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The large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called "nucleons") in a given atom is called the mass number. It is a positive integer and dimensionless (instead of having dimension of mass), because it expresses a count. An example of use o...
As even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about ). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one g...
When subjected to external forces, like electrical fields, the shape of an atom may deviate from spherical symmetry. The deformation depends on the field magnitude and the orbital type of outer shell electrons, as shown by group-theoretical considerations. Aspherical deviations might be elicited for instance in crystal...
Radioactive decay. Every element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over ...
Magnetic moment. Elementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is mea...
In ferromagnetic elements such as iron, cobalt and nickel, an odd number of electrons leads to an unpaired electron and a net overall magnetic moment. The orbitals of neighboring atoms overlap and a lower energy state is achieved when the spins of unpaired electrons are aligned with each other, a spontaneous process kn...
Energy levels. The potential energy of an electron in an atom is negative relative to when the distance from the nucleus goes to infinity; its dependence on the electron's position reaches the minimum inside the nucleus, roughly in inverse proportion to the distance. In the quantum-mechanical model, a bound electron ca...
For an electron to transition between two different states, e.g. ground state to first excited state, it must absorb or emit a photon at an energy matching the difference in the potential energy of those levels, according to the Niels Bohr model, what can be precisely calculated by the Schrödinger equation. Electrons j...
Close examination of the spectral lines reveals that some display a fine structure splitting. This occurs because of spin–orbit coupling, which is an interaction between the spin and motion of the outermost electron. When an atom is in an external magnetic field, spectral lines become split into three or more component...
Valence and bonding behavior. Valency is the combining power of an element. It is determined by the number of bonds it can form to other atoms or groups. The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in that shell are called valence electrons. The numbe...
The chemical elements are often displayed in a periodic table that is laid out to display recurring chemical properties, and elements with the same number of valence electrons form a group that is aligned in the same column of the table. (The horizontal rows correspond to the filling of a quantum shell of electrons.) T...
Identification. While atoms are too small to be seen, devices such as the scanning tunneling microscope (STM) enable their visualization at the surfaces of solids. The microscope uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would be insurmountable in the classical perspec...
Atoms can be easily identified by their mass. If an atom is ionized by removing one of its electrons, its trajectory when it passes through a magnetic field will bend. The radius by which the trajectory of a moving ion is turned by the magnetic field is determined by the mass of the atom. The mass spectrometer uses thi...
Spectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms. These colors can be replicated using a gas-discharge lamp containing the same e...
Up to 95% of the Milky Way's baryonic matter are concentrated inside stars, where conditions are unfavorable for atomic matter. The total baryonic mass is about 10% of the mass of the galaxy; the remainder of the mass is an unknown dark matter. High temperature inside stars makes most "atoms" fully ionized, that is, se...
Since the Big Bang, which produced no carbon or heavier elements, atomic nuclei have been combined in stars through the process of nuclear fusion to produce more of the element helium, and (via the triple-alpha process) the sequence of elements from carbon up to iron; see stellar nucleosynthesis for details. Isotopes s...
There are a few trace atoms on Earth that were not present at the beginning (i.e., not "primordial"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere. Some atoms on Earth have been artificially generated either deliberately or as by-products of nuclear reactors...
Rare and theoretical forms. Superheavy elements. All nuclides with atomic numbers higher than 82 (lead) are known to be radioactive. No nuclide with an atomic number exceeding 92 (uranium) exists on Earth as a primordial nuclide, and heavier elements generally have shorter half-lives. Nevertheless, an "island of stabil...
Arable land Arable land (from the , "able to be ploughed") is any land capable of being ploughed and used to grow crops. Alternatively, for the purposes of agricultural statistics, the term often has a more precise definition: A more concise definition appearing in the Eurostat glossary similarly refers to actual rathe...
Other non-arable land includes land that is not suitable for any agricultural use. Land that is not arable, in the sense of lacking capability or suitability for cultivation for crop production, has one or more limitationsa lack of sufficient freshwater for irrigation, stoniness, steepness, adverse climate, excessive w...
Changes in arability. Land conversion. Land incapable of being cultivated for the production of crops can sometimes be converted to arable land. New arable land makes more food and can reduce starvation. This outcome also makes a country more self-sufficient and politically independent, because food importation is redu...
