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Thomas Hakon Grönwall
Thomas Hakon Grönwall or Thomas Hakon Gronwall (January 16, 1877 in Dylta bruk, Sweden – May 9, 1932 in New York City, New York) was a Swedish mathematician. He studied at the University College of Stockholm and Uppsala University and completed his Ph.D. at Uppsala in 1898. Grönwall worked for about a year as a civil engineer in Germany before he emigrated to the United States in 1904. He later taught mathematics at Princeton University and from 1925 he was a member of the physics department at Columbia University. In 1925 he started to collaborate with Victor LaMer, which led to his joining the Department of Physics at Columbia University as an associate in 1927. This connection was a great opportunity. There were no teaching obligations; he had complete control of his own time and an abundance of new intriguing problems to address in physical chemistry and in atomic physics. He developed a solution to higher approximation in the Debye–Hückel theory. See also * Grönwa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sweden
Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, Finland to the east, and is connected to Denmark in the southwest by a bridgetunnel across the Öresund. At , Sweden is the largest Nordic country, the third-largest country in the European Union, and the fifth-largest country in Europe. The capital and largest city is Stockholm. Sweden has a total population of 10.5 million, and a low population density of , with around 87% of Swedes residing in urban areas in the central and southern half of the country. Sweden has a nature dominated by forests and a large amount of lakes, including some of the largest in Europe. Many long rivers run from the Scandes range through the landscape, primarily ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grönwall's Area Theorem
In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following: Koebe Quarter Theorem. The image of an injective analytic function f:\mathbf\to\mathbb from the unit disk \mathbf onto a subset of the complex plane contains the disk whose center is f(0) and whose radius is , f'(0), /4. The theorem is named after Paul Koebe, who conjectured the result in 1907. The theorem was proven by Ludwig Bieberbach in 1916. The example of the Koebe function shows that the constant 1/4 in the theorem cannot be improved (increased). A related result is the Schwarz lemma, and a notion related to both is conformal radius. Grönwall's area theorem Suppose that :g(z) = z +b_1z^ + b_2 z^ + \cdots is univalent in , z, >1. Then :\sum_ n, b_n, ^2 \le 1. In fact, if r > 1, the complement of the image of the disk , z, >r is a bounded domain X(r). Its area is given by : \int_ dx\,dy = \int_\overline\,dz = \int_\overline\,dg=\pi r^2 - \pi\sum n, b_n, ^2 r^. Since the area i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stockholm University Alumni
Stockholm () is the capital and largest city of Sweden as well as the largest urban area in Scandinavia. Approximately 980,000 people live in the municipality, with 1.6 million in the urban area, and 2.4 million in the metropolitan area. The city stretches across fourteen islands where Lake Mälaren flows into the Baltic Sea. Outside the city to the east, and along the coast, is the island chain of the Stockholm archipelago. The area has been settled since the Stone Age, in the 6th millennium BC, and was founded as a city in 1252 by Swedish statesman Birger Jarl. It is also the county seat of Stockholm County. For several hundred years, Stockholm was the capital of Finland as well (), which then was a part of Sweden. The population of the municipality of Stockholm is expected to reach one million people in 2024. Stockholm is the cultural, media, political, and economic centre of Sweden. The Stockholm region alone accounts for over a third of the country's GDP, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uppsala University Alumni
Uppsala (, or all ending in , ; archaically spelled ''Upsala'') is the county seat of Uppsala County and the fourth-largest city in Sweden, after Stockholm, Gothenburg, and Malmö. It had 177,074 inhabitants in 2019. Located north of the capital Stockholm it is also the seat of Uppsala Municipality. Since 1164, Uppsala has been the ecclesiastical centre of Sweden, being the seat of the Archbishop of the Church of Sweden. Uppsala is home to Scandinavia's largest cathedral – Uppsala Cathedral, which was the frequent site of the coronation of the Swedish monarch until the late 19th century. Uppsala Castle, built by King Gustav Vasa, served as one of the royal residences of the Swedish monarchs, and was expanded several times over its history, making Uppsala the secondary capital of Sweden during its greatest extent. Today it serves as the residence of the Governor of Uppsala County. Founded in 1477, Uppsala University is the oldest centre of higher education in Scandinavi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1932 Deaths
Year 193 ( CXCIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sosius and Ericius (or, less frequently, year 946 ''Ab urbe condita''). The denomination 193 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * January 1 – Year of the Five Emperors: The Roman Senate chooses Publius Helvius Pertinax, against his will, to succeed the late Commodus as Emperor. Pertinax is forced to reorganize the handling of finances, which were wrecked under Commodus, to reestablish discipline in the Roman army, and to suspend the food programs established by Trajan, provoking the ire of the Praetorian Guard. * March 28 – Pertinax is assassinated by members of the Praetorian Guard, who storm the imperial palace. The Empire is auctioned off ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1877 Births
