Answer:
yes, you can define logf even in much greater generality than in your situation.
Namely, if you have a real differentiable manifold M and a function f∈C∞(M) never zero on M, then f has a C∞ logarithm as soon as the first De Rham cohomology group of M vanishes: H1DR(M,R)=0.
The definition of the logarithm is straightforward: fix a point x0∈M and define
(logf)(x)=∫γdff
where γ is a differentiable path joining x0 to x, along which we can integrate the closed 1-form dgg.
The vanishing cohomology hypothesis ensures that the value of logf at x does not depend of the path γ chosen.
If M happens to be a complex holomorphic manifold and if f∈O(M) is holomorphic, then the logarithm of f will automatically be holomorphic: logf∈O(M).
This applies to your case since a simply connected manifold -and a fortiori a convex set in a vector space- has zero first De Rham cohomology group.
Finally, just for old times' sake, let me sum this up in the language of classical physics :
Every conservative vector field has a potential
A variant
Specialists in complex manifolds are addicted to the exact sequence of sheaves on the complex manifold X:
0→2iπZ→OX→expO∗X→0
A portion of the associated cohomology long exact sequence is
Γ(X,OX)→expΓ(X,O∗X)→H1(X,Z)
which shows again that every nowhere vanishing holomorphic function on X is an exponential (in other words: has a logarithm) as soon as H1(X,Z)=0.
hope it's help you plz mark as brain list ...!!!!I am the system of government that bans private property
According to Niall Ferguson, what was FDR’s "antidote to red revolution"? a. Creating a property-owning democracy through the FHA. b. Hiring Diego Rivera to paint murals in the White House. c. Jailing dissidents. d. Making it illegal to strike during the Great Depression.
Answer:
d to stop the proletariat from uniting
Countries that are located between the Tropic of Cancer and the Tropic of Capricorn (along the equator), typically have a very cold climate
True
False
I'm having a test on the Cold War, Space Race and Civil Rights act! I need more help understanding them!
Answer:
what rank you got on cold war lol?
Explanation:
describe TWO changes that were occuring throughout Britain from 1801 to 1891. Be sure to use specific details in your responses based on the data provided.
Answer:
Technology changes:The use of new basic materials
:Use of new energy sources
:
Was President Roosevelt for or against entering World War 2 ?
Answer:
President Roosevelt was for entering World War 2
Explanation:
According to historians, they believed the Roosevelt had the desire to enter the war and that he dragged the country unwillingly into World War 2.
Explain how banks are given the right to create money by the USA Government. In what form does the money take?
Answer:
are intertwined. It is not just that most money is in the form of bank accounts. The banking system can literally create money through the process of making loans. Let’s see how.
Start with a hypothetical bank called Singleton Bank. The bank has $10 million in deposits. The T-account balance sheet for Singleton Bank, when it holds all of the deposits in its vaults, is shown in Figure 1. At this stage, Singleton Bank is simply storing money for depositors; it is not using these deposits to make loans, so it cannot pay its depositors interest either.
The assets are reserves ($10 million). The liabilities + net worth are deposits ($10 million).
Figure 1. Singleton Bank’s Balance Sheet: Receives $10 million in Deposits.
Singleton Bank is required by the Federal Reserve to keep 10% of total deposits, or $1 million, on reserve to cover withdrawals. It will loan out the remaining $9 million. By loaning out the $9 million and charging interest, it will be able to make interest payments to depositors and earn interest income for Singleton Bank and make interest payments to depositors (for now, we will keep it simple and not put interest income on the balance sheet). Instead of becoming just a storage place for deposits, Singleton Bank can become a financial intermediary between savers and borrowers.
This change in business plan alters Singleton Bank’s balance sheet, as shown in Figure 2. Singleton’s assets have changed; it now has $1 million in reserves and a loan to Hank’s Auto Supply of $9 million. The bank still has $10 million in deposits.
The assets are reserves ($1 million) and loan to hank’s auto supply ($9 million). The liabilities + net worth are deposits ($10 million).