The use of artifices does not make the land arable. Rock still remains rock, and shallowless than turnable soil is still not considered toilable. The use of artifice is an open-air non-recycled water hydroponics relationship. The below described circumstances are not in perspective, have limited duration, and have a te...
Aluminium Aluminium (or aluminum in North American English) is a chemical element; it has symbol Al and atomic number 13. It has a density lower than that of other common metals, about one-third that of steel. Aluminium has a great affinity towards oxygen, forming a protective layer of oxide on the surface when exposed...
The discovery of aluminium was announced in 1825 by Danish physicist Hans Christian Ørsted. The first industrial production of aluminium was initiated by French chemist Henri Étienne Sainte-Claire Deville in 1856. Aluminium became much more available to the public with the Hall–Héroult process developed independently b...
Physical characteristics. Isotopes. Of aluminium isotopes, only is stable. This situation is common for elements with an odd atomic number. It is the only primordial aluminium isotope, i.e. the only one that has existed on Earth in its current form since the formation of the planet. It is therefore a mononuclidic eleme...
The remaining isotopes of aluminium, with mass numbers ranging from 21 to 43, all have half-lives well under an hour. Three metastable states are known, all with half-lives under a minute. Electron shell. An aluminium atom has 13 electrons, arranged in an electron configuration of , with three electrons beyond a stable...
Bulk. Aluminium metal has an appearance ranging from silvery white to dull gray depending on its surface roughness. Aluminium mirrors provides high reflectivity for light in the ultraviolet, visible (on par with silver), and the far infrared region. Aluminium is also good at reflecting solar radiation, although prolong...
Pure aluminium is quite soft and lacking in strength. In most applications various aluminium alloys are used instead because of their higher strength and hardness. The yield strength of pure aluminium is 7–11 MPa, while aluminium alloys have yield strengths ranging from 200 MPa to 600 MPa. Aluminium is ductile, with a ...
Aluminium combines characteristics of pre- and post-transition metals. Since it has few available electrons for metallic bonding, like its heavier group 13 congeners, it has the characteristic physical properties of a post-transition metal, with longer-than-expected interatomic distances. Furthermore, as Al3+ is a smal...
Aluminium has a high chemical affinity to oxygen, which renders it suitable for use as a reducing agent in the thermite reaction. A fine powder of aluminium reacts explosively on contact with liquid oxygen; under normal conditions, however, aluminium forms a thin oxide layer (~5 nm at room temperature) that protects th...
Aluminium reacts with most nonmetals upon heating, forming compounds such as aluminium nitride (AlN), aluminium sulfide (Al2S3), and the aluminium halides (AlX3). It also forms a wide range of intermetallic compounds involving metals from every group on the periodic table. Inorganic compounds. The vast majority of comp...
Aluminium hydroxide forms both salts and aluminates and dissolves in acid and alkali, as well as on fusion with acidic and basic oxides. This behavior of Al(OH)3 is termed amphoterism and is characteristic of weakly basic cations that form insoluble hydroxides and whose hydrated species can also donate their protons. O...
All four trihalides are well known. Unlike the structures of the three heavier trihalides, aluminium fluoride (AlF3) features six-coordinate aluminium, which explains its involatility and insolubility as well as high heat of formation. Each aluminium atom is surrounded by six fluorine atoms in a distorted octahedral ar...
Aluminium forms one stable oxide with the chemical formula Al2O3, commonly called alumina. It can be found in nature in the mineral corundum, α-alumina; there is also a γ-alumina phase. Its crystalline form, corundum, is very hard (Mohs hardness 9), has a high melting point of , has very low volatility, is chemically i...
The only stable chalcogenides under normal conditions are aluminium sulfide (Al2S3), selenide (Al2Se3), and telluride (Al2Te3). All three are prepared by direct reaction of their elements at about and quickly hydrolyze completely in water to yield aluminium hydroxide and the respective hydrogen chalcogenide. As alumini...
Aluminium alloys well with most other metals (with the exception of most alkali metals and group 13 metals) and over 150 intermetallics with other metals are known. Preparation involves heating fixed metals together in certain proportion, followed by gradual cooling and annealing. Bonding in them is predominantly metal...
