Max von Sydow was a Swedish actor who was perhaps best known for his dour brooding characterizations in the films of the Swedish director Ingmar Bergman. Interested in the theatre from childhood, von Sydow studied at the Royal Dramatic Theatre School in Stockholm (1948–51). He established his

Frank Tashlin was an American cartoonist, writer, animator, and film director who specialized in broad satirical comedies. Tashlin directed his animated cartoons like live-action films—employing a wide range of cinematic techniques—and transposed the elastic composition, loud colour, boisterous

Lars von Trier is a Danish film director and cofounder of the Dogme 95 movement, whose films are known for their bleak worldview and controversial subject matter. Von Trier attended the National Film School of Denmark, graduating in 1983. He was born Lars Trier, but while in school he added the

Volker Schlöndorff: …had appeared in the film, Margarethe von Trotta, with whom he collaborated professionally through the mid-1970s and who later directed films of her own. Notable among their collaborative works was Die verlorene Ehre der Katharina Blum (1975; The Lost Honor of Katharina Blum), adapted from the Heinrich Böll novel.

Heinrich Julius: Heinrich’s best work, the comedy Von Vincentio Ladislao (1594), showed his skill at characterization and used elements of the much-imitated style of the English actors, the exaggerated language and the pretensions of the braggart, as objects of satire. In 1607 he lost interest in the duchy and moved to Prague,…

von Willebrand disease, inherited blood disorder characterized by a prolonged bleeding time and a deficiency of factor VIII, an important blood-clotting agent. Von Willebrand disease is caused by deficiencies in von Willebrand factor (vWF), a molecule that facilitates platelet adhesion and is a

von Willebrand factor (vWF, or VWF), glycoprotein that plays an important role in stopping the escape of blood from vessels (hemostasis) following vascular injury. Von Willebrand factor (VWF) works by mediating the adherence of platelets to one another and to sites of vascular damage. VWF binds to

Jean-François Vonck was a lawyer who led the democratic faction, the Vonckists, in the Brabant Revolution, the southern Netherlands’ revolt against Austrian rule in 1789. Vonck worked as a lawyer in Brussels and in 1781 began to organize against the far-reaching administrative and religious reforms

Jean-François Vonck: …led the democratic faction, the Vonckists, in the Brabant Revolution, the southern Netherlands’ revolt against Austrian rule in 1789.

Joost van den Vondel was a Dutch poet and dramatist who produced some of the greatest works of Dutch literature. Van den Vondel’s Mennonite parents had fled from Antwerp to Cologne and ended up in Amsterdam. The young van den Vondel was largely self-educated. He taught himself French, and he also

Nikon: …led by the tsar’s confessor, Stefan Vonifatyev, and the priests Ivan Neronov and Avvakum Petrovich (all, like him, natives of the Nizhny Novgorod region). This group of priests strove to revitalize the church by bringing about closer contact with the mass of the faithful, and they also sought to purify…

palm: Characteristic morphological features: Nannorrhops, Nypa, Vonitra) appear to involve equal or subequal division at the apex that results in a forking habit. The two newly formed branches may continue equally, or one may be overtopped by the other (Nannorrhops). When thickening occurs, as in the royal palms (Roystonea) or in…

Lindsey Vonn is an American Alpine skier who won four women’s World Cup overall championships (2008–10 and 2012) and was the first woman to win 82 World Cup races. She also claimed three Olympic Winter Games medals and eight world championships medals during her international racing career. Kildow

Kurt Vonnegut was an American writer noted for his wryly satirical novels who frequently used postmodern techniques as well as elements of fantasy and science fiction to highlight the horrors and ironies of 20th-century civilization. Much of Vonnegut’s work is marked by an essentially fatalistic

Kurt Vonnegut was an American writer noted for his wryly satirical novels who frequently used postmodern techniques as well as elements of fantasy and science fiction to highlight the horrors and ironies of 20th-century civilization. Much of Vonnegut’s work is marked by an essentially fatalistic

Bessie Potter Vonnoh was an American sculptor known for her delicate portrayals in bronze of mothers and children and young women. Her Impressionistic style and intimate designs set her apart from other sculptors of her generation. After the death of her father, the Potter family moved from St.

