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Indian Reorganization Act

The Indian Reorganization Act (IRA) of June 18, 1934, or the Wheeler–Howard Act, was U.S. federal legislation that dealt with the status of American Indians in the United States. It was the centerpiece of what has been often called the "Indian New Deal".

The Act also restored to Indians the management of their assets—land and mineral rights—and included provisions intended to create a sound economic foundation for the residents of Indian reservations. Total U.S. spending on Indians averaged $38 million a year in the late 1920s, dropping to an all-time low of $23 million in 1933, and reaching $38 million in 1940.

The IRA was the most significant initiative of John Collier, who was President Franklin D. Roosevelt's Commissioner of the Bureau of Indian Affairs (BIA) from 1933 to 1945. He had long studied Indian issues and worked for change since the 1920s, particularly with the American Indian Defense Association. He intended to reverse the assimilationist policies that had resulted in considerable damage to American Indian cultures and to provide a means for American Indians to re-establish sovereignty and self-government, reduce the losses of reservation lands, and build economic self-sufficiency. He believed that Indian traditional culture was superior to that of modern America and thought it worthy of emulation. His proposals were considered highly controversial, as numerous powerful interests had profited from the sale and management of Native lands. Congress revised Collier's proposals and preserved oversight of tribes and reservations by the Bureau of Indian Affairs within the Department of Interior. Felix S. Cohen, an official at the Department of the Interior Solicitor's Office, was another significant architect of the Indian New Deal who helped draft the 1934 act.

The self-government provisions would automatically go into effect for a tribe unless a clear majority of the eligible Indians voted it down.

Background
At the time the Act passed, it was United States policy to eliminate Indian reservations, dividing the communal territory and allotting 160-acre plots to individual heads of households, to be owned in severalty. Before allotment, reservation territory was not owned in the usual European-American sense, but was reserved for the benefit of entire Indian tribes. The communal benefits were apportioned to tribe members according to tribal law and custom. Generally, Indians held the land in a communal fashion. Non-Indians were not allowed to own land on reservations, which limited the dollar value of the land since there was a smaller market capable of buying it.

The process of allotment started with the General Allotment Act of 1887. By 1934, two-thirds of Indian land had converted to traditional private ownership (i.e., it was owned in fee simple). Most of that had been sold by Indian allottees, often because they could not pay local taxes on the lands they were newly responsible for. The IRA provided a mechanism for the recovery of land that had been previously sold, including land that had been sold to tribal Indians. They would lose individual property under the law.

John Collier was appointed Commissioner of the Indian Bureau (it is now called the Bureau of Indian Affairs, BIA) in April 1933 by President Franklin Delano Roosevelt. He had the full support of his boss, Secretary of the Interior Harold L. Ickes, who was also an expert on Indian issues.

The federal government held land in trust for many tribes. Numerous claims cases had been presented to Congress because of failures in the government's management of such lands. There were particular grievances and claims due to the government's failure to provide for sustainable forestry. The Indian Claims Act of 1946 included a requirement that the Interior Department manage Indian forest resources "on the principle of sustained-yield management." Representative Edgar Howard of Nebraska, co-sponsor of the Act and Chairman of the House Committee on Indian Affairs, explained that the purpose of the provision was "to assure a proper and permanent management of the Indian Forest" under modern sustained-yield methods to "assure that the Indian forests will be permanently productive and will yield continuous revenues to the tribes."

Implementation and results
The act slowed the practice of allotting communal tribal lands to individual tribal members. It did not restore to Indians land that had already been patented to individuals. However, much land at that time was still unallotted or allotted to an individual but still held in trust for that individual by the U.S. government. Because the Act did not disturb existing private ownership of Indian reservation lands, it left reservations as a checkerboard of tribal or individual trust and fee land, which remains the case today.

However, the Act also allowed the U.S. to purchase some of the fee land and restore it to tribal trust status. Due to the Act and other federal courts and government actions, more than two million acres (8,000 km2) of land were returned to various tribes in the first 20 years after passage.

In 1954, the United States Department of the Interior (DOI) began implementing the termination and relocation phases of the Act, which had been added by Congress. These provisions resulted from the continuing interest of some members of Congress in having American Indians assimilate into the majority society. Among other effects, termination resulted in the legal dismantling of 61 tribal nations within the United States and ending their recognized relationships with the federal government. This also ended the eligibility of the tribal nations and their members for various government programs to assist American Indians. Of the "Dismantled Tribes" 46 regained their legal status as indigenous communities.

Constitutional challenges
Since the late 20th century and the rise of Indian activism over sovereignty issues, as well as many tribes' establishment of casino gambling on reservations as a revenue source, the U.S. Supreme Court has been repeatedly asked to address the IRA's constitutionality. A controversial provision of the Act allows the U.S. government to acquire non-Indian land (by voluntary transfer) and convert it to Indian land ("take it into trust"). In doing so, the U.S. government partially removes the land from the state's jurisdiction, allowing activities like casino gambling on the land for the first time. It also exempts the land from state property and other state taxes. Consequently, many state or local governments opposed the IRA and filed lawsuits challenging its constitutionality.

In 1995, South Dakota challenged the authority of the Interior Secretary, under the IRA, to take 91 acre of land into trust on behalf of the Lower Brule Sioux Tribe (based on the Lower Brule Indian Reservation) in South Dakota v. United States Dep't of the Interior, 69 F.3d 878, 881-85 (8th Cir. 1995). The Eighth Circuit Court of Appeals found Section 5 of the IRA to be unconstitutional, ruling that it violated the nondelegation doctrine and that the Secretary of Interior did not have the authority to take the land into trust.

The U.S. Department of the Interior (DOI) sought a U.S. Supreme Court review. But, as DOI was implementing new regulations related to land trusts, the agency asked the Court to remand the case to the lower court for reconsideration with the decision based on the new regulations. The U.S. Supreme Court granted the DOI's petition, vacated the lower court's ruling, and remanded the case back to the lower court.

Justices Antonin Scalia, Sandra Day O'Connor, and Clarence Thomas dissented, stating that "[t]he decision today—to grant, vacate, and remand in light of the Government's changed position—is both unprecedented and inexplicable." They went on, "[W]hat makes today's action inexplicable as well as unprecedented is the fact that the Government's change of legal position does not even purport to be applicable to the present case." Seven months after the Supreme Court's decision to grant, vacate, and remand, the DOI removed the land in question from trust.

In 1997, the Lower Brulé Sioux submitted an amended trust application to the DOI, requesting that the United States take the 91 acre of land into trust on the Tribe's behalf. South Dakota challenged this in 2004 in district court, which upheld DOI's authority to take the land in trust. The state appealed to the Eighth Circuit, but when the court reexamined the constitutionality issue, it upheld the constitutionality of Section 5 in agreement with the lower court. The U.S. Supreme Court denied the State's petition for certiorari. Since then, district and circuit courts have rejected claims of non-delegation by states. The Supreme Court refused to hear the issue in 2008.

In 2008 (before the U.S. Supreme Court heard the Carcieri case below), in MichGO v Kempthorne, Judge Janice Rogers Brown of the D.C. Circuit Court of Appeals wrote a dissent stating that she would have struck down key provisions of the IRA. Of the three circuit courts to address the IRA's constitutionality, Judge Brown is the only judge to dissent on the IRA's constitutionality. The majority opinion upheld its constitutionality. The U.S. Supreme Court did not accept the MichGO case for review, thus keeping the previous precedent in place. Additionally, the First, Eighth, and Tenth Circuits of the U.S. Court of Appeals have upheld the constitutionality of the IRA.

In 2008, Carcieri v Kempthorne was argued before the U.S. Supreme Court; the Court ruled on it in 2009, with the decision called Carcieri v. Salazar. In 1991, the Narragansett Indian tribe bought 31 acre of land. They requested that the DOI take it into trust, which the agency did in 1998, thus exempting it from many state laws. The State was concerned that the tribe would open a casino or tax-free business on the land and sued to block the transfer. The state argued that the IRA did not apply because the Narragansett was not "now under federal jurisdiction" as of 1934, as distinguished from "federally recognized." In fact, the Narragansett had been placed under Rhode Island guardianship since 1709. In 1880, the tribe was illegally pressured into relinquishing its tribal authority to Rhode Island. Some historians disagree that the action was illegal because, although not sanctioned by Congress, it was "desired" by the tribe members. The tribe did not receive federal recognition until 1983, after the 1934 passage of the IRA. The U.S. Supreme Court agreed with the State.

In a challenge to the U.S. DOI's decision to take land into trust for the Oneida Indian Nation in present-day New York, Upstate Citizens for Equality (UCE), New York, Oneida County, Madison County, the town of Verona, the town of Vernon, and others argued that the IRA is unconstitutional. Judge Kahn dismissed UCE's complaint, including the failed theory that the IRA is unconstitutional, on the basis of longstanding and settled law on this issue. The U.S. Court of Appeals for the Second Circuit affirmed the dismissal.

Approval by tribes
Section 18 of the IRA required that members of the affected Indian nation or tribe vote on whether to accept it within one year of the effective date of the act (25 U.S.C. 478) and had to approve it by a majority. There was confusion about who should be allowed to vote on creating new governments, as many non-Indians lived on reservations and many Indians owned no land there, and also over the effect of abstentions. Under the voting rules, abstentions were counted as yes votes, but in Oglala Lakota culture, for example, abstention had traditionally equaled a no vote. The resulting confusion caused disputes on many reservations about the results. When the final results were in, 172 tribes had accepted the act, and 75 had rejected it. The largest tribe, the Navajo, had been badly hurt by the federal Navajo Livestock Reduction Program, which took away half their livestock and jailed dissenters. They strongly opposed the act, the chief promoter John Collier, and the entire Indian New Deal. Historian Brian Dippie notes that the Indian Rights Association denounced Collier as a "dictator" and accused him of a "near reign of terror" on the Navajo reservation. Dippie adds, "[h]e became an object of 'burning hatred' among the very people whose problems so preoccupied him."

Legacy
Historians have mixed reactions to the Indian New Deal. Many praise Collier's energy and his initiative. Kenneth R. Philp praised Collier's Indian New Deal for protecting Indian freedom to engage in traditional religious practices, obtaining additional relief money for reservations, providing a structure for self-government, and enlisting the help of anthropologists who respected traditional cultures. However, he concludes that the Indian New Deal was unable to stimulate economic progress, nor did it provide a usable structure for Indian politics. Philp argues these failures gave ammunition to the return to the previous policy of termination that took place after Collier resigned in 1945. In surveying the scholarly literature, E. A. Schwartz concludes that there is:
 * a near consensus among historians of the Indian New Deal that Collier temporarily rescued Indian communities from federal abuses and helped Indian people survive the Depression but also damaged Indian communities by imposing his own social and political ideas on them.