Organoaluminium compounds and related hydrides. A variety of compounds of empirical formula AlR3 and AlR1.5Cl1.5 exist. The aluminium trialkyls and triaryls are reactive, volatile, and colorless liquids or low-melting solids. They catch fire spontaneously in air and react with water, thus necessitating precautions when...
The industrially most important aluminium hydride is lithium aluminium hydride (LiAlH4), which is used as a reducing agent in organic chemistry. It can be produced from lithium hydride and aluminium trichloride. The simplest hydride, aluminium hydride or alane, is not as important. It is a polymer with the formula (AlH...
Earth. Overall, the Earth is about 1.59% aluminium by mass (seventh in abundance by mass). Aluminium occurs in greater proportion in the Earth's crust than in the universe at large. This is because aluminium easily forms the oxide and becomes bound into rocks and stays in the Earth's crust, while less reactive metals s...
Although aluminium is a common and widespread element, not all aluminium minerals are economically viable sources of the metal. Almost all metallic aluminium is produced from the ore bauxite (AlO"x"(OH)3–2"x"). Bauxite occurs as a weathering product of low iron and silica bedrock in tropical climatic conditions. In 201...
Attempts to produce aluminium date back to 1760. The first successful attempt, however, was completed in 1824 by Danish physicist and chemist Hans Christian Ørsted. He reacted anhydrous aluminium chloride with potassium amalgam, yielding a lump of metal looking similar to tin. He presented his results and demonstrated ...
The first industrial large-scale production method was independently developed in 1886 by French engineer Paul Héroult and American engineer Charles Martin Hall; it is now known as the Hall–Héroult process. The Hall–Héroult process converts alumina into metal. Austrian chemist Carl Joseph Bayer discovered a way of puri...
By the mid-20th century, aluminium had become a part of everyday life and an essential component of housewares. In 1954, production of aluminium surpassed that of copper, historically second in production only to iron, making it the most produced non-ferrous metal. During the mid-20th century, aluminium emerged as a ci...
The real price for aluminium declined from $14,000 per metric ton in 1900 to $2,340 in 1948 (in 1998 United States dollars). Extraction and processing costs were lowered over technological progress and the scale of the economies. However, the need to exploit lower-grade poorer quality deposits and the use of fast incre...
Etymology. The names "aluminium" and "aluminum" are derived from the word "alumine", an obsolete term for "alumina", the primary naturally occurring oxide of aluminium. "Alumine" was borrowed from French, which in turn derived it from "alumen", the classical Latin name for alum, the mineral from which it was collected....
One example was "Essai sur la Nomenclature chimique" (July 1811), written in French by a Swedish chemist, Jöns Jacob Berzelius, in which the name "aluminium" is given to the element that would be synthesized from alum. (Another article in the same journal issue also refers to the metal whose oxide is the basis of sapph...
Ludwig Wilhelm Gilbert had proposed "Thonerde-metall", after the German "Thonerde" for alumina, in his "Annalen der Physik" but that name never caught on at all even in Germany. Joseph W. Richards in 1891 found just one occurrence of "argillium" in Swedish, from the French "argille" for clay. The French themselves had ...
The International Union of Pure and Applied Chemistry (IUPAC) adopted "aluminium" as the standard international name for the element in 1990. In 1993, they recognized "aluminum" as an acceptable variant; the most recent 2005 edition of the IUPAC nomenclature of inorganic chemistry also acknowledges this spelling. IUPAC...
According to the International Resource Panel's Metal Stocks in Society report, the global per capita stock of aluminium in use in society (i.e. in cars, buildings, electronics, etc.) is . Much of this is in more-developed countries ( per capita) rather than less-developed countries ( per capita). Bayer process. Bauxit...
Hall–Héroult process. The conversion of alumina to aluminium is achieved by the Hall–Héroult process. In this energy-intensive process, a solution of alumina in a molten () mixture of cryolite (Na3AlF6) with calcium fluoride is electrolyzed to produce metallic aluminium. The liquid aluminium sinks to the bottom of the ...
The Hall–Heroult process produces aluminium with a purity of above 99%. Further purification can be done by the Hoopes process. This process involves the electrolysis of molten aluminium with a sodium, barium, and aluminium fluoride electrolyte. The resulting aluminium has a purity of 99.99%. Electric power represents ...