Vonones I was the king of Parthia (reigned ad 7/8–11). Vonones was the eldest son of Phraates IV (q.v.) and was in Rome as a hostage when the Parthian king Orodes III died in about ad 7. The Parthians requested the return of one of the sons of Phraates IV, and the Roman emperor Tiberius sent

ancient Iran: Dissolution of the Parthian state: After the short reign of Vonones II (51), the throne passed to Vologeses I (reigned 51–80), an ardent anti-Roman. One of his brothers, Vonones, was made king of Media. Vologeses I wanted his second brother, Tiridates, to be king of Armenia—putting him in position to break with Rome, which opposed…

canon law: Independent churches of Eastern Christianity: …of the Middle East by Arthur Vööbus, an Estonian-American church historian. These manuscripts cover the period from the 3rd to the 14th century and deal with ecclesiastical regulations of the Syrian churches. Included among these manuscripts are the following: “The Canons of the Godly Monastery of St. Mār Mattai” (630),…

Vodou, a traditional Afro-Haitian religion. Vodou represents a syncretism of the West African Vodun religion and Roman Catholicism by the descendants of the Dahomean, Kongo, Yoruba, and other ethnic groups who had been enslaved and transported to colonial Saint-Domingue (as Haiti was known then)

Alfred Métraux: Le Vaudon haïtien (1958; Voodoo in Haiti), one of his two books on that island’s culture, presented voodoo as a structured, complex religious system, examined its African origins, and showed its relation to Roman Catholicism in Haiti.

William Plomer: …he founded a magazine called Voorslag (“Whiplash”) with which he intended to excoriate South African racist society. Public outrage silenced the journal, and Plomer and Campbell left the country.

Voortrekker, any of the Boers (Dutch settlers or their descendants), or, as they came to be called in the 20th century, Afrikaners, who left the British Cape Colony in Southern Africa after 1834 and migrated into the interior Highveld north of the Orange River. During the next 20 years, they

Marxism: Stalin: His work Voprosy leninizma (1926; Problems of Leninism), which appeared in 11 editions during his lifetime, sets forth an ideology of power and activism that rides roughshod over the more nuanced approach of Lenin.

Mikhail Bakhtin: …Voprosy literatury i estetiki (1975; The Dialogic Imagination), in which he postulated that, rather than being static, language evolves dynamically and is affected by and affects the culture that produces and uses it. Bakhtin also wrote Tvorchestvo Fransua Rable i narodnaya kultura srednevekovya i Renessansa (1965; Rabelais and His World).

radio range: (VOR) has been developed in various forms since about 1930. It transmits two signals simultaneously in all directions. Operating in the very high frequency (VHF) range, it is less subject than the lower-frequency radio range to disturbances by day-night alternation, weather, and other causes. The…

Leonid Maksimovich Leonov: …he followed with Vor (1927; The Thief), a pessimistic tale set in the Moscow criminal underworld.

vestibulo-ocular reflex (VOR), eye movement that functions to stabilize gaze by countering movement of the head. In VOR the semicircular canals of the inner ear measure rotation of the head and provide a signal for the oculomotor nuclei of the brainstem, which innervate the eye muscles. The muscles

Theodor Fontane: …56, Vor dem Sturm (1878; Before the Storm), considered to be a masterpiece in the genre of the historical novel. He portrayed the Prussian nobility both critically and sympathetically. His aim was, as he said, “the undistorted reflection of the life we lead.” In several of his novels Fontane also…

Fritz von Unruh: …expressed in the dramatic poem Vor der Entscheidung (1914; “Before the Decision”) are early variations on the two themes basic to his entire work: the nature of the social order into which the individual has to be integrated and the necessity to ground this order not in authority but in…

Johan Bojer: …immigrants, Vor egen stamme (1924; The Emigrants). Bojer’s international popularity survived into the 1940s.

Gerhart Hauptmann: …social drama Vor Sonnenaufgang (Before Dawn) made him famous overnight, though it shocked the theatregoing public. This starkly realistic tragedy, dealing with contemporary social problems, signaled the end of the rhetorical and highly stylized German drama of the 19th century. Encouraged by the controversy, Hauptmann wrote in rapid succession…

José Eustasio Rivera: …whose novel La vorágine (1924; The Vortex), a powerful denunciation of the exploitation of the rubber gatherers in the upper Amazon jungle, is considered by many critics to be the best of many South American novels with jungle settings.

Vorarlberg, Bundesland (federal state), far western Austria. It is bounded on the north by Bavaria (Germany) and Lake Constance (Bodensee), on the west by Switzerland (across the Rhine River) and Liechtenstein, on the south by Switzerland, and on the east (over the Arlberg Pass) by Tirol. With an

socialism: Revisionism and revolution: …to socialism, he argued in Evolutionary Socialism (1899), would be safer than the revolutionary route, with its dangerously vague and potentially tyrannical dictatorship of the proletariat.