Collier's reputation among the Indians was mixed—praised by some, vilified by others. He antagonized the Navajo, the largest tribe, as well as the Seneca people, Iroquois, and many others. Anthropologists criticized him for not recognizing the diversity of Native American lifestyles. Hauptman argues that his emphasis on Northern Pueblo arts and crafts and the uniformity of his approach to all tribes are partly explained by his belief that his tenure as Commissioner would be short, meaning that packaging large, lengthy legislative reforms seemed politically necessary.

The Reorganization Act was wide-ranging legislation authorizing tribal self-rule under federal supervision, ending land allotment, and generally promoting measures to enhance tribes and encourage education.

Having described the American society as "physically, religiously, socially, and aesthetically shattered, dismembered, directionless", Collier was later criticized for his romantic views about the moral superiority of traditional society as opposed to modernity. Philp says after his experience at the Taos Pueblo, Collier "made a lifelong commitment to preserve tribal community life because it offered a cultural alternative to modernity....His romantic stereotyping of Indians often did not fit the reality of contemporary tribal life."

The act has helped conserve the communal tribal land bases. Collier supporters blame Congress for altering the legislation proposed by Collier, so that it has not been as successful as possible. On many reservations, its provisions exacerbated longstanding differences between traditionals and those who had adopted more European-American ways. Many Native Americans believe their traditional systems of government were better for their culture.

title: Indian Reorganization Act


text:
Fordney–McCumber Tariff

The Fordney–McCumber Tariff of 1922 was a law that raised American tariffs on many imported goods to protect factories and farms. The US Congress displayed a pro-business attitude in passing the tariff and in promoting foreign trade by providing huge loans to Europe. That, in turn, bought more US goods. However, five years after the passage of the tariff, American trading partners had raised their own tariffs by a significant degree. France raised its tariffs on automobiles from 45% to 100%, Spain raised its tariffs on American goods by 40%, and Germany and Italy raised their tariffs on wheat. According to the American Farm Bureau, farmers lost more than $300 million annually as a result of the tariff.

Background
The first sector of the economy that was hit by a fall in postwar demand was agriculture. During World War I, the American agricultural industry had enjoyed prosperity through the raising of prices, which led to increased output that Americans used to supply Europe.

Farmers borrowed heavily to expand their acreage and had difficulty paying back the loans when prices fell. Some of the postwar problems for American agriculture come from the great surplus of farm goods, which could not be absorbed in the national market as European countries had recovered sufficiently from the war, with their markets no longer requiring large quantities of American agricultural products.

Gross farm income in 1919 amounted to $17.7 billion. By 1921, exports to Europe had plummeted, and farm income fell to $10.5 billion. Other sectors of the economy wanted to avoid a similar fate. The 1920 election put the conservative pro-business and pro-farm Republicans in control of both Congress and the White House.

Hearings were held by Congress and led to the creation of several new tools of protection. One was the scientific tariff to equalize production costs among countries; no country could undercut the prices charged by American companies. The difference of production costs was calculated by the Tariff Commission.

Another was the American selling price; it allowed the President to calculate the duty, which was based on the price of the American price of a good, not the imported good.

The bill also gave the President the power to raise or lower rates on products if that was recommended by the Tariff Commission.

In September 1922, the Fordney–McCumber Tariff bill (named after Joseph Fordney, the chair of the House Ways and Means Committee, and Porter McCumber, the chair of the Senate Finance Committee) was signed by President Warren Harding. In the end, the tariff law raised the American ad valorem tariff rate to an average of about 38.5% for dutiable imports and an average of 14% overall. The tariff was defensive, rather than offensive, as it was determined by the cost of production and the market value.

Economic effects
For agriculture, the tariff raised the purchasing power of the farmers by 2–3%, but other industries raised the price of some farm equipment. In September 1926, economic statistics released by farming groups revealed the rising cost of farm machinery.

For example, the average cost of a harness rose from $46 in 1918 to $75 in 1926, the 14-inch plow rose from $14 to $28, mowing machines rose from $45 to $95, and farm wagons rose from $85 to $150.

That triggered a tariff war against other European countries that traded with the United States. As US tariffs raised, those in other countries followed.

According to the American Farm Bureau, farmers lost more than $300 million annually as a result of the tariff.

Reactions
The tariff was supported by the Republican Party and conservatives and was generally opposed by the Democratic Party, liberals, and progressives. One purpose of the tariff was to help those returning from World War I have greater job opportunities.

Trading partners complained immediately. European nations affected by the war sought access for their exports to the American market to make payments to the war loans from America. Democratic Representative Cordell Hull warned, "Our foreign markets depend both on the efficiency of our production and the tariffs of countries in which we would sell. Our own [high] tariffs are an important factor in each. They injure the former and invite the latter."

Five years after the passage of the tariff, American trading partners had raised their own tariffs by a significant degree. France raised its tariffs on automobiles from 45% to 100%, Spain raised its tariffs on American goods by 40%, and Germany and Italy raised their tariffs on wheat.

In 1928, Henry Ford attacked the tariff and argued that the American automobile industry did not need protection since it dominated the domestic market. Its main interest was now to expand foreign sales.

Some farmers opposed the tariff and blamed it for the agricultural depression. The American Farm Bureau Federation claimed that because of the tariff, the raised price of raw wool cost to farmers $27 million. Democratic Senator David I. Walsh challenged the tariff by arguing that the farmers were net exporters and so did not need protection. They depended on foreign markets to sell their surplus. Walsh pointed out that during the first year of the tariff, the cost of living climbed higher than any other year except during the war. He presented a survey of the Department of Labor in which all of the 32 cities that were assessed had seen an increase in the cost of living. For example, the food costs increased 16.5% in Chicago and 9.4% in New York. Clothing prices rose by 5.5% in Buffalo and 10.2% in Chicago.

Republican Frank W. Murphy, the head of the Minnesota Farm Bureau, also claimed that the problem was not in the world price of farm products but in the things that farmers had to buy.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Fordney–McCumber Tariff


text:
Talk:Mercedes-Benz Group

Who owns Daimler Chrysler?
Interesting to note that the biggest shareholder in DaimlerChrysler is the government of Kuwait - one of the world's leading oil producers - I wouldn't be expecting too many eco-friendly cars from DaimlerChrysler anytime soon. jkm 10:00, 9 November 2006 (UTC)

I dont think the phrase "It is interesting to know..." is appropriate for the first paragraph of an enceclopedia article. Furthermore it indicates your assumption of any influence of Kuwait in DaimlerChryslers eco policy which is of course not proven. Other shareholders are not mentioned in the first paragraph as well. I would suggest to remove it.

 * I would agree it is probably inappropriate for the first paragraph of an encyclopedic article - but then - WHY does it mention in the first paragraph that Daimler Chrysler owns a major stake in EADS? How is that any more appropriate - in fact Daimler Chrysler is in the process of selling down its stake in EADS - so that is a declining interest. As to whether it indicates an assumption to say, "It is interesting to know..." - it does no such thing. Were you aware that the largest shareholder in DaimlerChrysler was the government of Kuwait? I wasn't - until I read that - and I did find that an interesting thing to know. I'm pretty sure that the largest shareholder in General Motors, Ford, Toyota - the other big carmakers - is not a nation reliant on sales of oil, maybe you can answer that question for us all - which entities own the largest stakes in these companies?
 * As to there being no mention of other shareholders in that paragraph - well, there's only 1 largest shareholder in DaimlerChrysler - and that is Kuwait. That is a fact - it can't be denied - why mention a whole bunch of minor shareholders with less that 1% of the company? Again I would say, why is DaimlerChrysler mentioned as a shareholder of EADS then? 155.143.221.252 12:15, 19 November 2006 (UTC)

''The company also owns a substatial share in the asian car company Mitsubishi. ''

Does Daimler own Maserati?
Does this company also own Maserati?

 * No. Fiat owns Maserati. --Robert Merkel 00:42 22 May 2003 (UTC)

 * Do you mean owns as in property, or do Fiats just kick ass compared to Maseratis? ;) --Dante Alighieri 00:44 22 May 2003 (UTC)

 * According to maserati.com, which we should consider authoritative, neither own Maserati. Ferrari owns Maserati, and Ferrari is now I believe independent of Fiat. --Morven 22:42, 23 Oct 2003 (UTC)

 * Nope, Ferrari is indeed owned by Fiat. Therefore, Maserati in turn is owned by Fiat as well. MikeZ 09:28, 6 June 2006 (UTC)

 * To clarify. Fiat as in the car maker does not own them.  The Fiat GROUP owns Fiat Auto and Ferrari.  Ferrari own Maserati.  So Fiat as in "Panda and Punto" doesn't own either.  But the same company owns both the Fiat carmaker and Ferrari.  A small distinction but quite an important one.  Fiat could theoretically sell off "Fiat cars" and not either of their sportscar makers. Duds 2k 17:47, 13 August 2007 (UTC)

RWD
Is it true that Chrysler is going RWD with all its sedans? That seems like a REALLY bad idea IMHO.