White dross from primary aluminium production and from secondary recycling operations still contains useful quantities of aluminium that can be extracted industrially. The process produces aluminium billets, together with a highly complex waste material. This waste is difficult to manage. It reacts with water, releasin...
The major uses for aluminium are in: Compounds. The great majority (about 90%) of aluminium oxide is converted to metallic aluminium. Being a very hard material (Mohs hardness 9), alumina is widely used as an abrasive; being extraordinarily chemically inert, it is useful in highly reactive environments such as high pre...
Many aluminium compounds have niche applications, for example: Biology. Despite its widespread occurrence in the Earth's crust, aluminium has no known function in biology. At pH 6–9 (relevant for most natural waters), aluminium precipitates out of water as the hydroxide and is hence not available; most elements behavin...
Effects. Aluminium, although rarely, can cause vitamin D-resistant osteomalacia, erythropoietin-resistant microcytic anemia, and central nervous system alterations. People with kidney insufficiency are especially at a risk. Chronic ingestion of hydrated aluminium silicates (for excess gastric acidity control) may resul...
Exposure to powdered aluminium or aluminium welding fumes can cause pulmonary fibrosis. Fine aluminium powder can ignite or explode, posing another workplace hazard. Exposure routes. Food is the main source of aluminium. Drinking water contains more aluminium than solid food; however, aluminium in food may be absorbed ...
Treatment. In case of suspected sudden intake of a large amount of aluminium, the only treatment is deferoxamine mesylate which may be given to help eliminate aluminium from the body by chelation therapy. However, this should be applied with caution as this reduces not only aluminium body levels, but also those of othe...
Aluminium is primary among the factors that reduce plant growth on acidic soils. Although it is generally harmless to plant growth in pH-neutral soils, in acid soils the concentration of toxic Al3+ cations increases and disturbs root growth and function. Wheat has developed a tolerance to aluminium, releasing organic c...
Advanced Chemistry Advanced Chemistry is a German hip hop group from Heidelberg in Baden-Württemberg, South Germany. Advanced Chemistry was founded in 1987 by Toni L, Linguist, Gee-One, DJ Mike MD (Mike Dippon) and MC Torch. Each member of the group holds German citizenship, and Toni L, Linguist, and Torch are of Itali...
This idea of national identity is important, as many rap artists in Germany have been of foreign origin. These so-called "Gastarbeiter" (guest workers) children saw breakdance, graffiti, rap music, and hip hop culture as a means of expressing themselves. Since the release of "Fremd im eigenen Land", many other German-l...
With the release of the single “Fremd im eigenen Land”, Advanced Chemistry separated itself from the rest of the rap being produced in Germany. This single was the first of its kind to go beyond simply imitating US rap and addressed the current issues of the time. Fremd im eigenen Land which translates to “foreign in m...
While Advanced Chemistry's use of the German language in their rap allows them to make claims to authenticity and true German heritage, bolstering pro-immigration sentiment, their style can also be problematic for immigrant notions of any real ethnic roots. Indeed, part of the Turkish ethnic minority of Frankfurt views...
It is quite possibly the feelings of alienation from the pure-blooded German demographic that drive Advanced Chemistry to attack nationalistic ideologies by asserting their "Germanness" as a group composed primarily of ethnic others. This cultural binary illustrates that rap has taken different routes in Germany and th...
Influences. Advanced Chemistry's work was rooted in German history and the country's specific political realities. However, they also drew inspiration from African-American hip-hop acts like A Tribe Called Quest and Public Enemy, who had helped bring a soulful sound and political consciousness to American hip-hop. One ...
Anglican Communion The Anglican Communion is the third-largest Christian communion after the Catholic and Eastern Orthodox churches, with approximately 85 - 91 million members. According to "Christianity Global: A Guide to the World's Largest Religion from Afghanistan to Zimbabwe", in 2020, there were an estimated 97.4...
As in the Church of England itself, the Anglican Communion includes the broad spectrum of beliefs and liturgical practises found in the Evangelical, Central and Anglo-Catholic traditions of Anglicanism; both the larger Reformed Anglican and the smaller Arminian Anglican theological perspectives have been represented. E...