Bavarian Forest: The Vorderer Forest, or Danube Hills, a rolling plateau situated to the southwest between the Danube and the Pfahl, seldom rises more than 3,300 feet (1,000 m) above sea level. Meadow, isolated farmsteads, and small hamlets dominate the landscape; only the higher and steeper slopes are…

Rhine River: Physiography: The Vorderrhein emerges from Lake Toma at 7,690 feet (2,344 metres), near the Oberalp Pass in the Central Alps, and then flows eastward past Disentis to be joined by the Hinterrhein from the south at Reichenau above Chur. (The Hinterrhein rises about five miles west of…

Vordingborg, city, southern Zealand (Sjælland), Denmark, on Masned Sound. Founded in the 12th century around its castle, which was built by Valdemar I as a defense against the Wends, the town of Vordingborg became a favourite meeting place of the Danehof (national assembly), at one of whose

Eifel: Voreifel. In the Schneifel (German: “Snow Eifel”), near the Belgian frontier, scrub and forest are common, with cultivation only on the richer soils. The Hocheifel (“High Eifel”), which includes the highest point in the plateau, Hohe Acht (2,451 feet [747 metres]), is a dissected highland…

Vørings Falls, waterfall, southwestern Norway. The waterfall, with a drop of 476 feet (145 metres), is located on Hardanger Fjord, 7 miles (11 km) southeast of Eidfjord. It is a popular tourist

Vørings Falls, waterfall, southwestern Norway. The waterfall, with a drop of 476 feet (145 metres), is located on Hardanger Fjord, 7 miles (11 km) southeast of Eidfjord. It is a popular tourist

Gulf of Euboea, arm of the Aegean Sea, between the island of Euboea (Modern Greek: Évvoia) to the northeast and the Greek mainland to the southwest. Trending northwest-southeast, the gulf is divided by the narrow Strait of Euripus, at the town of Chalkída. The northern part is about 50 miles (80

Vorkuta, city, Komi republic, northwestern Russia, on the Vorkuta River. Coal mining began in the area in 1932, but the industry and city did not grow significantly until World War II. Initially the coal exploitation used penal labour. The area subsequently became the site of some of Stalin’s

Julius Friedrich Cohnheim: Cohnheim’s Vorlesungen über allgemeine Pathologie, 2 vol. (1877–80; Lectures on General Pathology), far outlasted contemporary texts on the subject, and his method of freezing tissue before slicing it into thin sections for microscopic examination is now a standard clinical procedure.

aesthetics: Relationship between form and content: …Hegel, who argued, in his Vorlesungen über die Aesthetik (1832; “Lectures on Aesthetics”; Eng. trans. Aesthetics: Lectures on Fine Art), roughly as follows: Our sensuous appreciation of art concentrates upon the given “appearance”—the “form.” It is this that holds our attention and that gives to the work of art its…

history of logic: Ernst Schröder: …main work was his three-volume Vorlesungen über die Algebra der Logik (1890–1905; “Lectures on the Algebra of Logic”). This is an extensive and sometimes original presentation of all that was known about the algebra of logic circa 1890, together with derivations of thousands of theorems and an extensive bibliography of…

Scholasticism: …die Geschichte der Philosophie (1833–36; Lectures on the History of Philosophy), declared that he would “put on seven-league boots” in order to skip over the thousand years between the 6th and 17th centuries and, having at last arrived at René Descartes, said that now he could “cry land like the…

Salomon Bochner: 1959, Lectures on Fourier Integrals). He left Germany in 1933, shortly after Adolph Hitler came to power. (He later convinced his parents and sister’s family to move to England before they could be destroyed by the Holocaust.) Receiving an invitation to join the faculty at Princeton…

Moritz Benedikt Cantor: It was followed by his Vorlesungen über Geschichte der Mathematik (“Lectures on the History of Mathematics”), the first volume of which was published in 1880, the second in 1892, and the third in successive parts between 1894 and 1896. By this time Cantor was too old to undertake the fourth…

geometry: A grand synthesis: …Moritz Pasch (1843–1930), in his Vorlesungen über neuere Geometrie (1882; “Lectures on the New Geometry”), identified what was wanting: undefined concepts, axioms about those concepts, and more rigorous logic based on those axioms. The choice of undefined concepts and axioms is free, apart from the constraint of consistency. Mathematicians following…