 * Not that I'd heard. A few top-of-the-line models are going to be RWD, like the new Chrysler 300C (a car also notable in that the name is considered an insult to the marque's history by aficionados of historic Chryslers.  The next 300 letter-series car should be the 300N) --Morven 22:42, 23 Oct 2003 (UTC)

Also, does anyone think it's worth mentioning the class-action shareholder lawsuit against DC because the supposed "merger of equals" was clearly a takeover? -- stewacide 01:54 14 Jun 2003 (UTC)

 * I think so. It was clearly intended to pull the wool over the eyes of shareholders as well as the US public and regulatory bodies (who would have definitely bridled at the idea of Chrysler being bought out by a foreign manufacturer). --Morven 22:42, 23 Oct 2003 (UTC)

Holdings accuracy?
Does anyone know how accurate the "holdings" statistics are on this page? --Kylen1010 16:20, 18 October 2007 (UTC)

CEO's
Wasn't Dieter Zetsche recently replaced by a Chrysler executive as the CEO of the Chrysler branch? Gerdbrendel 04:11, 8 January 2006 (UTC)

 * His Wiki entry is a little hard to make sense of, but from what I can recall Dieter Zetsche was the CEO of the Chrysler Group up until January 1st 2006, when he succeeded Jürgen Schrempp as Chairman of DaimlerChrysler. Tom LaSorda took over the CEO role of the Chrysler Group the same day. 59.100.153.114 03:50, 23 August 2007 (UTC)

Daimler????
This will seem like a stupid question to many, but I'd love to know; why is the company called DaimlerChrysler? Exactly how does the Daimler name fit in to the firm's product line. I know it must be for historical reasons but surely when Daimler-Benz merged with Chrysler it would have been better to use the Mercedes name in the new title — their most important brand? Chrysler-Benz sounds good! Mark83 22:50, 2 April 2006 (UTC)
 * Well, Daimler refers to Gottlieb Daimler, Benz to Karl Benz, whereas Mercedes is just a brand named after the daughter of an early automobile dealer for the Daimler-Benz cars (see Mercedes (car)). After Wilhelm Maybach the Maybach brand was named. - But I don't have a clue why Daimler was chosen for the new firm's name instead of Benz or both ... DaimlerBenzChrysler, BenzChrysler, DaimlerChrysler ... :-) MikeZ 09:42, 6 June 2006 (UTC)
 * Daimler was the name chosen by Gottfried Daimler and Wihelm Maybach for the original company in Stuttgart, Daimler Motoren Gesellschaft (Daimler Motor Company) which later merged with Benz's company to form Daimler-Benz (changing their car brand from Mercedes to Mercedes-Benz brand in the process). -- Marcika 12:53, 18 June 2006 (UTC)

Unneeded text detected
Someone must have added usless text below the DAX box. I deleted it so that it won't interfere with this article. --megamanfan3 12:58 PM, 27 September 2006 (EDT)

The Takeover?
"In 2003, however, it was alleged by the Detroit News that the "merger of equals" was, in fact, a takeover"

It is not clear which corporation allegedly took over which, can someone please clear it out. Thank you. 74.117.68.16 21:41, 20 February 2007 (UTC)

Daimler took over Chrysler, as every current Chrysler is just a cheap Mercedes in the USA as the majority of the parts are marked Mercedes. Markthemac 21:00, 2 August 2007 (UTC)

The split up
Ok so 'Chrysler has been dumped by Daimler' (to quote evo mag, issue 106). Does this mean that DaimlerChrysler is now a nonexistent corporation to be consigned to the vaults of history, and Daimler and Chrysler are separate entities, (except for Daimler’s minority 20% stake in Chrysler). if this is the case why does the official DaimlerChrysler website still exist... this still the transitional period I guess. But the fact is DaimlerChrysler is now officially over. So shouldn’t a seperate Daimler AG Wikipedia page be created? —Preceding unsigned comment added by JanDaMa (talk • contribs)
 * Might I suggest you don't rely on Evo for your analysis of the corporate history of a company? DaimlerChrysler is not "officially over" - "Daimler AG" will not be adopted until "fall 2007." Mark83 22:49, 3 June 2007 (UTC)
 * The Chrysler Group has not been officially severed from DaimlerChrylser anyway, besides the fact that yes, the DaimlerChrysler name will remain until the stockholder meeting. KansasCity 01:31, 26 July 2007 (UTC)

In light of the finalization of Cerberus Capitals' purchase of an 80%+ stake of Chrysler (see any major financial publication),I think it is most prudent to wait and see what the name of the non-Chrysler portion of that which was Daimler-Chrysler calls itself, and then explore whether the Daimler-Benz and Daimler-Chrysler articles should be merged together. My thought is that they should remain separate, as they are different eras of what really are different corporations with components that were shared. Linked properly, a history of the component the reader is exploring could be learned.mercator079 2039 6 August 2007 (UTC)

Merge with Daimler-Benz
Daimler-Benz should be merged into this article a history section. It is widely known that the merger was actually a buyout of Chrysler, and having Daimler-Benz separate doesn't make sense. Also, when Chrysler is severed, it would really not make sense, as having two separate articles on Daimler would create the impression that there are two different entities named Daimler that have produced Mercedes-Benz vehicles, when in fact it has been the same one with three different names. KansasCity 01:31, 26 July 2007 (UTC)
 * Sounds like a good idea. The new Daimler AG (which will come into being in October) will also need to be incorporated. So what is the best name for a consolidated page? Paul Fisher 10:24, 6 August 2007 (UTC)
 * Surely it would be Daimler AG - the various articles discussed are just different incarnations/names, and as Daimler AG will be the 'current' name I suggest that should be the title. Mark83 10:49, 6 August 2007 (UTC)
 * I'm with Mercator079 (see comment above in the split section) - while the new Daimler AG has many components of the old Daimler Benz they are in fact different companies. I'd go with the idea of a overall history page and then a page for each company. This would provide more information and an idea of the historical flow. Saganaki- 00:11, 7 August 2007 (UTC)
 * I'm flexible Sagakaki, however I'm not entirely clear what you are proposing - what would that article be titled and how/where would we link it in each article? Mark83 13:52, 7 August 2007 (UTC)
 * Perhaps we could modify the Daimler disabmbig page? Make it slightly more historical and include it as a link at the top of all the pages of the related companies including current DaimlerChrysler page and new Daimler AG page we will presumably need to create.Saganaki- 00:35, 8 August 2007 (UTC)

 * The point of this discussion is the fact that Daimler AG is NOT a "new" company; rather, it is the same company founded as Daimler-Benz AG in 1926 and has simply changed its name over the years - to DaimlerChrysler in 1998, and eventually to Daimler in 2007. KansasCity 06:05, 10 August 2007 (UTC)
 * I thought the the topic of this discussion was whether the pages be merged (see the topic header). My view was oppose as they aren't really the same company and that readers would be better served by maintaining the pages separately and linking all the companies together via an overview page.Saganaki- 07:52, 10 August 2007 (UTC)
 * That is the point - to merge the pages because Daimler-Benz/DaimlerChrysler/Daimler are all the same company, with just different names throughout its history. Keeping the pages separate would be illogical - it would essentially keep 3 history pages for only one company, creating a large bit of redundancy. Daimler-Benz/DaimlerChrysler/Daimler are not "separate companies". I don't see how one could come to the conclusion unless believing a corporate name change also means reincorporating the company (which in some cases happens - however, with Daimler-Benz etc., it has yet to happen, leaving the true founding date of Daimler-Benz/DaimlerChrysler/Daimler as 1926). KansasCity 14:04, 10 August 2007 (UTC)
 * I don't think using incorporation necessarily demonstrates continuity, it's a legal device only. A case in point is backlisting where companies allow themselves to be acquired by listed companies in order to get a stock exchange listing. The acquiring listed company in effect becomes the acquired company but no reincorporation occurs. I'd suggest doing as the courts do and parting the veil of the legal fiction of incorporation and looking at the substance of the deal. Using that approach, the new Daimler AG looks like a descendent of Daimler Benz, but is not the same company. That would make the founding date for Daimler AG as 2007. Saganaki- 03:20, 28 August 2007 (UTC)

 * No, it wouldn't. It would be like saying a divorced woman is born again if she drops her surname after a divorce, or gets married and gets a new surname. Daimler has always been with the company since 1926. Just because a company changes its legal name does not mean it is a 'new company'. It would be like saying Macy's, Inc., AT&T Inc., and Verizon Communications were also new companies just because they changed their names. KansasCity 00:10, 29 August 2007 (UTC)
 * Your argument ignores the reality of companies as legal and economic entities. Companies are not people. People can't merge chunks of one another into each other, then spin them off and even reacquire them later. Nowhere in my argument, incidentally, do I sat that a legal name change amounts to a changed company - you have introduced this. My argument is that the entity which bears the name Daimler AG today is structurally different to the entity once known as Daimler Benz, including management, sales coverage and asset holdings. I don't believe you have addressed this issue in any of your arguments. Just because you say they are the same company doesn't make it so. Evidence is required.Saganaki- 00:23, 29 August 2007 (UTC)
 * Well, you have me that DaimlerChrysler was only founded in 1998. Reuters Stock Info. Therefore, I am dropping that merge request. However, I do say that this page should be moved to Daimler AG once the renaming takes effect, since it looks like a reincorporation is not in the works. Plus, Daimler AG will have the same assets following the renaming from DaimlerChrysler. What DaimlerChrysler is now is no different from what it will be the day after it renames itself Daimler AG. KansasCity 03:47, 29 August 2007 (UTC)

Merge
I think it should stay a sperate page because it is a diffrent company 71.249.1.239
 * No, it should not stay separate because Daimler-Benz is the old name of DaimlerChrysler before it bought Chrysler. KansasCity 17:19, 23 August 2007 (UTC)
 * At the very least, I would say from the comments so far that there is insufficient consensus to carry out the merger. Agree on that? Cheers Saganaki- 06:56, 24 August 2007 (UTC)