History. The Anglican Communion traces much of its growth to the older mission organisations of the Church of England such as the Society for Promoting Christian Knowledge (founded 1698), the Society for the Propagation of the Gospel in Foreign Parts (founded 1701) and the Church Missionary Society (founded 1799). The ...
The oldest-surviving Anglican church building outside the British Isles (Britain and Ireland) is St Peter's Church in St. George's, Bermuda, established in 1612 (though the actual building had to be rebuilt several times over the following century). This is also the oldest surviving non-Roman Catholic church in the New...
At about the same time, in the colonies which remained linked to the crown, the Church of England began to appoint colonial bishops. In 1787, Charles Inglis (Bishop of Nova Scotia) was appointed with a jurisdiction over all of British North America; in time several more colleagues were appointed to other cities in pres...
A crucial step in the development of the modern communion was the idea of the Lambeth Conferences (discussed above). These conferences demonstrated that the bishops of disparate churches could manifest the unity of the church in their episcopal collegiality despite the absence of universal legal ties. Some bishops were...
Many of the provinces in developed countries have continued to adopt more liberal stances on sexuality and other issues, resulting in a number of de facto schisms, such as the series of splits which led to the creation of the Anglican Church in North America. Many churches are now in full communion with only some other...
Rapid social change and the dissipation of British cultural hegemony over its former colonies contributed to disputes over the role of women, and the parameters of marriage and divorce. In the late 1970s, the Continuing Anglican movement produced a number of new church bodies in opposition to women's ordination, prayer...
The 1958 conference's "Family in Contemporary Society" report affirmed the following position on abortion and was commended by the 1968 conference: The subsequent Lambeth Conference, in 1978, made no change to this position and commended the need for "programmes at diocesan level, involving both men and women ... to em...
"The more liberal provinces that are open to changing Church doctrine on marriage in order to allow for same-sex unions include Brazil, Canada, New Zealand, Scotland, South India, South Africa, the US and Wales". In 2023, the Church of England announced that it will authorise "prayers of thanksgiving, dedication and fo...
The conservative Anglican churches encouraging the realignment movement are more concentrated in the Global South. For example, the Anglican Church of Kenya, the Church of Nigeria and the Church of Uganda have opposed homosexuality. GAFCON, a fellowship of conservative Anglican churches, has appointed "missionary bisho...
Debates about social theology and ethics have occurred at the same time as debates on prayer book revision and the acceptable grounds for achieving full communion with non-Anglican churches. Ecclesiology, polity and ethos. The Anglican Communion has no official legal existence nor any governing structure that might exe...
Originally, the Church of England was self-contained and relied for its unity and identity on its own history, its traditional legal and episcopal structure, and its status as an established church of the state. As such, Anglicanism was from the outset a movement with an explicitly episcopal polity, a characteristic th...
Protracted conflict through the 17th century, with radical Protestants on the one hand and Roman Catholics who recognised the primacy of the Pope on the other, resulted in an association of churches that was both deliberately vague about doctrinal principles, yet bold in developing parameters of acceptable deviation. T...
Chicago Lambeth Quadrilateral. One of the enduringly influential early resolutions of the conference was the so-called Chicago-Lambeth Quadrilateral of 1888. Its intent was to provide the basis for discussions of reunion with the Roman Catholic and Orthodox churches, but it had the ancillary effect of establishing para...
Those who objected condemned these actions as unscriptural, unilateral, and without the agreement of the communion prior to these steps being taken. In response, the American Episcopal Church and the Anglican Church of Canada answered that the actions had been undertaken after lengthy scriptural and theological reflect...
Organisation. Provinces. The Anglican Communion consists of forty-two autonomous provinces each with its own primate and governing structure. These provinces may take the form of national churches (such as in Canada, Uganda, or Japan) or a collection of nations (such as the West Indies, Central Africa, or Southeast Asi...
Historic episcopate. The churches of the Anglican Communion have traditionally held that ordination in the historic episcopate is a core element in the validity of clerical ordinations. The Roman Catholic Church, however, does not recognise Anglican orders (see "Apostolicae curae"). Some Eastern Orthodox churches have ...