August Wilhelm von Schlegel: …lectures were later published as Vorlesungen über schöne Literatur und Kunst (1884; “Lectures on Fine Art and Literature”). After his divorce from Michaelis, Schlegel accompanied Mme de Staël on travels in Germany, Italy, France, and Sweden, where he served in 1813–14 as press secretary to the crown prince Bernadotte. The…

Oskar Bolza: …in 1904, published a treatise, Lectures on the Calculus of Variations (revised and translated by him into German as Vorlesungen über Variationsrechnung, 1908), which became a classic in the field. Several of his papers published in 1913 and 1914 developed an original variational problem known as the problem of Bolza,…

Carl Jacobi: His Vorlesungenüber Dynamik (1866; “Lectures on Dynamics”) relates his work with differential equations and dynamics. The Hamilton-Jacobi equation now plays a significant role in the presentation of quantum mechanics.

polecat: The marbled polecat (Vormela peregusna), which inhabits foothills and steppes from southeastern Europe to southern Mongolia is similar to the European species in habits and appearance. Marbled polecats are slightly smaller, however, weighing 0.3–0.7 kg (0.7–1.5 pounds) and ranging in length from 44 to 66 cm…

Martinus Nijhoff: …apparent in his second volume, Vormen (1924; “Forms”), which also reveals Nijhoff’s realistic, direct approach to Christianity in, for example, “De soldaat die Jezus kruisigde” (“The Soldier Who Crucified Jesus”).

Belgian literature: After World War I: …the “personalistic” poets of the Vormen (1936–40; “Forms”) group, of whom Pieter Geert Buckinx is representative.

Richard Ten Eyck: Ten Eyck also designed the Vornado fan for the O.A. Sutton Corporation in Wichita (c. 1945–59), with later reincarnations by Vornado Air Circulators, Inc. (after 1988). These fans pushed a concentrated funnel of air in emulation of the turbines in jet engines and became an icon of the so-called Atomic…

Arkady Vorobyev was a weightlifter who won two Olympic gold medals and was the first Soviet light-heavyweight lifter to win the world championship. While stationed at Odessa in the Soviet army, Vorobyev worked as a deep-sea diver and began weight training. As a light-heavyweight lifter at the 1952

Arkady Vorobyev was a weightlifter who won two Olympic gold medals and was the first Soviet light-heavyweight lifter to win the world championship. While stationed at Odessa in the Soviet army, Vorobyev worked as a deep-sea diver and began weight training. As a light-heavyweight lifter at the 1952

Arkady Vorobyev was a weightlifter who won two Olympic gold medals and was the first Soviet light-heavyweight lifter to win the world championship. While stationed at Odessa in the Soviet army, Vorobyev worked as a deep-sea diver and began weight training. As a light-heavyweight lifter at the 1952

Arkady Vorobyev was a weightlifter who won two Olympic gold medals and was the first Soviet light-heavyweight lifter to win the world championship. While stationed at Odessa in the Soviet army, Vorobyev worked as a deep-sea diver and began weight training. As a light-heavyweight lifter at the 1952

elephant bird: >Vorombe), with the species V. titan being both the largest member of the family and the largest bird that ever lived.

elephant bird: and Vorombe), with the species V. titan being both the largest member of the family and the largest bird that ever lived.

Voronezh, oblast (region), western Russia. The oblast lies in the basin of the middle Don River, which bisects it north–south. The northeastern part of the oblast consists of the level Oka–Don Plain; west of the Don the land rises to the Central Russian Upland, which is greatly dissected by valleys

Voronezh, city and administrative centre of Voronezh oblast (region), western Russia. It lies along the right bank of the Voronezh River above its confluence with the Don. The city was founded in 1586 as a fortress, later forming part of the Belgorod defensive line. Peter I the Great built his

Voronezh, oblast (region), western Russia. The oblast lies in the basin of the middle Don River, which bisects it north–south. The northeastern part of the oblast consists of the level Oka–Don Plain; west of the Don the land rises to the Central Russian Upland, which is greatly dissected by valleys

Voronezh, city and administrative centre of Voronezh oblast (region), western Russia. It lies along the right bank of the Voronezh River above its confluence with the Don. The city was founded in 1586 as a fortress, later forming part of the Belgorod defensive line. Peter I the Great built his

St. Petersburg: Admiralty Side: …finest feature, was designed by Andrey Voronikhin in Russian Neoclassical style and has an interior rich in sculptures and paintings. A magnificent semicircular Corinthian colonnade dominates its exterior. Another interesting building is the department store Gostiny Dvor (1761–85), originally designed by Jean-Baptiste M. Vallin de la Mothe. This building forms…

Kara Sea: …(620 metres), and the parallel Voronin Trough, some 180 miles (290 km) east, with a depth of 1,475 feet (450 metres). East of Novaya Zemlya stretches the Novaya Zemlya Trough, 650–1,300 feet (200–400 metres) deep.