New Daimler AG page
I think the next step should be the creation of a new Daimler AG page. We'd retain the DaimlerChrysler page but re-craft it as an obituary as per the American Telephone & Telegraph page. Any thoughts? Cheers Saganaki- 09:38, 29 August 2007 (UTC)
 * I agree that this page should be moved to Daimler AG when the renaming occurs, but this page should not become an obituary as DaimlerChrysler will continue to exist under the new name Daimler AG. The assets, corporate structure, etc. it holds this very day will be the same the day following the corporate renaming. The difference between this and American Telephone & Telegraph/AT&T is that American Telephone & Telegraph is legally defunct while AT&T is a separate company; DaimlerChrysler will simply slash the Chrysler name from its corporate name, not become defunct. KansasCity 14:17, 29 August 2007 (UTC)
 * DaimlerChrysler AG will become a defunct legal entity as you have already demonstrated. The new entity, Daimler AG, will contain many of the assets formerly owned by DaimlerChrysler AG, DaimlerChrysler AG itself will become defunct. Daimler AG's corporate structure will certainly not remain the same as DaimlerChrysler, check recent news reports. Also By preserving the DaimlerChrysler AG page, we maintain an notable chapter in automotive history. Saganaki- 00:04, 30 August 2007 (UTC)
 * As I myself have demonstrated, Daimler-Benz AG is most certainly a defunct entity. DaimlerChrysler AG will not become a defunct entity, because that entity will merely be renamed to Daimler AG following stockholder approval. Check Sprint Nextel for a situation where most assets were retained while others were split off, but that doesn't change the fact that Sprint Nextel was founded in 1938 as United Utilities. Hence the reason there is not a separate page for United Utilities, United Telecommunications, etc. because they are all former names of Sprint Nextel Corporation. If the Daimler AG will indeed be a new, separately incorporated entity, then all the more reason to separate that page from DaimlerChrysler. However, if it doesn't reincorporate itself, then DaimlerChrysler should merely be renamed. I cannot comprehend as to why you insist on splitting Daimler AG as an entirely new page keeping DaimlerChrysler intact, as it would create the fiction that DaimlerChrysler is defunct, while it is really going to be renamed. And, no, it would not eliminate a chapter in automotive history from Wikipedia. KansasCity 03:37, 30 August 2007 (UTC)
 * I agree with KansasCity. DaimlerChrysler AG and Cerberus have set up a new company, Chrysler Holding LLC, to hold the Chrysler Corporation. DaimlerChrysler AG is only subject to a name change pending an Extraordinary Shareholders’ Meeting.(MuteJoe 15:12, 31 August 2007 (UTC))
 * Suggested compromise: The new Daimler AG company page should be a fairly long and well referenced article. It will be one of the top 10 automakers and there will be a substantial amount of detail required to flesh out the article and sub articles are likely to be required (see for example the sub articles for the Toyota Motor Corporation page). Why not retain the Daimler Chrysler AG page with some of its existing content as one of these sub-pages linking from the Daimler AG history section? The majority of DaimlerChrysler AG content could be shifted to the Daimler AG page. The rump Daimler Chrysler AG page would contain a potted history of the merger and outline how big the company was at the time? Saganaki- 00:32, 7 September 2007 (UTC)
 * This suggestion is not at all in the best interests in keeping Wikipedia an accurate source of information. It is so amazing that someone cannot seem to understand that a company that was incorporated in 1998 only wants to change its name, not become a 'new' company. To divide up the history sections would still create the impression that DaimlerChrysler is going to be an 'old' company, which it really isn't, since it is only changing its legal name. I have yet to see support for your side, and I think MuteJoe has summed up the position that we've been standing with in the best 3 sentences I have read on this talk page. KansasCity 23:06, 10 September 2007 (UTC)

I don't believe you addressed my suggestions at all in that comment:
 * "This suggestion is not at all in the best interests in keeping Wikipedia an accurate source of information." You don't provide any evidence to back this up.
 * "It is so amazing that someone cannot seem to understand...". Insult? Not sure if that advances your argument either.
 * "a company that was incorporated in 1998 only wants to change its name, not become a 'new' company": Umm, my last comment didn't cover that issue...so straw man? Incorporation date would be irrelevant anyway.
 * "To divide up the history sections would still create the impression that DaimlerChrysler is going to be an 'old' company, which it really isn't". You don't provide evidence to back this up.
 * "I have yet to see support for your side,". Side? thought wikipedia worked by working towards consensus? So far there have only been comments by three users on the latest thread (you, me, MuteJoe), and only you have replied to my last comment where, incidentally, I suggested a change of tack. It's just been you and me so far kid.

So here's my suggestion again if you'd care to respond to it. Many other company articles have separate sub articles where important eras in their histories are fleshed out. They are clearly marked on the main page and on the sub page as subsections of the main article. It's an established way of breaking up large articles. I propose we do the same for DaimlerChrysler as a subsection of Daimler AG. Here are some examples IBM - two related history pages, Ford, General Motors... I can provide more if it's of help to you. What's more we could also provide a link back to Daimler Benz and other earlier iterations of the company, IBM uses that technique for instance. At your service...Saganaki- 01:07, 11 September 2007 (UTC)

Here is my response to this, and my reasoning why this must remain as one page.

 * "This suggestion is not at all in the best interests in keeping Wikipedia an accurate source of information." You don't provide any evidence to back this up.
 * Evidence? Here's your evidence: If we split off the DaimlerChrysler history from the Daimler AG page, it would distort the factual quality of the article, creating the impression in reader's minds that Daimler AG is a totally new, fresh company compared to what it is now as DaimlerChrysler, which is not true at all. The DaimlerChrysler today is the exact same company that will be around under the name Daimler AG the day it changes its name.
 * "a company that was incorporated in 1998 only wants to change its name, not become a 'new' company": Umm, my last comment didn't cover that issue...so straw man? Incorporation date would be irrelevant anyway.
 * How is the incorporation date irrelevent? The incorporation date is what keeps a company's history straight. That is what the founding date of the current AT&T comes down to is its date of incorporation. It is not the same AT&T that was around in 1984, as it was created in 1983 as a Baby Bell. The same can be said for DaimlerChrysler after its renaming. It is not the same Daimler-Benz created in 1926, rather, it was created in 1998 as the holding company for the former assets of Chrysler Corporation and to inherit the assets of Daimler-Benz.

Also, do you realize that if the History of General Motors was included with the main General Motors article, it would make General Motors extremely long? Providing a link to the Daimler-Benz page will suffice, as it is a separate company from what will be renamed Daimler AG. Since DaimlerChrysler was founded in 1998 (legally speaking), its history is less than 10 years now. To split off the history of DaimlerChrysler from the buyout of Chrysler by Daimler to the point where we are now, it would be a truly short article. It would not harm a soul in the world to keep the fact that, at one point, Daimler AG was once named DaimlerChrysler and that it owned all of Chrysler for 9 years. KansasCity 20:03, 16 September 2007 (UTC)

Move to Daimler AG
yesterday the shareholders approved the new name, today it was changed (see www.daimler.com). Please move the article acordingly to this.--79.214.69.57 11:09, 5 October 2007 (UTC)
 * A move request has been lodged at WP:RM. Gr1st 11:22, 5 October 2007 (UTC)
 * done. Agathoclea 11:58, 5 October 2007 (UTC)
 * Category:DaimlerChrysler will need untangling by someone who know what belongs where. Agathoclea 20:51, 5 October 2007 (UTC)

I think it should be separated from Daimler to keep it as reference --  MJKubba  | talk  |  contributions  01:05, 4 November 2007 (UTC)

world's ##'s producer
Daimler is "the world's thirteenth largest car manufacturer. By revenue it is the largest German company." says on http://en.wikipedia.org/wiki/Daimler-Chrysler

Volkswagen is "world's fourth largest car producer after Toyota, GM, and Ford, respectively" says on http://en.wikipedia.org/wiki/Volkswagen

Is there something I am missing about their Math? How can a 13th place have higher revenue than 4th place? Unless they get a lot of money from some kind of viral weaponry sales that I am personally not aware of... ;) —Preceding unsigned comment added by 24.199.204.242 (talk) 01:03, 27 November 2007 (UTC)

 * Yep. You are missing some math. Volkswagens do not cost US$426,000. :)  spryde |  talk  02:44, 27 November 2007 (UTC)
 * Each.  spryde |  talk  02:46, 27 November 2007 (UTC)

Cars account for around 50% of Daimler's revenues, with trucks, vans & buses making up the balance. I suspect that the VW group has a much lower percentage of commercial vehicles in its product mix. Paul Fisher (talk) 13:32, 27 November 2007 (UTC)

My bad :) I did not think other areas of Daimler were that profitable :) Newsweek: 2006 revenues at Volkswagen AG totaled €104.9B, while annual earnings equaled €5.99 per share. from: http://investing.businessweek.com/research/stocks/earnings/earnings.asp?symbol=VOWG.DE

2006 revenues at Daimler AG totaled €151.6B, while annual earnings equaled €3.14 per share. from: http://investing.businessweek.com/research/stocks/earnings/earnings.asp?symbol=DAIGn.DE —Preceding unsigned comment added by EL GhouL (talk • contribs) 21:09, 27 November 2007 (UTC)

SPLIT
The DaimlerChrysler era should be in a separate article. Daimler is not one of the Big-3 North American makers, DC was. 70.51.11.201 (talk) 07:14, 4 September 2008 (UTC)

 * No split - Long and wordy...just needs cleaning up.--Tomtom9041 (talk) 03:50, 24 September 2008 (UTC)
 * Comment this comment was added after this talk page had the rationale removed by an editor previous to Tomtom9041, thus making the reasoning unclear... 76.66.195.159 (talk) 14:45, 12 December 2008 (UTC)
 * It should be split, and it should be WikiProject US, because Daimler-Chrysler is important to the US and Canada. This is the Daimler-Chrysler article, thus IT IS one of the Big 3 articles. 76.66.195.159 (talk) 14:43, 12 December 2008 (UTC)
 * A split should be reconsidered; Daimler-Benz gets its own page, so DaimlerChrysler deserves its own page for a clearer article of the merger saga, and the Daimler AG page could then feature a historical overview of all its predecessors, and more detail of its contemporary situation and current alliances. Warren (talk) 11:08, 22 November 2011 (UTC)

Renault-Nissan and Daimler Alliance
This need a reference that is publicly available: only the first paragraph is available for public reading. It should be changed to something more open.

Here are a few from Reuter:

http://www.reuters.com/article/idUSTOE63605Q20100407 http://www.reuters.com/article/idUSTFA00661720100407 http://www.reuters.com/article/idUSTRE6351C620100407

Bribery?
I was looking up information on the bribery charges. I am not aware of such a news article. I was wondering where the citation of that particular article. I do not seem to see it in the references section.

