Gyeonggi-do is the most populous province in South Korea. Its name, Gyeonggi means "the area surrounding the capital", thus Gyeonggi-do can be translated as "province surrounding Seoul". The provincial capital is Suwon. Seoul—South Korea's largest city and national capital—is in the heart of the province but has been separately administered as a provincial-level special city since 1946. Incheon—South Korea's third-largest city—is on the coast of the province and has been administered as a provincial-level metropolitan city since 1981; the three jurisdictions are collectively referred to as Sudogwon and cover 11,730 km2, with a combined population of 25.5 million—amounting to over half of the entire population of South Korea. Gyeonggi-do has been a politically important area since 18 BCE, when Korea was divided into three nations during the Three Kingdoms period. Since King Onjo, the founder of Baekje, founded the government in Wiryeseong of Hanam, the Han River Valley was absorbed into Goguryeo in the mid-fifth century, became Silla's territory in the year 553.
Afterward, the current location of Gyeonggi-do, one of the nine states of Later Silla, was called Hansanju. The Gyeonggi region started to rise as the central region of Goryeo as King Taejo of Goryeo set up the capital in Gaesong. Since 1018, this area has been called "Gyeonggi." During the Joseon, founded after the Goryeo, King Taejo of Joseon set the capital in Hanyang, while restructuring Gyeonggi's area to include Gwangju, Suwon and Anseong, along with the southeast region. Since the period of King Taejong and Sejong the Great, the Gyeonggi region has been similar to the current administrative area of Gyeonggi-do. In 1895 the 23-Bu system, which reorganized administrative areas, was effected; the Gyeonggi region was divided into Hanseong, Chungju and Kaesong. During the Japanese colonial period, Hanseong-bu was incorporated into Gyeonggi-do. On October 1, 1910, it was renamed Keijo and a provincial government was placed in Keijo according to the reorganization of administrative districts. After liberation and the foundation of two Korean governments, Gyeonggi-do and its capital, were separated with partial regions of Gyeonggi-do being incorporated into Seoul thereafter.
Additionally, Kaesong became North Korean territory, the only city to change control after the countries were divided at the 38th parallel, now part of North Korea's North Hwanghae Province. In 1967 the seat of the Gyeonggi provincial government was transferred from Seoul to Suwon. After Incheon separated from Gyeonggi-do in 1981, Gyeonggi regions such as Ongjin County and Ganghwa County were incorporated into Incheon in 1995. Gyeonggi-do is the western central region of the Korean Peninsula, vertically situated in Northeast Asia and is between east longitude of 126 and 127, north latitude of 36 and 38, its dimension is 10 % of 10,171 square kilometres. It is in contact with 86 kilometres of cease-fire line to the north, 413 kilometres of coastline to the west, Gangwon-do to the east, Chungcheongbuk-do and Chungcheongnam-do to the south, has Seoul, the capital of the Republic of Korea, in its center, its provincial government is in Suwon, but some of its government buildings are in Uijeongbu for the administrative conveniences of the northern region.
The climate of Gyeonggi-do is the continental climate, which has a severe differentiation of temperature between summer and winter, has distinctions of four seasons. Spring is warm, summer is hot and humid, autumn is cool, winter is cold and snowy; the annual average temperature is between 11–13 °C, where the temperature in the mountainous areas to the northeast is lower and the coastal areas to the southwest is higher. For January's average temperature, the Gyeonggi Bay is −4 °C, the Namhangang Basin is −4 to −6 °C, the Bukhangang and Imjingang Basins are −6 to −8 °C, it becomes higher in temperature differentiation from coastal to inland areas. Summer has a lower local differentiation compared to winter; the inland areas are hotter than the Gyeonggi Bay area, the hottest area is Pyeongtaek, making the average temperature of August 26.5 °C. The annual average precipitation is around 1,100 millimetres, with a lot of rainfall, it is dry during winter. The northeastern inland areas of Bukhangang and the upper stream of Imjingang has a precipitation of 1,300–1,400 millimetres, whereas the coastal area has only 900 millimetres of precipitation.