Arne Kaijser Arne Kaijser (born 1950) is a professor emeritus of history of technology at the KTH Royal Institute of Technology in Stockholm, and a former president of the Society for the History of Technology. Kaijser has published two books in Swedish: "Stadens ljus. Etableringen av de första svenska gasverken" and ...
Archipelago An archipelago ( ), sometimes called an island group or island chain, is a chain, cluster, or collection of islands. An archipelago may be in an ocean, a sea, or a smaller body of water. Example archipelagos include the Aegean Islands (the origin of the term), the Canadian Arctic Archipelago, the Stockholm ...
Depending on their geological origin, islands forming archipelagos can be referred to as "oceanic islands", "continental fragments", or "continental islands". Oceanic islands. Oceanic islands are formed by volcanoes erupting from the ocean floor. The Hawaiian Islands and Galapagos Islands in the Pacific, and Mascarene ...
Artificial archipelagos have been created in various countries for different purposes. Palm Islands and The World Islands in Dubai were or are being created for leisure and tourism purposes. Marker Wadden in the Netherlands is being built as a conservation area for birds and other wildlife. Superlatives. The largest ar...
Author In legal discourse, an author is the creator of an original work that has been published, whether that work is in written, graphic, or recorded medium. The creation of such a work is an act of authorship. Thus, a sculptor, painter, or composer, is an author of their respective sculptures, paintings, or compositi...
Some works are considered to be author-less. For example, the monkey selfie copyright dispute in the 2010s involved photographs taken by Celebes crested macaques using equipment belonging to a nature photographer. The photographer asserted authorship of the photographs, which the United States Copyright Office denied, ...
The copyrights on intellectual work expire after a certain time. It enters the public domain, where it can be used without limit. Copyright laws in many jurisdictions – mostly following the lead of the United States, in which the entertainment and publishing industries have very strong lobbying power – have been amende...
In the United States, the Copyright Clause of the Constitution of the United States () provides the Congress with the power of "securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries". The language regarding authors was derived from proposals by Charles Pinc...
In literary theory, critics find complications in the term "author" beyond what constitutes authorship in a legal setting. In the wake of postmodern literature, critics such as Roland Barthes and Michel Foucault have examined the role and relevance of authorship to the meaning or interpretation of a literary text. Bart...
Michel Foucault argues in his essay "What is an author?" (1969) that all authors are writers, but not all writers are authors. He states that "a private letter may have a signatory—it does not have an author." For a reader to assign the title of author upon any written work is to attribute certain standards upon the te...
Literary critics Barthes and Foucault suggest that readers should not rely on or look for the notion of one overarching voice when interpreting a written work, because of the complications inherent with a writer's title of "author." They warn of the dangers interpretations could suffer from when associating the subject...
Vanity publishing. Vanity publishers normally charge a flat fee for arranging publication, offer a platform for selling, and then take a percentage of the sale of every copy of a book. The author receives the rest of the money made. Most materials published this way are for niche groups and not for large audiences. Van...
There are three principal kinds of editing: Pierre Bourdieu's essay "The Field of Cultural Production" depicts the publishing industry as a "space of literary or artistic position-takings," also called the "field of struggles," which is defined by the tension and movement inherent among the various positions in the fi...
According to the studies of James Curran, the system of shared values among editors in Britain has generated a pressure among authors to write to fit the editors' expectations, removing the focus from the reader-audience and putting a strain on the relationship between authors and editors and on writing as a social act...
In some countries, authors also earn income from a government scheme such as the ELR (educational lending right) and PLR (public lending right) schemes in Australia. Under these schemes, authors are paid a fee for the number of copies of their books in educational and/or public libraries. These days, many authors suppl...
Andrey Markov Andrey Andreyevich Markov (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. He was also a strong, close to master-level, chess player. Markov and his younger brother Vladimir ...
Timeline. In 1877, Markov was awarded a gold medal for his outstanding solution of the problem "About Integration of Differential Equations by Continued Fractions with an Application to the Equation" formula_1. During the following year, he passed the candidate's examinations, and he remained at the university to prepa...
One year after the defense of his doctoral thesis, Markov was appointed extraordinary professor (1886) and in the same year he was elected adjunct to the Academy of Sciences. In 1890, after the death of Viktor Bunyakovsky, Markov became an extraordinary member of the academy. His promotion to an ordinary professor of S...

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