Roseynose (talk) 01:59, 19 March 2012 (UTC)

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Article lead and Holdings section
The article lead and the Holdings section have info from 2014 and 2015 recpectivelly. I don't know about the other brands/companies but MV Agusta hasnt been a part of Daimler for 7 months, but its still listed there. I left it there, since it says "as of 2015" its technicaly correct. Chris Ssk talk 12:30, 13 June 2018 (UTC)

Merger proposal
I propose to merge Daimler-Benz into Daimler AG. It makes little sense for the Daimler-Benz article, small as it is, to exist on its own when the content would make for a more substantial history section within the Daimler article. Also, the infoboxes would imply that Daimler-Benz is a "defunct" company and Daimler is a company with only 10ish years of history, while the content in the articles (and the Chrysler article for that matter) reads that the company was Daimler-Benz, which was renamed DaimlerChrysler when it acquired Chrysler, and was renamed to simply Daimler when Chrysler was sold off; no defuncts here, just renaming with the times. A merge would streamline many of these discontinuities. WikiRedactor (talk) 21:11, 10 January 2019 (UTC)

Descriptions in hatnote
can you explain the reason why the Daimler Company should be described in the hatnote any differently from how it is described in its own article, that is as a "British motor vehicle manufacturer"? --Deeday-UK (talk) 12:42, 31 May 2020 (UTC)
 * Yes, times have changed and the use of words with them. While I'm here. Why is Mercedes so very very anxious to call itself Daimler ? The British company had a high repute but isn't Mercedes' behaviour a bit over the top? Eddaido (talk) 00:40, 1 June 2020 (UTC)
 * Ok, I think we agree that it's better to keep the hatnote description as clear and consistent with the related article as possible. --Deeday-UK (talk) 20:06, 2 June 2020 (UTC)
 * "Ok, I think we agree" I seem to have missed something here, would you mind explaining. Thanks, Eddaido (talk) 23:23, 2 June 2020 (UTC)
 * you are reverting without engaging in meaningful discussion. I'll ask you again: Daimler Company is described in its article as a "British motor vehicle manufacturer". For clarity and consistency, the best thing to do is to use the same description in the hatnote of this article. Now please state your case as to why describing Daimler Company as an automotive corporation in the hatnote would be preferable to motor vehicle manufacturer  (considering also that it introduces unnecessary repetition). --Deeday-UK (talk) 09:09, 3 June 2020 (UTC)
 * OK I ask you again why do you think I agree? Is that meaningful enough? Eddaido (talk) 09:11, 3 June 2020 (UTC)

I have read the portion of the article concerning the loss of rights to the Daimler name and I see it is plain wrong ! and I see that the explanation given in the article about Gottlieb Daimler has lost all its citations. I have ordered and am waiting on the references supplied by the various editors. Yes, I do think the two businesses were of comparable status and should be described as having been equals. You have not responded to my question to you "Why is Mercedes so very very anxious to call itself Daimler ? The British company had a high repute but isn't Mercedes' behaviour a bit over the top?". Cheers, Eddaido (talk) 09:17, 3 June 2020 (UTC)

 * Eddaido, this is not a forum and your question about Mercedes is off-topic. We are talking about the hatnote here. You say that "the two businesses were of comparable status and should be described as having been equals", so why isn't Daimler Company described the same as Daimler AG in their respective articles? Do you think that is wrong? (oh and please stop rearranging other people's posts as you think appropriate; it doesn't help the discussion) --Deeday-UK (talk) 09:45, 3 June 2020 (UTC)

 * I'd say it was right exactly on topic. We are discussing matters in the hatnote and (incorrectly) covered in portions of the article (possibly intended to be deliberately misleading for readers like DA1). About the description of the businesses I'd say the two articles, Daimler Company and Daimler AG are by different editors. Wouldn't you agree? Its all about "taste" and stuff like that. So what does your "clarity and consistency" relate to? Surely to another article. The best thing for your ideal of "clarity and consistency" is to describe the two equivalent businesses in the same terms within the one article. Eddaido (talk) 10:10, 3 June 2020 (UTC)

Financial Numbers
Example: €2.709 billion

If we read that as a British or American person, we see that as "two point seven oh nine billion euros". But when it comes to Euros, all of the member countries of the Euro currency don't use the period as the decimal place, they use it to indicate a thousand. So €1.234,56 is "one thousand two hundred and thirty four euros and fifty six cents". The comma and period are swapped. So back to that initial example, taken from the numbers on this page. Is that really "two thousand seven hundred and nine billion" ? It's hard to imagine Daimler Benz having numbers that go into the trillions like that. — Preceding unsigned comment added by 2001:A61:5020:6C01:D09F:5113:1AB8:5C80 (talk) 09:48, 21 October 2020 (UTC)

Ownership
English 102.66.72.39 (talk) 11:48, 27 April 2022 (UTC)

if we have on German choice already made

 * 1) becker

Would there be a second from Mercedes

Like a Trump Recovery hs girl?

Quora? 2600:1016:B02C:EAE6:64F0:5FD:26CE:DFA6 (talk) 00:03, 25 November 2022 (UTC)

What form of ownership is Mercedes Benz
Business project 41.114.182.69 (talk) 14:38, 17 August 2023 (UTC)
 * Read the article! "Mercedes-Benz Group AG" Mark83 (talk) 11:09, 18 August 2023 (UTC)

W220 s280 2000 need help
0166563395 malaysia 2402:1980:8251:874:9C7E:D469:C575:41C7 (talk) 15:49, 14 December 2023 (UTC)

Woman architect perspective on what to include in a car
1- built in vacuum 2- a location for tissues box 3- a lication for a woman handbag 4- a location for a small disposable garbage bag i hate when I enter a car with people and I am driving with no place for handbag and tissues box 2001:8F8:1DC7:575C:85F3:61CE:8BBC:ABD5 (talk) 09:33, 3 January 2024 (UTC)

Original Founders of Mercedes-Benz
As specified in the article, Daimler-Benz (aka: Mercedes-Benz) was formed by the merger of Benz & Cie and Daimler Motoren Gesellschaft(DMG) in 1926. Based on his biographical article, it makes sense to list Carl Benz as one of Daimler-Benz's founders because he was still involved in Benz & Cie's management at the time of the merger and ultimately became a director of the newly formed company. Conversely, the same cannot be said of the original founders of DMG, Gottlieb Daimler and Wilhelm Maybach, because both left that company by the time of its merger with Benz & Cie in 1926.

With that being said, does anyone know who was in control of DMG at the time of Daimler-Benz's formation? If so, can you provide sources that corroborate this fact?

Such information is necessary in order to determine who Daimler-Benz's founders were. Thank you. Emiya1980 (talk) 21:23, 3 April 2024 (UTC)

title: Talk:Mercedes-Benz Group


text:
Shepard tone

A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the bass pitch of the tone moving upward or downward, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that seems to continually ascend or descend in pitch, yet which ultimately gets no higher or lower.

Construction
Each square in Figure 1 indicates a tone, with any set of squares in vertical alignment together making one Shepard tone. The color of each square indicates the loudness of the note, with purple being the quietest and green the loudest. Overlapping notes that play at the same time are exactly one octave apart, and each scale fades in and fades out so that hearing the beginning or end of any given scale is impossible. As a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C4 (middle C) and a loud C5 (an octave higher). The next would be a slightly louder C♯4 and a slightly quieter C♯5; the next would be a still louder D4 and a still quieter D5. The two frequencies would be equally loud at the middle of the octave (F♯4 and F♯5), and the twelfth tone would be a loud B4 and an almost inaudible B5 with the addition of an almost inaudible B3. The thirteenth tone would then be the same as the first, and the cycle could continue indefinitely. (In other words, each tone consists of two sine waves with frequencies separated by octaves; the intensity of each is e.g. a raised cosine function of its separation in semitones from a peak frequency, which in the above example would be B4. According to Shepard, "almost any smooth distribution that tapers off to subthreshold levels at low and high frequencies would have done as well as the cosine curve actually employed."

The theory behind the illusion was demonstrated during an episode of the BBC's show Bang Goes the Theory, where the effect was described as "a musical barber's pole".

The scale as described, with discrete steps between each tone, is known as the discrete Shepard scale. The illusion is more convincing if there is a short time between successive notes (staccato or marcato rather than legato or portamento).

Shepard–Risset glissando
Jean-Claude Risset subsequently created a version of the scale where the tones glide continuously, and it is appropriately called the continuous Risset scale or Shepard–Risset glissando. When done correctly, the tone appears to rise (or fall) continuously in pitch, yet return to its starting note. Risset has also created a similar effect with rhythm in which tempo seems to increase or decrease endlessly.

Tritone paradox
A sequentially played pair of Shepard tones separated by an interval of a tritone (half an octave) produces the tritone paradox. Shepard had predicted that the two tones would constitute a bistable figure, the auditory equivalent of the Necker cube, that could be heard ascending or descending, but never both at the same time. In 1986, Diana Deutsch discovered that the perception of which tone was higher depended on the absolute frequencies involved and that an individual would usually hear the same pitch as the highest (this is determined by the absolute pitch of the notes). Interestingly, different listeners may perceive the same pattern as being either ascending or descending, depending on the language or dialect of the listener (Deutsch, Henthorn, and Dolson found that native speakers of Vietnamese, a tonal language, heard the tritone paradox differently from Californians who were native speakers of English).

Perpetual melody
Pedro Patricio observed in 2012 that, by using a Shepard tone as a sound source and applying it to a melody, he could reproduce the illusion of a continuously ascending or descending movement characteristic of the Shepard Scale. Regardless of the tempo and the envelope of the notes, the auditory illusion is effectively maintained. The uncertainty of the scale the Shepard tones pertain allows composers to experiment with deceiving and disconcerting melodies.