The topography of Gyeonggi-do is divided into southern and northern areas by the Han River, which flows from east to west. The area north to the Han River is mountainous, while the southern area is plain; the configuration of Gyeonggi-do is represented by Dong-go-seo-jeo, where the Gwangju Mountain Range and the Charyeong Mountain Range spreads from the east and drops in elevation in the west. The fields of Gimpo and Pyeongtaek extend to the west. Gyeonggi-do boasts beautiful nature stocked with rivers, lakes and seas, its representative rivers are the Hangang and Anseongcheon, which flow into the Yellow Sea, with Gyeonggi Plain, Yeonbaek Plain and Anseong Plain forming a fertile field area around the rivers. The Gwangju Mountain Range and the Charyeong Mountain Range stre
The Schrödinger equation is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system. It is a key result in quantum mechanics, its discovery was a significant landmark in the development of the subject; the equation is named after Erwin Schrödinger, who derived the equation in 1925, published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. In classical mechanics, Newton's second law is used to make a mathematical prediction as to what path a given physical system will take over time following a set of known initial conditions. Solving this equation gives the position and the momentum of the physical system as a function of the external force F on the system; those two parameters are sufficient to describe its state at each time instant. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation; the concept of a wave function is a fundamental postulate of quantum mechanics.
Using these postulates, Schrödinger's equation can be derived from the fact that the time-evolution operator must be unitary, must therefore be generated by the exponential of a self-adjoint operator, the quantum Hamiltonian. This derivation is explained below. In the Copenhagen interpretation of quantum mechanics, the wave function is the most complete description that can be given of a physical system. Solutions to Schrödinger's equation describe not only molecular and subatomic systems, but macroscopic systems even the whole universe. Schrödinger's equation is central to all applications of quantum mechanics including quantum field theory which combines special relativity with quantum mechanics. Theories of quantum gravity, such as string theory do not modify Schrödinger's equation; the Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. The other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, the path integral formulation, developed chiefly by Richard Feynman.
Paul Dirac incorporated the Schrödinger equation into a single formulation. The form of the Schrödinger equation depends on the physical situation; the most general form is the time-dependent Schrödinger equation, which gives a description of a system evolving with time: where i is the imaginary unit, ℏ = h 2 π is the reduced Planck constant, Ψ is the state vector of the quantum system, t is time, H ^ is the Hamiltonian operator. The position-space wave function of the quantum system is nothing but the components in the expansion of the state vector in terms of the position eigenvector | r ⟩, it is a scalar function, expressed as Ψ = ⟨ r | Ψ ⟩. The momentum-space wave function can be defined as Ψ ~ = ⟨ p | Ψ ⟩, where | p ⟩ is the momentum eigenvector; the most famous example is the nonrelativistic Schrödinger equation for the wave function in position space Ψ of a single particle subject to a potential V, such as that due to an electric field. Where m is the particle's mass, ∇ 2 is the Laplacian.
This is a diffusion equation, but unlike the heat equation, this one is a wave equation given the imaginary unit present in the transient term. The term "Schrödinger equation" can refer to both the general equation, or the specific nonrelativistic version; the general equation is indeed quite general, used throughout quantum mechanics, for everything from the Dirac equation to quantum field theory, by plugging in diverse expressions for the Hamiltonian. The specific nonrelativistic version is a classical approximation to reality and yields accurate results in many situations, but only to a certain extent. To apply the Schrödinger equation, write down the Hamiltonian for the system, accounting for the kinetic and potential energies of the particles constituting the system insert it into the Schrödinger equation; the resulting partial differential equation is solved for the wave function, which contains information about the system. The time-dependent Schrödinger equation described above predicts that wave functions can form standing waves, called stationary states.
