### Co-authors

Seyed Mohammad Moosavi Nejad (Yazd univ. IRAN) Dr Hamzeh Khanpour (Institute for Research in Fundamental Sciences (IPM), IRAN)

### Presentation materials

There are no materials yet.


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# Very usefull class, thnak you very much! Let me note that ere...

 SEO Report > All threads > Very usefull class, thnak you very much! Let me note that ere... > (Un) Subscribe thread alerts
Subject: Very usefull class, thnak you very much! Let me note that ere... Package rating comment 2 Laszlo Varkondi 2012-09-05 08:34:21 2012-09-05 08:41:18

Laszlo Varkondi rated this package as follows:

Utility: Good Good Sufficient

 1. Very usefull class, thnak you very much! Let me note that ere... Reply
 Laszlo Varkondi 2012-09-05 08:34:21 Very usefull class, thnak you very much! Let me note that ereg_replace is deprecated and should be changed to preg replace.

 2. Re: Very usefull class, thnak you very much! Let me note that er Reply
 chema garrido 2012-09-05 08:41:18 - In reply to message 1 from Laszlo Varkondi that's correct I will change it. Thanks!


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## 315 Extrapolation of Simulated Scattering Matrix for Large Size Parameter Values

Wednesday, 9 July 2014
Teemu Mäkinen, Finnish Meteorological Institute, Helsinki, Finland; and T. Nousiainen

Handout (454.8 kB)

In order to compute the radiative effects due to atmospheric aerosol particles, their single-scattering properties are needed. For non-spherical, inhomogeneous particles such as mineral dust, solving these properties accurately can be extremely challenging. For particles clearly larger than the wavelength, the computation of these properties require considerable simplifications to the characteristics of the model particles, the physics in the computational method, or both.

In a recent paper[1] light scattering by single, inhomogeneous dust particles was simulated using the discrete-dipole approximation, based on shapes and compositions derived directly from measurements of real particles. The components of the scattering matrix $S$ as a function of the scattering angle $\theta$ were calculated for size parameters $x=2\pi {a}_{eq}∕\lambda$ from 0.5 to 16. Computational cost makes it infeasible to use the approach directly to size parameters much larger than that. Instead of resorting to simplifications to deal with larger particle size parameters, we propose an alternative method based on extrapolation, which may prove to be preferable at least in some cases. A simple extrapolation scheme is described, providing a reasonable solution to extending the range of available values. Within the scope of this abstract, we restrict ourselves to discussing the scheme for component ${S}_{11}$ of the matrix.

A stable extrapolation can only be obtained if the asymptotic behavior of a function is known. Ignoring the extinction effect, the relation $\int d\theta {S}_{11}\left(x,\theta \right)\sim {x}^{2}$ holds for large $x$. However, while the behavior of ${S}_{11}$ for side scattering angles can to a reasonable degree be separated as ${S}_{11}\left(x,\theta \right)=f\left(x\right)g\left(\theta \right)$, the prominent back- and forward-scattering peaks only become asymptotically separated in a different set of coordinates, as ${S}_{11}\left(x,\theta \right)=f\left(xcos\left(\theta \right)\right)g\left(xsin\left(\theta \right)\right)$, necessitating the separate modeling of the peaks.

Here, the extrapolating size parameter functions $f\left(x\right)$ for all features were defined as parametrizable hyperbolic curves with the property ${f}^{\prime }\left(x\right)\to 2$ as $x\to \infty$. The asymptotic shape of $g\left(\theta \right)$ and the parameters of $f\left(x\right)$ for the side-scattering model were represented by spline curves. The back- and forward-scattering peaks were modeled with a series of generalized sinc functions, as ${\sum }_{n}{c}_{n}{sinc}_{n}^{2}\left(qxsin\left(\theta \right)\right)$ where $q$ is a scale parameter. The parameters of this model were determined by fitting it to simulated values for size parameters between 10 and 16. This allows the evaluation of ${S}_{11}$ for arbitrary values of $x$ and $\theta$ as shown in Fig. 1. Since the approach is stable, an error estimate can be derived by comparing the model directly to simulated values.

A similar approach of identifying the features and modeling them separately applies to other components of the scattering matrix, as well. Furthermore, it is possible to take into account theoretical values for the $x\to \infty$ limit, essentially turning the extrapolation into interpolation.

References

[1]   H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen. Single scattering by realistic, inhomogeneous mineral dust particles with stereogrammetric shapes. Atmos. Chem. Phys., 14:143157, 2014.

, 14:143157, 2014.

- Indicates paper has been withdrawn from meeting
- Indicates an Award Winner