Examples

 * James Tenney's For Ann (rising) consists entirely of a Shepard tone glissando with gradual modulations.
 * A section near the end of Karlheinz Stockhausen's Hymnen incorporates multiple descending Shepard tone glissandos.
 * The ending of The Beatles' "I Am the Walrus" incorporates a Shepard tone with a chord progression built on ascending and descending lines in the bass and strings that line up to create the auditory illusion.
 * The ending of Pink Floyd's "Echoes" from their 1971 album Meddle features an ascending Shepard tone created using a feedback technique involving two tape recorders sharing a single tape, with one set to play and the other to record.
 * Queen's 1976 album A Day at the Races opens and closes with a Shepard tone.
 * In his 1979 book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter explained how Shepard scales could be used on the Canon a 2, per tonos in Bach's Musical Offering (called the Endlessly Rising Canon by Hofstadter ) for making the modulation end in the same pitch instead of an octave higher.
 * In 1995, Ira Braus argued that the final sequence of Franz Liszt's 1885 piano piece Bagatelle sans tonalité could be continued to produce a Shepard scale using Hofstadter's technique.
 * In a 1967 AT&T film by Shepard and E. E. Zajac, a Shepard tone accompanies the ascent of an analogous Penrose stair.
 * In the video game Super Mario 64 (1996) for the Nintendo 64 console, a piece that plays when the player tries to climb the neverending stairs located in the penultimate room of Peach's Castle incorporates a slightly modified Shepard scale played in the background. This auditory illusion complements the spatial loop effect, seemingly giving the impression that the stairs never end.
 * In Godspeed You! Black Emperor's "The Dead Flag Blues" from their 1997 album F♯ A♯ ∞, a section mainly consisting of slide guitar is briefly looped into itself to create a downward Shepard tone.
 * On their 1998 album LP5, English electronic duo Autechre employed a decelerating Risset rhythm for the track "Fold4,Wrap5".
 * Austrian composer Georg Friedrich Haas incorporates Shepard tones at various points in his orchestral piece in vain (2000/02).
 * Christopher Nolan said in an interview that the soundtrack of his 2006 film The Prestige (composed by David Julyan) explores the potential of Shepard tones as a fundamental basis for compositions. This is fully realised in his 2017 film Dunkirk where a Shepard tone is used to create the illusion of an ever increasing moment of intensity across intertwined storylines.
 * In Stephin Merritt's 2007 song "Man of a Million Faces", composed for NPR's "Project Song", the Shepard tone is a key aspect.
 * In the 2008 film The Dark Knight and its 2012 followup The Dark Knight Rises, a Shepard tone was used to create the sound of the Batpod, a motorcycle that the filmmakers did not want to change gear and tone abruptly but to accelerate constantly.
 * The 2009 progressive house song "Leave the World Behind" by Swedish House Mafia features a Shepard tone in the form of an ongoing "riser" to build up the tension throughout the track.
 * In Lucrecia Martel's feature film Zama (2017), there is extensive use of the Shepard tone creating a "loud and shreechy soundscape, in order to achieve closeness to the viewer", according to the director.
 * The 2018 track "Always Ascending" by Franz Ferdinand from the album of the same name features a rising Shepard tone throughout the song. The video for the song echoes the effect, with the camera apparently rising continually throughout.
 * In Sumio Kobayashi's piano work "Unreal Rain", the Shepard tone is entirely used.

title: Shepard tone


text:
Emergency Quota Act

The Emergency Quota Act, also known as the Emergency Immigration Act of 1921, the Immigration Restriction Act of 1921, the Per Centum Law, and the Johnson Quota Act (ch. 8, of May 19, 1921), was formulated mainly in response to the large influx of Southern and Eastern Europeans and restricted their immigration to the United States. Although intended as temporary legislation, it "proved, in the long run, the most important turning-point in American immigration policy" because it added two new features to American immigration law: numerical limits on immigration and the use of a quota system for establishing those limits, which came to be known as the National Origins Formula.

The Emergency Quota Act restricted the number of immigrants admitted from any country annually to 3% of the number of residents from that country living in the United States as of the 1910 Census. That meant that people from Northern and Western Europe had a higher quota and were more likely to be admitted to the US than those from Eastern or Southern Europe or from non-European countries.

However, professionals were to be admitted without regard to their country of origin. Also, no limits were set on immigration from Canada, Newfoundland, Cuba, Mexico, or the countries of Central America and South America or "adjacent islands." The act did not apply to countries with bilateral agreements with the US or to Asian countries listed in the Immigration Act of 1917, known as the Asiatic Barred Zone Act.

The Immigration Act of 1924 reduced the quota to 2% of countries' representation in the 1890 census, when a fairly small percentage of the population was from the regions some regarded as less than desirable. To execute the new quota, a visa system was implemented in 1924. It mandated non-citizens seeking to enter the US to obtain and present a visa obtained from a US embassy or consulate before arriving in the US. The visa regulations were later substantially revised by the Immigration and Nationality Act of 1952 and ultimately replaced by the Immigration and Nationality Act of 1965. Non-citizens of the U.S. who are citizens or nationals of 40 countries are currently exempted from a visa requirement under the Visa Waiver Program.

Immigration inspectors differently handle visa packets depending on whether they are non-immigrant (visitor) or immigrant (permanent admission). Under the original, unmodified law, non-immigrant visas were kept at the ports of entry and were later destroyed, but immigrant visas were sent to the Central Office, in Washington, DC, for processing and filing.

Based on the new formula, the number of new immigrants admitted fell from 805,228 in 1920 to 309,556 in 1921–22. The average annual inflow of immigrants prior to 1921 was 175,983 from Northern and Western Europe and 685,531 from other countries, mainly Southern and Eastern Europe. In 1921, there was a drastic reduction in immigration levels from other countries, principally Southern and Eastern Europe.

The act, sponsored by US Representative Albert Johnson (R-Washington), was passed without a recorded vote in the US House of Representatives and by a vote of 90-2-4 in the US Senate.

The act was revised by the Immigration Act of 1924.

The use of the National Origins Formula continued until it was replaced by the Immigration and Nationality Act of 1965, which introduced a system of preferences, based on immigrants' skills and family relationships with US citizens or US residents.

Quotas by country under successive laws
Listed below are historical quotas on immigration from the Eastern Hemisphere, by country, as applied in given fiscal years ending June 30, calculated according to successive immigration laws and revisions from the Emergency Quota Act of 1921 to the final quota year of 1965. The 1922 and 1925 systems based on dated census records of the foreign-born population were intended as temporary measures, and were replaced by the 1924 Act's National Origins Formula based on the 1920 Census of the total U.S. population, effective July 1, 1929.

title: Emergency Quota Act


text:
Esch–Cummins Act

The Transportation Act, 1920, commonly known as the Esch–Cummins Act, was a United States federal law that returned railroads to private operation after World War I, with much regulation. It also officially encouraged private consolidation of railroads and mandated that the Interstate Commerce Commission (ICC) ensure their profitability. The act was named after Rep. John J. Esch and Sen. Albert B. Cummins.

Background
The United States had entered World War I in April 1917, and the government found that the nation's railroads were not prepared to serve the war effort. On December 26, 1917, President Woodrow Wilson had ordered that U.S. railroads be nationalized in the public interest. This order was implemented through the creation of the United States Railroad Administration. Congress ratified the order in the Railway Administration Act of 1918.

Major provisions

 * Terminated federal control of railroads from March 1, 1920.
 * Authorized the government to make settlements with railroad carriers for matters caused by nationalization, such as compensation and other expenses.
 * Directed the ICC to prepare and adopt a plan for the consolidation of the railway properties of the United States into a limited number of systems. See Ripley Plan to consolidate railroads into regional systems.
 * Granted authority to the ICC to set minimum shipping rates, oversee railroads' financial operations, and regulate acquisitions and mergers.
 * Established procedures for settling labor disputes between railroads and employees. A Railroad Labor Board was created to regulate wages and settle disputes.

Subsequent legislation
Title III of the Esch–Cummins Act, which pertained to labor disputes, was repealed in 1926 by the Railway Labor Act.

title: Esch–Cummins Act


text:
Volstead Act

The National Prohibition Act, known informally as the Volstead Act, was an act of the 66th United States Congress designed to execute the 18th Amendment (ratified January 1919) which established the prohibition of alcoholic drinks. The Anti-Saloon League's Wayne Wheeler conceived and drafted the bill, which was named after Andrew Volstead, chairman of the House Judiciary Committee, who managed the legislation.

Historical context
The Volstead Act had a number of contributing factors that led to its ratification in 1919. For example, the formation of the Anti-Saloon League in 1893. The league used the after effects of World War I to push for national prohibition because there was a lot of prejudice and suspicion of foreigners after WWI. Many reformers used the war to get measures passed and a major example of this was national prohibition. The league was successful in getting many states to ban alcohol prior to 1917 by claiming that to drink was to be pro-German and this had the intended results because many of the major breweries at the time had German names. Additionally, many saloons were immigrant-dominated which further supported the narrative that the Anti-Saloon League was pushing for. Another factor that led to the passage of the Volstead Act was the idea that in order to feed the allied nations there was a greater need for the grain that was being used to make whiskey. Prohibitionists also argued that the manufacture and transportation of liquor was taking away from the needed resources that were already scarce going into WWI. They argued that Congress would have conserved food and coal much earlier had not liquor interests been placed above public welfare. This led to the War Time Prohibition Act in 1918. The case for wartime prohibition was strong and the prohibitionists could use their early successes under the necessities of mobilization to make the change permanent through a constitutional amendment in 1919.

Passage of the Volstead Act
H.R. 6810, was the full name given to the National Prohibition Act, which in short meant, "An act to prohibit intoxicating beverages, and to regulate the manufacture, production, and sale of high-proof spirits for other than beverage purposes, and to ensure an ample supply of alcohol and promote its use in scientific research and in the development of fuel, dye, and other lawful industries." Prohibition was originally proposed by a man by the name of Richmond Hobson, and the proposition was brought to Congress as an amendment to the Constitution. Later, attorney Wayne Wheeler proposed the first version of the bill, which Congress amended many times. President Woodrow Wilson vetoed the bill, Congress overrode his veto, and the bill went through on October 28, 1919. The Volstead Act went into play on January 16, 1920, where it became a challenge for the United States Supreme Court to navigate through. The Volstead Act was presented to help promote the togetherness of federal and state legislation in regulating alcohol.

Content of the Volstead Act
The Volstead Act consists of three main sections: (1) previously enacted war Prohibition, (2) Prohibition as designated by the Eighteenth Amendment, and (3) industrial alcohol use. Before the ratification of the Eighteenth Amendment, the War Time Prohibition Act was approved on November 21, 1918. This was passed to conserve grain by prohibiting its usage in the production of spirits. Title II of the Volstead Act, "Permanent National Prohibition," which was defined as "intoxicating beverages" containing greater than 0.5 percent alcohol. This section also set forth the fines and jail sentences for the manufacture, sale and movement of alcoholic beverages, as well as set forth regulations that described those who would enforce the laws, what search and seizure powers law enforcement had or did not have, as well as how adjunction of violations would be in place, among many others. Despite these strict laws on alcohol commerce, there were numerous ways in which the possession and personal use of alcohol remained legal under the Volstead Act. It was in fact legal to own alcoholic beverages that were obtained before the Prohibition, as well as serve these types of drinks to family or guests in the home with proof of purchase on hand. This allowed numerous individuals, specifically those who were wealthy to stockpile these beverages before Prohibition. Alcohol that was used for medical purposes remained legal under the Volstead Act. Physicians were limited on what they could prescribe their patients. They were allowed one pint of spirits every ten days, a restriction the American Medical Associate opposed for being inadequate. Pastors, priests, ministers, rabbis and others who practiced religious actions could acquire a permit to provide alcohol for sacramental purposes only. Alcohol for any industrial purposes were allowed in Title III of the Volstead Act, titled "Industrial Purposes."