These states are important as their individual study simplifies the task of solving the time-dependent Schrödinger equation for any state. Stationary states can be described by a simpler form of the Schrödinger equation, the time-independe
South Korea the Republic of Korea, is a country in East Asia, constituting the southern part of the Korean Peninsula and lying to the east of the Asian mainland. The name Korea is derived from Goguryeo, one of the great powers in East Asia during its time, ruling most of the Korean Peninsula, parts of the Russian Far East and Inner Mongolia, under Gwanggaeto the Great. South Korea has a predominantly mountainous terrain, it comprises an estimated 51.4 million residents distributed over 100,363 km2. Its capital and largest city is Seoul, with a population of around 10 million. Archaeology indicates that the Korean Peninsula was inhabited by early humans starting from the Lower Paleolithic period; the history of Korea begins with the foundation of Gojoseon in 2333 BCE by the mythic king Dangun, but no archaeological evidence and writing was found from this period. The Gija Joseon was purportedly founded in 11th century BCE, its existence and role has been controversial in the modern era; the written historical record on Gojoseon was first mentioned in Chinese records in the early 7th century BCE.
Following the unification of the Three Kingdoms of Korea under Unified Silla in CE 668, Korea was subsequently ruled by the Goryeo dynasty and the Joseon dynasty. It was annexed by the Empire of Japan in 1910. At the end of World War II, Korea was divided into Soviet and U. S. zones of occupations. A separate election was held in the U. S. zone in 1948 which led to the creation of the Republic of Korea, while the Democratic People's Republic of Korea was established in the Soviet zone. The United Nations at the time passed a resolution declaring the ROK to be the only lawful government in Korea; the Korean War began in June 1950. The war lasted three years and involved the U. S. China, the Soviet Union and several other nations; the border between the two nations remains the most fortified in the world. Under long-time military leader Park Chung-hee, the South Korean economy grew and the country was transformed into a G-20 major economy. Military rule ended in 1987, the country is now a presidential republic consisting of 17 administrative divisions.
South Korea is a developed country and a high-income economy, with a "very high" Human Development Index, ranking 22nd in the world. The country is considered a regional power and is the world's 11th largest economy by nominal GDP and the 12th largest by PPP as of 2010. South Korea is a global leader in the industrial and technological sectors, being the world's 5th largest exporter and 8th largest importer, its export-driven economy focuses production on electronics, ships, machinery and robotics. South Korea is a member of the ASEAN Plus mechanism, the United Nations, Uniting for Consensus, G20, the WTO and OECD and is a founding member of APEC and the East Asia Summit; the name Korea derives from the name Goryeo. The name Goryeo itself was first used by the ancient kingdom of Goguryeo in the 5th century as a shortened form of its name; the 10th-century kingdom of Goryeo succeeded Goguryeo, thus inherited its name, pronounced by the visiting Persian merchants as "Korea". The modern spelling of Korea first appeared in the late 17th century in the travel writings of the Dutch East India Company's Hendrick Hamel.
Despite the coexistence of the spellings Corea and Korea in 19th century publications, some Koreans believe that Imperial Japan, around the time of the Japanese occupation, intentionally standardised the spelling on Korea, making Japan appear first alphabetically. After Goryeo was replaced by Joseon in 1392, Joseon became the official name for the entire territory, though it was not universally accepted; the new official name has its origin in the ancient country of Gojoseon. In 1897, the Joseon dynasty changed the official name of the country from Joseon to Daehan Jeguk; the name Daehan, which means "Great Han" derives from Samhan, referring to the Three Kingdoms of Korea, not the ancient confederacies in the southern Korean Peninsula. However, the name Joseon was still used by Koreans to refer to their country, though it was no longer the official name. Under Japanese rule, the two names Han and Joseon coexisted. There were several groups who fought for independence, the most notable being the Provisional Government of the Republic of Korea.