Events January–March * January 1 – Queen Victoria is proclaimed ''Empress of India'' by the ''Royal Titles Act 1876'', introduced by Benjamin Disraeli, the Prime Minister of the United Kingdom . * January 8 – Great Sioux War of 1876 – Battle of Wolf Mountain: Crazy Horse and his warriors fight their last battle with the United States Cavalry in Montana. * January 20 – The Conference of Constantinople ends, with Ottoman Turkey rejecting proposals of internal reform and Balkan provisions. * January 29 – The Satsuma Rebellion, a revolt of disaffected samurai in Japan, breaks out against the new imperial government; it lasts until September, when it is crushed by a professionally led army of draftees. * February 17 – Major General Charles George Gordon of the British Army is appointed Governor-General of the Sudan. * March – ''The Nineteenth Century (periodical), The Nineteenth Century'' magazine is founded in London. * Marc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor Function
In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (including 1 and the number itself). It appears in a number of remarkable identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who gave a number of important Modular arithmetic, congruences and identity (mathematics), identities; these are treated separately in the article Ramanujan's sum. A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function. Definition The sum of positive divisors function σ''z''(''n''), for a real or complex number ''z'', is defined as the summation, sum of the ''z''th Exponentiation, powers of the positive divisors of ''n''. It can be expressed in Summation#Capital ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grönwall's Inequality
In mathematics, Grönwall's inequality (also called Grönwall's lemma or the Grönwall–Bellman inequality) allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation. There are two forms of the lemma, a differential form and an integral form. For the latter there are several variants. Grönwall's inequality is an important tool to obtain various estimates in the theory of ordinary and stochastic differential equations. In particular, it provides a comparison theorem that can be used to prove uniqueness of a solution to the initial value problem; see the Picard–Lindelöf theorem. It is named for Thomas Hakon Grönwall (1877–1932). Grönwall is the Swedish spelling of his name, but he spelled his name as Gronwall in his scientific publications after emigrating to the United States. The inequality was first proven by Grönwall in 1919 (the integral form belo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debye–Hückel Theory
The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized Poisson–Boltzmann model, which assumes an extremely simplified model of electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution. The Debye–Hückel equation provides a starting point for modern treatments of non-ideality of electrolyte solutions. Overview In the chemistry of electrolyte solutions, an ideal solution is a solution whose colligative properties are proportional to the concentration of the solute. Real solutions may show departures from this kind of ideality. In order to accommodate these effects in the thermodynamics of solutions, the concept of activity was introduced: the properties are then proportional to the activities of the ions. Activity, ''a'', is proportional to concentration, ''c''. The proport ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the List of United States cities by population density, most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York (state), New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban area, urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous Megacity, megacities, and over 58 million people live within of the city. New York City is a global city, global Culture of New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Victor LaMer
Victor Kuhn LaMer or La Mer (1895 – 1966) was an American chemist. He has been described as "the father of colloid chemistry". Early life and education LaMer was born in Leavenworth, Kansas on June 15, 1895. He was the son of Joseph Secondule LaMer and Anna Pauline Kuhn. He obtained his AB degree from the University of Kansas in 1915. Over the next two years, he did a number of jobs, which include a high school teacher, a student at the University of Chicago, and a research chemist at the Carnegie Institution of Washington. In 1917 he joined the Sanitary Corps of the U.S. Army and was commissioned as a 1st Lieutenant. In 1921, he obtained his PhD from Columbia University. His doctoral thesis was ''The effect of temperature and hydrogen ion concentration upon the rate of destruction of the antiscorbutic vitamin''. The thesis was summarized in 1921 in the ''Proceedings of the National Academy of Sciences'', and more thouroughly in 1922 in the ''Journal of the American Ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhattan, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence. It is a member of the Ivy League. Columbia is ranked among the top universities in the world. Columbia was established by royal charter under George II of Great Britain. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University. Columbia scientists and scholars have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