Vladimir Voronin was a Moldovan politician who served as president of Moldova from 2001 to 2009. Voronin graduated from the Technical College of Chișinǎu in 1961 and from the Union Institute of Food Industry in 1971. After serving as a bread-factory director in the 1960s, he began a career as an

White Sea: …prevail in the Gorlo Strait, Voronka, and the Mezen mouth. The sea’s chief hollow is separated from the Barents Sea by a sill 130 feet deep, which restricts deepwater exchange between the two bodies of water.

Battle of Stalingrad: Zhukov, Aleksandr Mikhailovich Vasilevsky, and Nikolay Nikolayevich Voronov. It was launched in two spearheads, some 50 miles (80 km) north and south of the German salient whose tip was at Stalingrad. The counteroffensive utterly surprised the Germans, who thought the Soviets incapable of mounting such an attack. The operation was…

St. Petersburg: The rise to splendour: …the Smolny Convent, and the Vorontsov and Stroganov palaces, among others; outside the city were built the summer palaces of Peterhof and of Tsarskoye Selo (now Pushkin). After a transitional period dominated by the architecture of Jean-Baptiste M. Vallin de la Mothe and Aleksandr Kokorinov, toward the end of the…

Mikhail Illarionovich Vorontsov: In addition, Roman’s son Aleksandr (1741–1805) became a noted diplomat and statesman, serving as Russia’s minister to Great Britain and to the Dutch Netherlands, as president of the department of trade (1773–92), and as chancellor (1802–04). His brother Semyon (1744–1832) also served as Russia’s minister to Great Britain (1784–1806),…

Mikhail Illarionovich Vorontsov was a Russian statesman who played a major role, particularly in foreign affairs, during the reign (1741–62) of Empress Elizabeth. A member of a family that became prominent in Russian court circles in the 18th century, he was appointed a page in the court of

Mikhail Semyonovich, Prince Vorontsov was a Russian military and government official who was an outstanding imperial administrator. The son of the diplomat Semyon R. Vorontsov, he was born into a family that had become highly influential in Russian political affairs in the 18th century. He entered

Mikhail Illarionovich Vorontsov: His brother Semyon (1744–1832) also served as Russia’s minister to Great Britain (1784–1806), and, although his determined pro-English attitudes brought occasional disgrace upon him, he was offered the post of chancellor, which he refused.

Yekaterina Romanovna Vorontsova, Princess Dashkova was an associate of Empress Catherine II the Great and a prominent patroness of the literary arts in 18th-century Russia. A member of the influential Vorontsov family, Yekaterina Romanovna married Prince Mikhail Ivanovich Dashkov in 1759. After

Kliment Yefremovich Voroshilov was a military and political leader of the Soviet Union who served as head of state after the death of his close friend and collaborator Joseph Stalin. A Bolshevik activist from 1903, Voroshilov participated in the civil war that followed the Bolshevik takeover in

Luhansk, city, eastern Ukraine. It lies along the Luhan (Lugan) River at the latter’s confluence with the Vilkhivka (Olkhovaya) River. The city dates from 1795, when a state iron foundry was established there to supply ordnance to the Black Sea fleet. Luhansk grew with the development of the Donets

Stavropol, city and administrative centre of Stavropol kray (territory), southwestern Russia, situated on the Stavropol Upland near the source of the Grachovka River. It was founded in 1777 as a fortress. Although it was at first a major route and administrative centre, the city was later bypassed

Alchevsk, city, eastern Ukraine. It lies along the railway from Luhansk to Debaltseve. Alchevsk was founded in 1895 with the establishment of the Donetsko-Yuryevsky ironworks. The plant developed into a large, integrated ironworks and steelworks, which was expanded greatly in the 1950s and ’60s.