Following the surrender of Japan, in 1945, the Republic of Korea was adopted as the legal English name for the new country. Since the government only controlled the southern part of the Korean Peninsula, the informal term South Korea was coined, becoming common in the Western world. While South Koreans use Han to refer to the entire country, North Koreans and ethnic Koreans living in China and Japan use the term Joseon as the name of the country; the Korean name "Daehan Minguk" is sometimes used by South Koreans as a metonym to refer to the Korean ethnicity as a whole, rather than just the South Korean state. The history of Korea begins with the founding of Joseon in 2333 BCE by Dangun, according to Korea's foundation mythology. Gojoseon expanded until it controlled parts of Manchuria. Gija Joseon was purportedly founded in the 12th century BC, but its existence and role have been controversial in the modern era. In 108 BCE, the Han dynasty defeated Wiman Joseon and installed four commanderies in the n
ArXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, astronomy, electrical engineering, computer science, quantitative biology, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month. ArXiv was made possible by the compact TeX file format, which allowed scientific papers to be transmitted over the Internet and rendered client-side. Around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Paul Ginsparg recognized the need for central storage, in August 1991 he created a central repository mailbox stored at the Los Alamos National Laboratory which could be accessed from any computer.
Additional modes of access were soon added: FTP in 1991, Gopher in 1992, the World Wide Web in 1993. The term e-print was adopted to describe the articles, it began as a physics archive, called the LANL preprint archive, but soon expanded to include astronomy, computer science, quantitative biology and, most statistics. Its original domain name was xxx.lanl.gov. Due to LANL's lack of interest in the expanding technology, in 2001 Ginsparg changed institutions to Cornell University and changed the name of the repository to arXiv.org. It is now hosted principally with eight mirrors around the world, its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv; the annual budget for arXiv is $826,000 for 2013 to 2017, funded jointly by Cornell University Library, the Simons Foundation and annual fee income from member institutions.
This model arose in 2010, when Cornell sought to broaden the financial funding of the project by asking institutions to make annual voluntary contributions based on the amount of download usage by each institution. Each member institution pledges a five-year funding commitment to support arXiv. Based on institutional usage ranking, the annual fees are set in four tiers from $1,000 to $4,400. Cornell's goal is to raise at least $504,000 per year through membership fees generated by 220 institutions. In September 2011, Cornell University Library took overall administrative and financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a life sentence". However, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. Although arXiv is not peer reviewed, a collection of moderators for each area review the submissions; the lists of moderators for many sections of arXiv are publicly available, but moderators for most of the physics sections remain unlisted.
Additionally, an "endorsement" system was introduced in 2004 as part of an effort to ensure content is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, but to check whether the paper is appropriate for the intended subject area. New authors from recognized academic institutions receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for restricting scientific inquiry. A majority of the e-prints are submitted to journals for publication, but some work, including some influential papers, remain purely as e-prints and are never published in a peer-reviewed journal. A well-known example of the latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman in November 2002.
Perelman appears content to forgo the traditional peer-reviewed journal process, stating: "If anybody is interested in my way of solving the problem, it's all there – let them go and read about it". Despite this non-traditional method of publication, other mathematicians recognized this work by offering the Fields Medal and Clay Mathematics Millennium Prizes to Perelman, both of which he refused. Papers can be submitted in any of several formats, including LaTeX, PDF printed from a word processor other than TeX or LaTeX; the submission is rejected by the arXiv software if generating the final PDF file fails, if any image file is too large, or if the total size of the submission is too large. ArXiv now allows one to store and modify an incomplete submission, only finalize the submission when ready; the time stamp on the article is set. The standard access route is through one of several mirrors. Sev
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. Other forms of nuclear matter are studied. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons. Discoveries in nuclear physics have led to applications in many fields; this includes nuclear power, nuclear weapons, nuclear medicine and magnetic resonance imaging and agricultural isotopes, ion implantation in materials engineering, radiocarbon dating in geology and archaeology. Such applications are studied in the field of nuclear engineering. Particle physics evolved out of nuclear physics and the two fields are taught in close association. Nuclear astrophysics, the application of nuclear physics to astrophysics, is crucial in explaining the inner workings of stars and the origin of the chemical elements; the history of nuclear physics as a discipline distinct from atomic physics starts with the discovery of radioactivity by Henri Becquerel in 1896, while investigating phosphorescence in uranium salts.