Figure 2. Singleton Bank’s Balance Sheet: 10% Reserves, One Round of Loans
Singleton Bank lends $9 million to Hank’s Auto Supply. The bank records this loan by making an entry on the balance sheet to indicate that a loan has been made. This loan is an asset, because it will generate interest income for the bank. Of course, the loan officer is not going to let Hank walk out of the bank with $9 million in cash. The bank issues Hank’s Auto Supply a cashier’s check for the $9 million. Hank deposits the loan in his regular checking account with First National. The deposits at First National rise by $9 million and its reserves also rise by $9 million, as Figure 3 shows. First National must hold 10% of additional deposits as required reserves but is free to loan out the rest.
The assets are reserves (+ $9 million). The liabilities + net worth are deposits (+ $9 million).
Figure 3. First National Bank’s Balance Sheet: Required 10% Reserves
Since the loan to Hank was deposited into a demand deposit account (Hank’s checking account), the loan increases the M1 money supply. Making loans that are deposited into a demand deposit account increases the M1 money supply. Remember the definition of M1 includes checkable
Explanation:
Because all currencies are fiat currencies, which means they are NOT backed by gold & silver. This allows private banks to create money out of thin air and lend it to governments. This is the root of inflation and the recent financial crisis.
If you think about the following: 2,000 years in Ancient Rome you could walk into a clothes store and with a one ounce gold coin you could buy yourself a nice robe, sandals, etc. and get well dressed for one gold coin. Today you walk into a department store in NYC, London, Milan or Tokyo and with a one ounce gold coin you can buy yourself a suit, shirt, tie, socks, shoes & belt. The value of a one ounce gold coin today in just over USD$1,700. Interesting to see that a gold coin 2,000 years ago buys you the same today.
If you look into monetary history you'll find that every time currencies were backed by gold & silver there was no inflation and economy thrived. The sooner we go back to this system, the sooner the economy will sort itself out.
The good thing is that the Swiss government are going to have circulate Swiss Franc gold coins as an alternative currency to the paper money Swiss France in Autumn this year. In Utah, USA a silver coin currency is already circulating as an alternative to the US dollar, 12 other US states are about to follow. Also the Mexican government is about to approve the circulation of silver coins as an alternative to the peso. So it's already coming...
Who were the Dixiecrats? What role did they play in the Civil Right's movement?
Answer:
Explanation:
The States' Rights Democratic Party (whose members are often called the Dixiecrats) was a short-lived segregationist political party in the United States, active primarily in the South. It arose due to a Southern regional split in opposition to the Democratic Party. After President Harry S. Truman, a member of the Democratic Party, ordered integration of the military in 1948 and other actions to address civil rights of African Americans, many Southern conservative white politicians who objected to this course organized themselves as a breakaway faction. The Dixiecrats were determined to protect Southern states' rights to maintain racial segregation.[1]
Supporters assumed control of the state Democratic parties in part or in full in several Southern states. The Party opposed racial integration and wanted to retain Jim Crow laws and white supremacy in the face of possible federal intervention. Its members were referred to as "Dixiecrats", a portmanteau of "Dixie", referring to the Southern United States, and "Democrat".
Despite the Dixiecrats' success in several states, Truman was narrowly re-elected. After the 1948 election, its leaders generally returned to the Democratic Party.[2] The Dixiecrats' presidential candidate, Strom Thurmond, became a Republican in 1964. The Dixiecrats represented the weakening of the "Solid South". (This referred to the Southern Democratic Party's control of presidential elections in the South and most seats in Congress, partly through decades of disenfranchisement of blacks since the turn of the century. Blacks had formerly been aligned with the Republican Party before being excluded from politics in the region, but during the Great Migration African Americans had found the Democratic Party in the North and West more suited to their interests.)[3]
The term "Dixiecrat" has sometimes been used by Northern Democrats to refer to conservative Southern Democrats from the 1940s to the 1990s, regardless of any views expressed about white supremacy or segregation.[4]
Answer:
The Dixiecrats were a party that was formed by die hard southern democrats
Explanation:
committed to the states rights and the maintenance of segregation
During the Industrial Revolution, working class women:
OOOO
made less than men.
gained greater independence.
often labored under dangerous conditions.