Enforcement and impact
The production, importation, and distribution of alcoholic beverages—once the province of legitimate business—was taken over by criminal gangs, which fought each other for market control in violent confrontations, including murder. Major gangsters, such as Omaha's Tom Dennison and Chicago's Al Capone, became rich, and were admired locally and nationally. Enforcement was difficult because the gangs became so rich that they were often able to bribe underpaid and understaffed law-enforcement personnel, and afford expensive lawyers. Many citizens were sympathetic to bootleggers, and respectable citizens were lured by the romance of illegal speakeasies, also called "blind tigers." The loosening of social mores during the 1920s included popularizing the cocktail and the cocktail party among higher socioeconomic groups. Those inclined to help authorities were often intimidated and even murdered. In several major cities – notably those that served as major points of liquor importation, including Chicago and Detroit – gangs wielded significant political power. A Michigan State Police raid on Detroit's Deutsches Haus once netted the mayor, the sheriff, and the local congressman.

Prohibition came into force at 12:00:01 am on January 17, 1920, and the first documented infringement of the Volstead Act occurred in Chicago on January 17 at 12:59 am. According to police reports, six armed men stole $100,000 worth of "medicinal" whiskey from two freight-train cars. This trend in bootlegging liquor created a domino effect among criminals across the United States. Some gang leaders had been stashing liquor months before the Volstead Act was enforced. The ability to sustain a lucrative business in bootlegging liquor was largely helped by the minimal police surveillance at the time. There were only 134 agents designated by the Prohibition Unit to cover all of Illinois, Iowa, and parts of Wisconsin. According to Charles C. Fitzmorris, Chicago's chief of police during the beginning of the Prohibition period, "Sixty percent of my police [were] in the bootleg business."

Section 29 of the Act allowed 200 gallons (the equivalent of about 1000 750-ml bottles) of "non-intoxicating cider and fruit juice" to be made each year at home. Initially "intoxicating" was defined as exceeding 0.5% alcohol by volume, but the Bureau of Internal Revenue struck that down in 1920, effectively legalizing home winemaking. For beer, however, the 0.5% limit remained until 1933. Some vineyards embraced the sale of grapes for making wine at home. Zinfandel grapes were popular among home winemakers living near vineyards, but their tight bunches left their thin skins vulnerable to rot from rubbing and abrasion on the long journey to East Coast markets. The thick skins of Alicante Bouschet were less susceptible to rot, so that and similar varieties were widely planted for the home winemaking market.

The Act contained a number of exceptions and exemptions. Many of them were used to evade the law's intended purpose. For example, the Act allowed a physician to prescribe whiskey for his patients but limited the amount that could be prescribed. Subsequently, the House of Delegates of the American Medical Association voted to submit to Congress a bill to remove the limit on the amount of whiskey that could be prescribed and questioned the ability of a legislature to determine the therapeutic value of any substance. Vine-Glo was produced ostensibly to let people make grape juice from concentrate but it included a warning on its packaging telling people how to make wine from it.

According to Neely, "The Act called for trials for anyone charged with an alcohol-related offense, and juries often failed to convict. Under the state of New York's Mullan–Gage Act, a short-lived local version of the Volstead Act, the first 4,000 arrests led to just six convictions and not one jail sentence".

While the production, transport and sale of intoxicating liquor was illegal, their purchase was ruled legal in United States v. Norris.

Repeal
Prohibition lost support because ignoring the law gained increasing social acceptance and organized crime violence increased. By 1933, public opposition to prohibition had become overwhelming. In March of that year, Congress passed the Cullen–Harrison Act, which legalized "3.2 beer" (i.e. beer containing 3.2% alcohol by weight or 4% by volume) and wines of similarly low alcohol content, rather than the 0.5% limit defined by the original Volstead Act.

In February 1933, Congress passed the Blaine Act, a proposed constitutional amendment to repeal the Eighteenth Amendment to end prohibition. On December 5, 1933, Utah became the 36th state to ratify the Twenty-first Amendment, which repealed the Eighteenth Amendment, voiding the Volstead Act and restoring control of alcohol to the states. All states either made alcohol legal, or passed control over alcohol production and consumption to the counties and provinces they comprise. That led to the creation of dry counties, most of which are in the South.

title: Volstead Act


text:
Harmonic function

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function $$f\colon U \to \mathbb R,$$ where $U$ is an open subset of $\mathbb R^n,$ that satisfies Laplace's equation, that is, $$ \frac{\partial^2f}{\partial x_1^2} + \frac{\partial^2f}{\partial x_2^2} + \cdots + \frac{\partial^2f}{\partial x_n^2} = 0$$ everywhere on $U$. This is usually written as $$ \nabla^2 f = 0 $$ or $$\Delta f = 0$$

Etymology of the term "harmonic"
The descriptor "harmonic" in the name harmonic function originates from a point on a taut string which is undergoing harmonic motion. The solution to the differential equation for this type of motion can be written in terms of sines and cosines, functions which are thus referred to as harmonics. Fourier analysis involves expanding functions on the unit circle in terms of a series of these harmonics. Considering higher dimensional analogues of the harmonics on the unit n-sphere, one arrives at the spherical harmonics. These functions satisfy Laplace's equation and over time "harmonic" was used to refer to all functions satisfying Laplace's equation.

Examples
Examples of harmonic functions of two variables are:
 * The real or imaginary part of any holomorphic function.
 * The function $$\,\! f(x, y) = e^{x} \sin y;$$ this is a special case of the example above, as $$f(x, y) = \operatorname{Im}\left(e^{x+iy}\right) ,$$ and $$e^{x+iy}$$ is a holomorphic function. The second derivative with respect to x is $$\,\! e^{x} \sin y,$$ while the second derivative with respect to y is $$\,\! -e^{x} \sin y.$$
 * The function $$\,\! f(x, y) = \ln \left(x^2 + y^2\right)$$ defined on $$\mathbb{R}^2 \smallsetminus \lbrace 0 \rbrace .$$ This can describe the electric potential due to a line charge or the gravity potential due to a long cylindrical mass.

Examples of harmonic functions of three variables are given in the table below with $$r^2=x^2+y^2+z^2:$$

 * {| class="wikitable"

! Function !! Singularity
 * align=center|$$\frac{1}{r}$$
 * Unit point charge at origin
 * align=center|$$\frac{x}{r^3}$$
 * x-directed dipole at origin
 * align=center|$$-\ln\left(r^2 - z^2\right)\,$$
 * Line of unit charge density on entire z-axis
 * align=center|$$-\ln(r + z)\,$$
 * Line of unit charge density on negative z-axis
 * align=center|$$\frac{x}{r^2 - z^2}\,$$
 * Line of x-directed dipoles on entire z axis
 * align=center|$$\frac{x}{r(r + z)}\,$$
 * Line of x-directed dipoles on negative z axis
 * }
 * align=center|$$\frac{x}{r^2 - z^2}\,$$
 * Line of x-directed dipoles on entire z axis
 * align=center|$$\frac{x}{r(r + z)}\,$$
 * Line of x-directed dipoles on negative z axis
 * }
 * }

Harmonic functions that arise in physics are determined by their singularities and boundary conditions (such as Dirichlet boundary conditions or Neumann boundary conditions). On regions without boundaries, adding the real or imaginary part of any entire function will produce a harmonic function with the same singularity, so in this case the harmonic function is not determined by its singularities; however, we can make the solution unique in physical situations by requiring that the solution approaches 0 as r approaches infinity. In this case, uniqueness follows by Liouville's theorem.

The singular points of the harmonic functions above are expressed as "charges" and "charge densities" using the terminology of electrostatics, and so the corresponding harmonic function will be proportional to the electrostatic potential due to these charge distributions. Each function above will yield another harmonic function when multiplied by a constant, rotated, and/or has a constant added. The inversion of each function will yield another harmonic function which has singularities which are the images of the original singularities in a spherical "mirror". Also, the sum of any two harmonic functions will yield another harmonic function.

Finally, examples of harmonic functions of $n$ variables are:

 * The constant, linear and affine functions on all of $\mathbb R^n$ (for example, the electric potential between the plates of a capacitor, and the gravity potential of a slab)
 * The function $$ f(x_1, \dots, x_n) = \left({x_1}^2 + \cdots + {x_n}^2\right)^{1-n/2}$$ on $$\mathbb{R}^n \smallsetminus \lbrace 0 \rbrace$$ for $n > 2$.

Properties
The set of harmonic functions on a given open set $U$ can be seen as the kernel of the Laplace operator $Δ$ and is therefore a vector space over $\mathbb R\! :$ linear combinations of harmonic functions are again harmonic.

If $f$ is a harmonic function on $U$, then all partial derivatives of $f$ are also harmonic functions on $U$. The Laplace operator $Δ$ and the partial derivative operator will commute on this class of functions.

In several ways, the harmonic functions are real analogues to holomorphic functions. All harmonic functions are analytic, that is, they can be locally expressed as power series. This is a general fact about elliptic operators, of which the Laplacian is a major example.

The uniform limit of a convergent sequence of harmonic functions is still harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider the sequence on $(-\infty,0) \times \mathbb R$ defined by $f_n(x,y) = \frac 1 n \exp(nx)\cos(ny);$ this sequence is harmonic and converges uniformly to the zero function; however note that the partial derivatives are not uniformly convergent to the zero function (the derivative of the zero function). This example shows the importance of relying on the mean value property and continuity to argue that the limit is harmonic.

Connections with complex function theory
The real and imaginary part of any holomorphic function yield harmonic functions on $\mathbb R^2$ (these are said to be a pair of harmonic conjugate functions). Conversely, any harmonic function $u$ on an open subset $Ω$ of $\mathbb R^2$ is locally the real part of a holomorphic function. This is immediately seen observing that, writing $$z = x + iy,$$ the complex function $$g(z) := u_x - i u_y$$ is holomorphic in $Ω$ because it satisfies the Cauchy–Riemann equations. Therefore, $g$ locally has a primitive $f$, and $u$ is the real part of $f$ up to a constant,  as $ux$ is the real part of $$f' = g.$$

Although the above correspondence with holomorphic functions only holds for functions of two real variables, harmonic functions in $n$ variables still enjoy a number of properties typical of holomorphic functions. They are (real) analytic; they have a maximum principle and a mean-value principle; a theorem of removal of singularities as well as a Liouville theorem holds for them in analogy to the corresponding theorems in complex functions theory.

Properties of harmonic functions
Some important properties of harmonic functions can be deduced from Laplace's equation.