The discovery of the electron by J. J. Thomson a year was an indication that the atom had internal structure. At the beginning of the 20th century the accepted model of the atom was J. J. Thomson's "plum pudding" model in which the atom was a positively charged ball with smaller negatively charged electrons embedded inside it. In the years that followed, radioactivity was extensively investigated, notably by Marie and Pierre Curie as well as by Ernest Rutherford and his collaborators. By the turn of the century physicists had discovered three types of radiation emanating from atoms, which they named alpha and gamma radiation. Experiments by Otto Hahn in 1911 and by James Chadwick in 1914 discovered that the beta decay spectrum was continuous rather than discrete; that is, electrons were ejected from the atom with a continuous range of energies, rather than the discrete amounts of energy that were observed in gamma and alpha decays. This was a problem for nuclear physics at the time, because it seemed to indicate that energy was not conserved in these decays.
The 1903 Nobel Prize in Physics was awarded jointly to Becquerel for his discovery and to Marie and Pierre Curie for their subsequent research into radioactivity. Rutherford was awarded the Nobel Prize in Chemistry in 1908 for his "investigations into the disintegration of the elements and the chemistry of radioactive substances". In 1905 Albert Einstein formulated the idea of mass–energy equivalence. While the work on radioactivity by Becquerel and Marie Curie predates this, an explanation of the source of the energy of radioactivity would have to wait for the discovery that the nucleus itself was composed of smaller constituents, the nucleons. In 1906 Ernest Rutherford published "Retardation of the α Particle from Radium in passing through matter." Hans Geiger expanded on this work in a communication to the Royal Society with experiments he and Rutherford had done, passing alpha particles through air, aluminum foil and gold leaf. More work was published in 1909 by Geiger and Ernest Marsden, further expanded work was published in 1910 by Geiger.
In 1911–1912 Rutherford went before the Royal Society to explain the experiments and propound the new theory of the atomic nucleus as we now understand it. The key experiment behind this announcement was performed in 1910 at the University of Manchester: Ernest Rutherford's team performed a remarkable experiment in which Geiger and Marsden under Rutherford's supervision fired alpha particles at a thin film of gold foil; the plum pudding model had predicted that the alpha particles should come out of the foil with their trajectories being at most bent. But Rutherford instructed his team to look for something that shocked him to observe: a few particles were scattered through large angles completely backwards in some cases, he likened it to firing a bullet at tissue paper and having it bounce off. The discovery, with Rutherford's analysis of the data in 1911, led to the Rutherford model of the atom, in which the atom had a small dense nucleus containing most of its mass, consisting of heavy positively charged particles with embedded electrons in order to balance out the charge.
As an example, in this model nitrogen-14 consisted of a nucleus with 14 protons and 7 electrons and the nucleus was surrounded by 7 more orbiting electrons. Around 1920, Arthur Eddington anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper The Internal Constitution of the Stars. At that time, the source of stellar energy was a complete mystery; this was a remarkable development since at that time fusion and thermonuclear energy, that stars are composed of hydrogen, had not yet been discovered. The Rutherford model worked quite well until studies of nuclear spin were carried out by Franco Rasetti at the California Institute of Technology in 1929. By 1925 it was known that protons and electrons each had a spin of +/-1⁄2. In the Rutherford model of nitrogen-14, 20 of the total 21 nuclear particles should have paired up to cancel each other's spin, the final odd particle should have left the nucleus with a net spin of 1⁄2. Rasetti discovered, that nitrogen-14 had a spin of 1.