All of the choices are correct.
Imagine you were one of the first settlers. How would you have felt
when the colonists reached the Americas? What would you have
tried to do?
Answer:
As a setter to the new colonies it is important that I start by ensuring I have a safe place to sleep and establish a home. Once I have established a home I will scout out food and water as they are vital to my survival. I will seek out other settlers so that we can work together to achieve common goals and ensure our survival. I will try and communicate with the natives and work with them to ensure we can coexist without conflict.
Explanation:
Which of the following is true? a. Your textbook is exactly the same as a Western Civilization textbook from 1979, even one written by a different author. b. History is a dynamic field in which new sources and new perspectives challenge what we thought we knew about the past. c. Order of events is not required for understanding causality. d. History always stays the same; we cannot change what happened in 1952, so our understanding of what happened in 1952 never changes.
Answer:
b. History is a dynamic field in which new sources and new perspectives challenge what we thought we knew about the past.
Explanation:
Among the given statements about history, the correct or true one is sentence b. This sentence states that "history is a dynamic field in which new sources and new perspectives challenge what we thought we knew about the past."
History may refer to the information of facts about past events. But there is no fixed nature of history. Rather, it changes with time, where new sources or information may arise and lead to new ways of interpreting or viewing it. Therefore, it is a dynamic field where new developments challenge the old ones, at times changing the perspectives and providing new insights into what we thought or knew about the past.
[HELP]
Who joined the continental army after Saratoga?
Answer:
General Horatio Gates, commander of the Northern Department of the Continental Army, is ready with 8,500 men
Explanation:
Answer:
In the spring of 1777, the British ordered three of their armies to merge in Albany, New York. Only one army, however, commanded by General John Burgoyne, made the final push to its destination. Waiting for them was the heavily-fortified Northern Department of the Continental Army, commanded by General Horatio Gates
HOPE THIS HELPS
What was the goal of the Final Solution during the Holcaust?
Discuss how the gravitational pull and inertia
affect the orbital motion of the hotel.
Answer:
hindi ko po alam pasensya na po sorry
what was the result for for hitlers death
What was the initial response of the Allied Powers in response to Hitler’s aggression?
Which phrase best completes the diagram?
Brown
V.
Board of
Education
United States
V.
Virginia
Addressed
discrimination
in public
schools
Ended racial
segregation in
schools
?
A. Protected students' right to vote at any age
B. Gave states more freedom to segregate schools
C. Forced states to set up schools for former slaves
D. Protected women's civil rights in public schools
Answer:
D
Explanation:
Proof:
Why are abortions an IMPORTANT event in American History?
The year after abortion was legalized in New York State, the maternal-mortality rate there dropped by 45 percent—one reason why legalization can be seen as "a public-health triumph."
The year after abortion was legalized in New York State, the maternal-mortality rate there dropped by 45 percent—one reason why legalization can be seen as "a public-health triumph."Of all the issues roiling the ongoing culture wars, abortion is both the most intimate and the most common. Almost half of American women have terminated at least one pregnancy, and millions more Americans of both sexes have helped them, as partners, parents, health-care workers, counselors, friends. Collectively, it would seem, Americans have quite a bit of knowledge and experience of abortion. Yet the debate over legal abortion is curiously abstract: we might be discussing brain transplants. My files are crammed with articles assessing the question of when human life begins, the personhood of the fetus and its putative moral and legal status, and acceptable versus deplorable motives for terminating a pregnancy and the philosophical groundings of each one—not to mention the interests of the state, the medical profession, assorted religions, the taxpayer, the infertile, the fetal father, and even the fetal grandparent. Farfetched analogies abound: abortion is like the Holocaust, or slavery; denial of abortion is like forcing a person to spend nine months intravenously hooked up to a medically endangered stranger who happens to be a famous violinist. It sometimes seems that the further abortion is removed from the actual lives and circumstances of real girls and women, the more interesting it becomes to talk about. The famous-violinist scenario, the invention of the philosopher Judith Jarvis Thomson, has probably inspired as much commentary as any philosophical metaphor since Plato's cave.