Luhansk, city, eastern Ukraine. It lies along the Luhan (Lugan) River at the latter’s confluence with the Vilkhivka (Olkhovaya) River. The city dates from 1795, when a state iron foundry was established there to supply ordnance to the Black Sea fleet. Luhansk grew with the development of the Donets

Mihály Vörösmarty was a poet and dramatist who helped make the literature of Hungary truly Hungarian during the era (1825–49) of social reforms. By ridding Hungarian literature of overwhelming classical and German influence, he made it national not only in language but in spirit. Born into an

Armenia: Drainage: …Arpa (80 miles), and the Vorotan (Bargyushad; 111 miles), serve to irrigate most of Armenia. The tributaries of the Kura—the Debed (109 miles), the Aghstev (80 miles), and others—pass through Armenia’s northeastern regions. Lake Sevan, with a capacity in excess of 9 cubic miles (39 cubic kilometres) of water, is…

Pomerania: …in the name of Mecklenburg-West Pomerania Land (state). The region is generally flat, and there are numerous small rivers and, along the east coast, many lakes.

Vorschule, (German: “preparatory school”), a type of private elementary school that developed in Prussia and other north German states in the mid-19th century to prepare upper-class children for secondary schools. Theoretically, any Prussian boy who had completed the Volksschule (a free, universal,

Battle of the Vorskla River: …toward the Dnieper, at the Vorskla, a tributary of the lower Dnieper. Although Vytautas’ force, which was well organized and armed with cannon, fared well in a battle of several hours against the main body of the Mongol army, commanded by Edigü, it was unable to withstand a rear attack…

Battle of the Vorskla River, (Aug. 12, 1399), major victory of the Golden Horde (the westernmost division of the Mongol empire, which had suzerainty over the Russian lands) over the Lithuanian ruler Vytautas, which ended his attempt to extend his control over all southern Russia. As a result of

legal profession: Classical beginnings: …fashion but as interpreters (Vorsprecher) for those who wished to present a case but felt uncomfortable doing so themselves. The peculiar system of development of early Roman law, by annual edict and by the extension of trial formulas, gave the Roman patrician legal expert an influential position. He became…

John Vorster was a far-right Nationalist politician who served as prime minister (1966–78) and president (1978–79) of South Africa. He was forced to resign from the presidency because of a political scandal. Vorster was the 13th child of a wealthy Afrikaner sheep farmer. He studied at the

John Vorster was a far-right Nationalist politician who served as prime minister (1966–78) and president (1978–79) of South Africa. He was forced to resign from the presidency because of a political scandal. Vorster was the 13th child of a wealthy Afrikaner sheep farmer. He studied at the

John Vorster was a far-right Nationalist politician who served as prime minister (1966–78) and president (1978–79) of South Africa. He was forced to resign from the presidency because of a political scandal. Vorster was the 13th child of a wealthy Afrikaner sheep farmer. He studied at the

Theodor Julius Geiger: …of public order, he wrote Vorstudien zu einer Soziologie des Rechts (1947; reprinted 1964; “Preliminary Studies on the Sociology of Law”), which dealt with law and regulation in society. Several of his works were published posthumously: Ideologie und Wahrheit (1953; “Ideology and Truth”) discusses ideology and its role in the…

Zacharias Frankel: Frankel also published Vorstudien zur Septuaginta (1841; “Preliminary Studies in the Septuagint”), in which he, the only major 19th-century Jewish scholar who wrote on the Septuagint (the first Greek version of the Old Testament), sought to show the necessary connection between Talmudic and Septuagintic exegesis. It is considered…

topology: History of topology: …mathematician Johann Listing, who published Vorstudien zur Topologie (1847; “Introductory Studies in Topology”), which is often cited as the first print occurrence of the term topology. In 1851 the German mathematician Bernhard Riemann considered surfaces related to complex number theory and, hence, utilized combinatorial topology as a tool for analyzing…

voršud, among the Finno-Ugric Udmurt (Votyak) people, a family spirit, literally “luck protector”; the term also designates a birchbark container kept in the family shrine, or kuala, as a receptacle for offerings and possibly an image of the protector. The voršud was believed to watch over the

whirlpool: …a central downdraft are termed vortexes and occur where coastal and bottom configurations provide narrow passages of considerable depth. Slightly different is vortex motion in streams; at certain stages of turbulent flow, rotating currents with central updrafts are formed. These are called kolks, or boils, and are readily visible on…

fluid mechanics: Potential flow with circulation: vortex lines: …then referred to as a vortex line. Each small element of fluid outside the core, if examined in isolation for a short interval of time, appears to be undergoing translation without rotation, and the local vorticity is zero. Were it not so, the viscous torques would not cancel and the…

fluid mechanics: Potential flow with circulation: vortex lines: …then referred to as a vortex line. Each small element of fluid outside the core, if examined in isolation for a short interval of time, appears to be undergoing translation without rotation, and the local vorticity is zero. Were it not so, the viscous torques would not cancel and the…