In 1932 Chadwick realized that radiation, observed by Walther Bothe, Herbert Becker, Irène and Frédéric Joliot-Curie was due to a neutral particle of about the same mass as the proton, that he called the neutron (following a su
In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, twisting and bending, but not tearing or gluing. An n-dimensional topological space is a space with certain properties of connectedness and compactness; the space discrete. It can be closed. Topology developed as a field of study out of geometry and set theory, through analysis of concepts such as space and transformation; such ideas go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs and analysis situs. Leonhard Euler's Seven Bridges of Königsberg Problem and Polyhedron Formula are arguably the field's first theorems; the term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. By the middle of the 20th century, topology had become a major branch of mathematics. Topology, as a well-defined mathematical discipline, originates in the early part of the twentieth century, but some isolated results can be traced back several centuries.
Among these are certain questions in geometry investigated by Leonhard Euler. His 1736 paper on the Seven Bridges of Königsberg is regarded as one of the first practical applications of topology. On 14 November 1750, Euler wrote to a friend that he had realised the importance of the edges of a polyhedron; this led to his polyhedron formula, V − E + F = 2. Some authorities regard this analysis as the first theorem. Further contributions were made by Augustin-Louis Cauchy, Ludwig Schläfli, Johann Benedict Listing, Bernhard Riemann and Enrico Betti. Listing introduced the term "Topologie" in Vorstudien zur Topologie, written in his native German, in 1847, having used the word for ten years in correspondence before its first appearance in print; the English form "topology" was used in 1883 in Listing's obituary in the journal Nature to distinguish "qualitative geometry from the ordinary geometry in which quantitative relations chiefly are treated". The term "topologist" in the sense of a specialist in topology was used in 1905 in the magazine Spectator.
Their work was corrected and extended by Henri Poincaré. In 1895, he published his ground-breaking paper on Analysis Situs, which introduced the concepts now known as homotopy and homology, which are now considered part of algebraic topology. Unifying the work on function spaces of Georg Cantor, Vito Volterra, Cesare Arzelà, Jacques Hadamard, Giulio Ascoli and others, Maurice Fréchet introduced the metric space in 1906. A metric space is now considered a special case of a general topological space, with any given topological space giving rise to many distinct metric spaces. In 1914, Felix Hausdorff coined the term "topological space" and gave the definition for what is now called a Hausdorff space. A topological space is a slight generalization of Hausdorff spaces, given in 1922 by Kazimierz Kuratowski. Modern topology depends on the ideas of set theory, developed by Georg Cantor in the part of the 19th century. In addition to establishing the basic ideas of set theory, Cantor considered point sets in Euclidean space as part of his study of Fourier series.
For further developments, see point-set topology and algebraic topology. Topology can be formally defined as "the study of qualitative properties of certain objects that are invariant under a certain kind of transformation those properties that are invariant under a certain kind of invertible transformation." Topology is used to refer to a structure imposed upon a set X, a structure that characterizes the set X as a topological space by taking proper care of properties such as convergence and continuity, upon transformation. Topological spaces show up in every branch of mathematics; this has made topology one of the great unifying ideas of mathematics. The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. For example, the square and the circle have many properties in common: they are both one dimensional objects and both separate the plane into two parts, the part inside and the part outside.
In one of the first papers in topology, Leonhard Euler demonstrated that it was impossible to find a route through the town of Königsberg that would cross each of its seven bridges once. This result did not depend on the lengths of the bridges or on their distance from one another, but only on connectivity properties: which bridges connect to which islands or riverbanks; this Seven Bridges of Königsberg problem led to the branch of mathematics known as graph theory. The hairy ball theorem of algebraic topology says that "one cannot comb the hair flat on a hairy ball without creating a cowlick." This fact is convincing to most people though they might not recognize the more formal statement of the theorem, that there is no nonvanishing continuous tangent vector field on the sphere. As with the Bridges of Königsberg, the result does not depend on the shape of t
A Korean name consists of a family name followed by a given name, as used by the Korean people in both South Korea and North Korea. In the Korean language, ireum or seongmyeong refers to the family name and given name together. Traditional Korean family names consist of only one syllable. There is no middle name in the English language sense. Many Koreans have their given names made of a generational name syllable and an individually distinct syllable, though this practice is declining in the younger generations; the generational name syllable is shared by siblings in North Korea, by all members of the same generation of an extended family in South Korea. Married men and women keep their full personal names, children inherit the father's family name unless otherwise settled when registering the marriage; the family names are subdivided into bon-gwan, i.e. extended families which originate in the lineage system used in previous historical periods. Each clan is identified by a specific place, traces its origin to a common patrilineal ancestor.