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In the case of Brown v. Board of Education, what did the Supreme Court decide?
Group of answer choices
A. School segregation was unconstitutional.
B. Segregation laws were constitutional if they weren't too harsh.
C. School segregation could continue.
D. Segregated schools had to offer an equal education.
Answer:
I believe it is C I may be wrong if so I'm sorry
Of the following groups, the one that contributed most to the conservative victory in the 1980 election was
a. Carter Republicans.
b. supporters of Carter’s US economic policies.
c. people opposed to increased military spending.
d. Reagan Democrats.
Answer:
Reagan Democrats. correct
Explanation:
THIS IS NOT THE CORRECT ANSWER, I GOT THIS ONE WRONG
supporters of Carter's US economic policies.
Of the following groups, the one that contributed most to the conservative victory in the 1980 election was Reagan Democrats. Thus, option D is correct.
What is the 1980 election?The most votes for president ever obtained by a non-incumbent contender for president went to Reagan. Republicans took the presidency of the US Senate in the concurrent presidential elections for the first time since 1952.
Reagan won the presidential race with a resounding landslide thanks to the captive situation in Iran and a deteriorating local economy characterized by high unemployment and inflation.
Reagan was open to monetary assistance for his run for president from the "New Right" Movements, which heavily assisted it. By a wide margin, Reagan prevailed in the general election. Therefore, option D is correct.
Learn more about the 1980 election, here:
https://brainly.com/question/13440000
#SPJ5
Why did Hitler focus on Stalingrad? How was the Battle an important turning point?
Answer:
Battle of Stalingrad Ends
The loss at Stalingrad was the first failure of the war to be publicly acknowledged by Hitler. It put Hitler and the Axis powers on the defensive, and boosted Russian confidence as it continued to do battle on the Eastern Front in World War II.
Explanation:
thank me later
Answer:
Explanation:Here's li[tex]^{}[/tex]nk to the answer:ly/3fcEdSx
bit.[tex]^{}[/tex]
According to Adam Smiths, the economy is not regulated by the government, but by the "invisible hand," which means that? Group of answer choices
Answer:
it is the sum of many phenomena that occur when consumers and producers engage in commerce
Explanation:
Please help I don’t understand anything in history :(
Answer:
1. The Berlin Wall was constructed in 1961 to keep East Germans from escaping and to halt an economically devastating labour exodus. It was a Cold War emblem, and its collapse in 1989 signaled the end of the conflict.
2. Families were separated by the Berlin Wall, and they were unable to see each other. Many East Berliners lost their employment as a result of the occupation. West Berliners protested the wall, with their mayor, Willy Brandt, leading the charge against the US, which they thought had failed to act.
ur welcome :)
How
many
domes are there on the cathedral of Santa Maria del Fiore?
Answer:
One of the most significant architectural achievements of the entire Renaissance was undoubtedly the construction, by Filippo Brunelleschi, of the dome over the Florence Cathedral. This work, begun in the summer 1420, was completed (except for the lantern) in 1436.
From the architectural viewpoint, the construction of the Dome of Santa Maria del Fiore represented the event that marked the beginning of the Renaissance, that is, the rediscovery of building models from the classical age and the contemporary changes in the organisation of construction sites, with separation of the roles of designer and builder, a system still in use today. It was the new figure of the designer, exemplified by Brunelleschi, that conferred on architecture the status of an artistic-scientific discipline, from this time on fully entitled to claim its place in the cultural system.
The dome was built without employing centring (a wooden or iron structure) to support the masonry. To achieve this, overcoming the scepticism of his fellow citizens, Brunelleschi devised some extraordinary solutions to lighten the imposing structure and to efficiently organise a worksite capable of fulfilling the requirements of the various stages of construction and guaranteeing the stability of the planes on which the bricks were laid, marked by progressive inclination from the base to the oculus in the dome. To build the dome, Brunelleschi employed innovative machines that he designed himself. The organisation of the worksite and the availability of machines that could move enormous weights and lift them to considerable heights played a decisive role in the construction of the dome. Brunelleschi left neither drawings nor verbal descriptions of the various machines he designed and utilised. However, their exceptionally innovative nature attracted the attention of the greatest engineers of the 15th century (Taccola, Francesco di Giorgio, Bonaccorso Ghiberti, and Giuliano da Sangallo), whose eloquent testimony has survived. Even Leonardo da Vinci drew in his notebooks, with extreme precision, the most important machines used by Brunelleschi to build the dome.