Regularity theorem for harmonic functions
Harmonic functions are infinitely differentiable in open sets. In fact, harmonic functions are real analytic.

Maximum principle
Harmonic functions satisfy the following maximum principle: if $K$ is a nonempty compact subset of $U$, then $f$ restricted to $K$ attains its maximum and minimum on the boundary of $K$. If $U$ is connected, this means that $f$ cannot have local maxima or minima, other than the exceptional case where $f$ is constant. Similar properties can be shown for subharmonic functions.

The mean value property
If $B(x, r)$ is a ball with center $x$ and radius $r$ which is completely contained in the open set $$\Omega \subset \R^n,$$ then the value $u(x)$ of a harmonic function $$u: \Omega \to \R$$ at the center of the ball is given by the average value of $u$ on the surface of the ball; this average value is also equal to the average value of $u$  in the interior of the ball. In other words, $$u(x) = \frac{1}{n\omega_n r^{n-1}}\int_{\partial B(x,r)} u\, d\sigma = \frac{1}{\omega_n r^n}\int_{B(x,r)} u\, dV$$ where $ωn$ is the volume of the unit ball in $n$ dimensions and $σ$ is the $(n − 1)$-dimensional surface measure.

Conversely, all locally integrable functions satisfying the (volume) mean-value property are both infinitely differentiable and harmonic.

In terms of convolutions, if $$\chi_r := \frac{1}{|B(0, r)|}\chi_{B(0, r)} = \frac{n}{\omega_n r^n}\chi_{B(0, r)}$$ denotes the characteristic function of the ball with radius $r$ about the origin, normalized so that $\int_{\R^n}\chi_r\, dx = 1,$ the function $u$ is harmonic on $Ω$ if and only if $$u(x) = u*\chi_r(x)\;$$ as soon as $$B(x,r) \subset \Omega.$$

Sketch of the proof. The proof of the mean-value property of the harmonic functions and its converse follows immediately observing that the non-homogeneous equation, for any $0 < s < r$ $$\Delta w = \chi_r - \chi_s\;$$ admits an easy explicit solution $wr,s$ of class $C^{1,1}$ with compact support in $B(0, r)$. Thus, if $u$ is harmonic in $Ω$ $$0=\Delta u * w_{r,s} = u*\Delta w_{r,s}= u*\chi_r - u*\chi_s\;$$ holds in the set $Ωr$ of all points $x$ in $Ω$ with $$\operatorname{dist}(x,\partial\Omega) > r.$$

Since $u$ is continuous in $Ω$, $$u * \chi_s$$ converges to $u$ as $s → 0$ showing the mean value property for $u$ in $Ω$. Conversely, if $u$ is any $$L^1_{\mathrm{loc}}\;$$ function satisfying the mean-value property in $Ω$, that is, $$u*\chi_r = u*\chi_s\;$$ holds in $Ωr$ for all $0 < s < r$ then, iterating $m$ times the convolution with $χr$ one has: $$u = u*\chi_r = u*\chi_r*\cdots*\chi_r\,,\qquad x\in\Omega_{mr},$$ so that $u$ is $$C^{m-1}(\Omega_{mr})\;$$ because the $m$-fold iterated convolution of $χr$ is of class $$C^{m-1}\;$$ with support $B(0, mr)$. Since $r$ and $m$ are arbitrary, $u$ is $$C^{\infty}(\Omega)\;$$ too. Moreover, $$\Delta u * w_{r,s} = u*\Delta w_{r,s} = u*\chi_r - u*\chi_s = 0\;$$ for all $0 < s < r$ so that $Δu = 0$ in $Ω$ by the fundamental theorem of the calculus of variations, proving the equivalence between harmonicity and mean-value property.

This statement of the mean value property can be generalized as follows: If $h$ is any spherically symmetric function supported in $B(x, r)$ such that $\int h = 1,$ then $$u(x) = h * u(x).$$ In other words, we can take the weighted average of $u$ about a point and recover $u(x)$. In particular, by taking $h$ to be a $C^{∞}$ function, we can recover the value of $u$ at any point even if we only know how $u$ acts as a distribution. See Weyl's lemma.

Harnack's inequality
Let $$V \subset \overline{V} \subset \Omega$$ be a connected set in a bounded domain $Ω$. Then for every non-negative harmonic function $u$, Harnack's inequality $$\sup_V u \le C \inf_V u$$ holds for some constant $C$ that depends only on $V$ and $Ω$.

Removal of singularities
The following principle of removal of singularities holds for harmonic functions. If $f$ is a harmonic function defined on a dotted open subset $$\Omega \smallsetminus \{x_0\}$$ of $\R^n$, which is less singular at $x0$ than the fundamental solution (for $n > 2$), that is $$f(x)=o\left( \vert x-x_0 \vert^{2-n}\right),\qquad\text{as }x\to x_0,$$ then $f$ extends to a harmonic function on $Ω$ (compare Riemann's theorem for functions of a complex variable).

Liouville's theorem
Theorem: If $f$ is a harmonic function defined on all of $\R^n$ which is bounded above or bounded below, then $f$ is constant.

(Compare Liouville's theorem for functions of a complex variable).

Edward Nelson gave a particularly short proof of this theorem for the case of bounded functions, using the mean value property mentioned above: "Given two points, choose two balls with the given points as centers and of equal radius. If the radius is large enough, the two balls will coincide except for an arbitrarily small proportion of their volume. Since $f$ is bounded, the averages of it over the two balls are arbitrarily close, and so $f$ assumes the same value at any two points." The proof can be adapted to the case where the harmonic function $f$ is merely bounded above or below. By adding a constant and possibly multiplying by –1, we may assume that $f$ is non-negative. Then for any two points $x$ and $y$, and any positive number $R$, we let $$r=R+d(x,y).$$ We then consider the balls $BR(x)$ and $Br(y)$ where by the triangle inequality, the first ball is contained in the second.

By the averaging property and the monotonicity of the integral, we have $$f(x)=\frac{1}{\operatorname{vol}(B_R)}\int_{B_R(x)}f(z)\, dz\leq \frac{1}{\operatorname{vol}(B_R)} \int_{B_r(y)}f(z)\, dz.$$ (Note that since $vol BR(x)$ is independent of $x$, we denote it merely as $vol BR$.) In the last expression, we may multiply and divide by $vol Br$ and use the averaging property again, to obtain $$f(x)\leq \frac{\operatorname{vol}(B_r)}{\operatorname{vol}(B_R)}f(y).$$ But as $$R\rightarrow\infty ,$$ the quantity $$\frac{\operatorname{vol}(B_r)}{\operatorname{vol}(B_R)} = \frac{\left(R+d(x,y)\right)^n}{R^n}$$ tends to 1. Thus, $$f(x)\leq f(y).$$ The same argument with the roles of $x$ and $y$ reversed shows that $$f(y)\leq f(x)$$, so that $$f(x) = f(y).$$

Another proof uses the fact that given a Brownian motion $Bt$ in $\R^n,$ such that $$B_0 = x_0,$$ we have $$E[f(B_t)] = f(x_0)$$ for all $t ≥ 0$. In words, it says that a harmonic function defines a martingale for the Brownian motion. Then a probabilistic coupling argument finishes the proof.

Weakly harmonic function
A function (or, more generally, a distribution) is weakly harmonic if it satisfies Laplace's equation $$\Delta f = 0\,$$ in a weak sense (or, equivalently, in the sense of distributions). A weakly harmonic function coincides almost everywhere with a strongly harmonic function, and is in particular smooth. A weakly harmonic distribution is precisely the distribution associated to a strongly harmonic function, and so also is smooth. This is Weyl's lemma.

There are other weak formulations of Laplace's equation that are often useful. One of which is Dirichlet's principle, representing harmonic functions in the Sobolev space $H^{1}(Ω)$ as the minimizers of the Dirichlet energy integral $$J(u):=\int_\Omega |\nabla u|^2\, dx$$ with respect to local variations, that is, all functions $$u\in H^1(\Omega)$$ such that $$J(u) \leq J(u+v)$$ holds for all $$v\in C^\infty_c(\Omega),$$ or equivalently, for all $$v\in H^1_0(\Omega).$$

Harmonic functions on manifolds
Harmonic functions can be defined on an arbitrary Riemannian manifold, using the Laplace–Beltrami operator $Δ$. In this context, a function is called harmonic if $$\ \Delta f = 0.$$ Many of the properties of harmonic functions on domains in Euclidean space carry over to this more general setting, including the mean value theorem (over geodesic balls), the maximum principle, and the Harnack inequality. With the exception of the mean value theorem, these are easy consequences of the corresponding results for general linear elliptic partial differential equations of the second order.

Subharmonic functions
A $C^{2}$ function that satisfies $Δf ≥ 0$ is called subharmonic. This condition guarantees that the maximum principle will hold, although other properties of harmonic functions may fail. More generally, a function is subharmonic if and only if, in the interior of any ball in its domain, its graph lies below that of the harmonic function interpolating its boundary values on the ball.

Harmonic forms
One generalization of the study of harmonic functions is the study of harmonic forms on Riemannian manifolds, and it is related to the study of cohomology. Also, it is possible to define harmonic vector-valued functions, or harmonic maps of two Riemannian manifolds, which are critical points of a generalized Dirichlet energy functional (this includes harmonic functions as a special case, a result known as Dirichlet principle). This kind of harmonic map appears in the theory of minimal surfaces. For example, a curve, that is, a map from an interval in $\R$ to a Riemannian manifold, is a harmonic map if and only if it is a geodesic.

Harmonic maps between manifolds
If $M$ and $N$ are two Riemannian manifolds, then a harmonic map $$u: M \to N$$ is defined to be a critical point of the Dirichlet energy $$D[u] = \frac{1}{2} \int_M \left\|du\right\|^2 \, d\operatorname{Vol}$$ in which $$du: TM \to TN $$ is the differential of $u$, and the norm is that induced by the metric on $M$ and that on $N$ on the tensor product bundle $$T^\ast M \otimes u^{-1} TN.$$

Important special cases of harmonic maps between manifolds include minimal surfaces, which are precisely the harmonic immersions of a surface into three-dimensional Euclidean space. More generally, minimal submanifolds are harmonic immersions of one manifold in another. Harmonic coordinates are a harmonic diffeomorphism from a manifold to an open subset of a Euclidean space of the same dimension.

title: Harmonic function