Early names based on the Korean language were recorded in the Three Kingdoms period, but with the growing adoption of the Chinese writing system, these were replaced by names based on Chinese characters. During periods of Mongol influence, the ruling class supplemented their Korean names with Mongolian names; because of the many changes in Korean romanization practices over the years, modern Koreans, when using languages written in Latin script, romanize their names in various ways, most approximating the pronunciation in English orthography. Some keep the original order of names, while others reverse the names to match the usual Western pattern. According to the population and housing census of 2000 conducted by the South Korean government, there are a total of 286 surnames and 4,179 clans. Fewer than 300 Korean family names were in use in 2000, the three most common account for nearly half of the population. For various reasons, there is a growth in the number of Korean surnames; each family name is divided into one or more clans.
For example, the most populous clan is Gimhae Kim. Clans are further subdivided into various pa, or branches stemming from a more recent common ancestor, so that a full identification of a person's family name would be clan-surname-branch. For example, "Gyeongju Yissi" romanized as "Gyeongju Leessi" and "Yeonan-Yissi" are, technically speaking different surnames though both are, in most places referred to as "Yi" or "Lee"; this means people from the same clan are considered to be of same blood, such that marriage of a man and a woman of same surname and bon-gwan is considered a strong taboo, regardless of how distant the actual lineages may be to the present day. Traditionally, Korean women keep their family names after their marriage, but their children take the father's surname. In the premodern, patriarchal Korean society, people were conscious of familial values and their own family identities. Korean women keep their surnames after marriage based on traditional reasoning that it is inherited from their parents and ancestors, cannot be changed.
According to traditions, each clan publishes a comprehensive genealogy every 30 years. Around a dozen two-syllable surnames are used; the five most common family names, which together make up over half of the Korean population, are used by over 20 million people in South Korea. After the 2015 census, it was revealed that foreign-origin family names were becoming more common in South Korea, due to naturalised citizens transcribing their surnames in hangul. Between 2000 and 2015, more than 4,800 new surnames were registered. During the census, a total of 5,582 distinct surnames were collected, 73% of which do not have corresponding hanja characters, it was revealed that despite the surge in the number of surnames, the ratio of top 10 surnames had not changed. 44.6% of South Koreans are still named Kim, Lee or Park, while the rest of the top 10 are made up of Choi, Kang, Jo, Yoon and Lim. Traditionally, given names are determined by generation names, a custom originating in China. One of the two characters in a given name is unique to the individual, while the other is shared by all people in a family generation.
In both North and South Korea, generational names are no longer shared by cousins, but are still shared by brothers and sisters. Given names are composed of hanja, or Chinese characters. In North Korea, the hanja are no longer used to write the names, but the meanings are still understood. In South Korea, section 37 of the Family Registry Law requires that the hanja in personal names be taken from a restricted list. Unapproved hanja must be represented by hangul in the family registry. In March 1991, the Supreme Court of South Korea published the Table of Hanja for Personal Name Use, which allowed a total of 2,854 hanja in new South Korean given names; the list was expanded in 1994, 1997, 2001, 2005, 2007, 2008, 2010, 2013 and 2015. Thus, 8,142 hanja are now permitted in South Korean names, in addition to a small number of alternative forms; the use of an official list is similar to Japan's use of the jinmeiyō kanji. While the traditional practice is still followed, since the lat