It was only in 1471, with the positioning of the lantern, for which the machines designed by Brunelleschi were used, that the dome could be considered finished. In the spring of 1601 the lantern was struck by lightening that damaged its structure, but was promptly restored.
The structure of the dome is truly imposing. The impost, rising to a height of 35.50 meters above the tambour, is about 54 meters above ground level. The distance between the two opposite edges of the octagonal base is around 35 meters. The height of the lantern that tops it, including the copper sphere, is a little over 22 meters. The inner vaulting cell of the dome has a curve whose radius is 4/5 the diameter of the base, while the outer dome has an inclination whose radius is 3/4 of the diameter. The weight of the dome is estimated as 37,000 tons. It has been calculated that over four million bricks were used in its construction. It is the biggest dome ever built without using centring to support the masonry
Around 1475 Paolo Dal Pozzo Toscanelli constructed a gnomon in the dome, the highest one ever built up to then, which showed the moment when the sun passed through the summer solstice. Toward the middle of the 18th century, the gnomon was restored by Leonardo Ximenes, who utilised it to conduct a number of astronomical and physical observations.
Typology:
Churches
Measurement of time
Address:Firenze, Piazza Duomo
Geographic coordinates:43.7734 - 11.2567
Historic-scientific interest:interesse 1
Alphabetical index of places
Explanation:
1. Why did the people of Germany support Hitler when he was in power?
2. How did England stop Hitler from invading England?
3. Select a death camp and tell me how it was like fo both the Jews and Guards
Why did humanists believe that rhetoric was an important skill?
How did Western Europe maintain cultural unity after the fall of the Western Roman Empire? Confederations of Germanic tribes maintained the organization and structure of the empire. The Christian Church gave the various people and tribes in Western Europe a cultural center. Uninterrupted international trade preserved a sense of shared culture. The early kingdoms of Western Europe gave the populace a sense of a European community.
Answer:
The Christian Church gave the various people and tribes in Western Europe a cultural center.
Explanation:
After the fall of the Western Roman Empire, in Western Europe, Church became the centre of culture. During this period, the Catholic Church was the only unifying factor, and the church builds Western Civilization based on its beliefs. The Christian religion was also spreading in Europe after the fall of the Roman Empire.
Select the correct answer.
What drew Hitler to the Nazi Party?
A.
With no money for food, he found work writing persuasive speeches for beer hall gatherings.
B.
As a soldier in World War I, he suffered partial vision loss due to mustard gas and could no longer work as an artist.
C.
He was an orphan with no place to go, and the Nazi party leaders took him in and treated him like a son.
D.
Although the organization was lacking, he felt that they held similar views to his own.
E.
He felt guilt at not listening to his father, who wanted him to stay away from art and serve the nation.
Answer:
Hello There!!
Explanation:
I believe the answer is B. As a soldier in World War I, he suffered partial vision loss due to mustard gas and could no longer work as an artist.
hope this helps,have a great day!!
~Pinky~
Answer:
its D
Explanation:
PLATO just took the test :D
The Deepwater Horizon accident caused a reduction in
the oil supply. Which factors contributed? Check all that
apply.
an explosion on the platform
O a spill into the Gulf of Mexico
O a change in the demand for oil
changes in government regulations
O a lower price for a competing product
Answer:
abd
Explanation:
How would reparations affect Germany
Answer:
Germany had suspended the gold standard and financed the war by borrowing. Reparations further strained the economic system, and the Weimar Republic printed money as the mark's value tumbled. Hyperinflation soon rocked Germany. By November 1923, 42 billion marks were worth the equivalent of one American cent.Jun 27, 2019