Moscow is the capital and most populous city of Russia, with 13.2 million residents within the city limits, 17 million within the urban area and 20 million within the metropolitan area. Moscow is one of Russia's federal cities. Moscow is the major political, economic and scientific center of Russia and Eastern Europe, as well as the largest city on the European continent. By broader definitions, Moscow is among the world's largest cities, being the 14th largest metro area, the 18th largest agglomeration, the 14th largest urban area, the 11th largest by population within city limits worldwide. According to Forbes 2013, Moscow has been ranked as the ninth most expensive city in the world by Mercer and has one of the world's largest urban economies, being ranked as an alpha global city according to the Globalization and World Cities Research Network, is one of the fastest growing tourist destinations in the world according to the MasterCard Global Destination Cities Index. Moscow is the coldest megacity on Earth.
It is home to the Ostankino Tower, the tallest free standing structure in Europe. By its territorial expansion on July 1, 2012 southwest into the Moscow Oblast, the area of the capital more than doubled, going from 1,091 to 2,511 square kilometers, resulting in Moscow becoming the largest city on the European continent by area. Moscow is situated on the Moskva River in the Central Federal District of European Russia, making it Europe's most populated inland city; the city is well known for its architecture its historic buildings such as Saint Basil's Cathedral with its colorful architectural style. With over 40 percent of its territory covered by greenery, it is one of the greenest capitals and major cities in Europe and the world, having the largest forest in an urban area within its borders—more than any other major city—even before its expansion in 2012; the city has served as the capital of a progression of states, from the medieval Grand Duchy of Moscow and the subsequent Tsardom of Russia to the Russian Empire to the Soviet Union and the contemporary Russian Federation.
Moscow is a seat of power of the Government of Russia, being the site of the Moscow Kremlin, a medieval city-fortress, today the residence for work of the President of Russia. The Moscow Kremlin and Red Square are one of several World Heritage Sites in the city. Both chambers of the Russian parliament sit in the city. Moscow is considered the center of Russian culture, having served as the home of Russian artists and sports figures and because of the presence of museums and political institutions and theatres; the city is served by a transit network, which includes four international airports, nine railway terminals, numerous trams, a monorail system and one of the deepest underground rapid transit systems in the world, the Moscow Metro, the fourth-largest in the world and largest outside Asia in terms of passenger numbers, the busiest in Europe. It is recognized as one of the city's landmarks due to the rich architecture of its 200 stations. Moscow has acquired a number of epithets, most referring to its size and preeminent status within the nation: The Third Rome, the Whitestone One, the First Throne, the Forty Soroks.
Moscow is one of the twelve Hero Cities. The demonym for a Moscow resident is "москвич" for male or "москвичка" for female, rendered in English as Muscovite; the name "Moscow" is abbreviated "MSK". The name of the city is thought to be derived from the name of the Moskva River. There have been proposed several theories of the origin of the name of the river. Finno-Ugric Merya and Muroma people, who were among the several Early Eastern Slavic tribes which inhabited the area, called the river Mustajoki, it has been suggested. The most linguistically well grounded and accepted is from the Proto-Balto-Slavic root *mŭzg-/muzg- from the Proto-Indo-European *meu- "wet", so the name Moskva might signify a river at a wetland or a marsh, its cognates include Russian: музга, muzga "pool, puddle", Lithuanian: mazgoti and Latvian: mazgāt "to wash", Sanskrit: májjati "to drown", Latin: mergō "to dip, immerse". In many Slavic countries Moskov is a surname, most common in Bulgaria, Russia and North Macedonia. There exist as well similar place names in Poland like Mozgawa.
The original Old Russian form of the name is reconstructed as *Москы, *Mosky, hence it was one of a few Slavic ū-stem nouns. As with other nouns of that declension, it had been undergoing a morphological transformation at the early stage of the development of the language, as a result the first written mentions in the 12th century were Московь, Moskovĭ, Москви, Moskvi, Москвe/Москвѣ, Moskve/Moskvě. From the latter forms came the modern Russian name Москва, a result of morphological generalisation with the numerous Slavic ā-stem nouns. However, the form Moskovĭ has left some traces in many other languages, such as English: Moscow, German: Moskau, French: Moscou, Georgian: მოსკოვი, Latvian: Maskava, Ottoman Turkish: Moskov, Tatar: Мәскәү, Mäskäw, Kazakh: Мәскеу, Mäskew, Chuvash: Мускав, etc. In a similar manner the Latin name Moscovia has been formed it became a collo
The Soviet Union the Union of Soviet Socialist Republics, was a socialist state in Eurasia that existed from 1922 to 1991. Nominally a union of multiple national Soviet republics, its government and economy were centralized; the country was a one-party state, governed by the Communist Party with Moscow as its capital in its largest republic, the Russian Soviet Federative Socialist Republic. Other major urban centres were Leningrad, Minsk, Alma-Ata, Novosibirsk, it spanned over 10,000 kilometres east to west across 11 time zones, over 7,200 kilometres north to south. It had five climate zones: tundra, steppes and mountains; the Soviet Union had its roots in the 1917 October Revolution, when the Bolsheviks, led by Vladimir Lenin, overthrew the Russian Provisional Government which had replaced Tsar Nicholas II during World War I. In 1922, the Soviet Union was formed by a treaty which legalized the unification of the Russian, Transcaucasian and Byelorussian republics that had occurred from 1918. Following Lenin's death in 1924 and a brief power struggle, Joseph Stalin came to power in the mid-1920s.
Stalin committed the state's ideology to Marxism–Leninism and constructed a command economy which led to a period of rapid industrialization and collectivization. During his rule, political paranoia fermented and the Great Purge removed Stalin's opponents within and outside of the party via arbitrary arrests and persecutions of many people, resulting in at least 600,000 deaths. In 1933, a major famine struck the country. Before the start of World War II in 1939, the Soviets signed the Molotov–Ribbentrop Pact, agreeing to non-aggression with Nazi Germany, after which the USSR invaded Poland on 17 September 1939. In June 1941, Germany broke the pact and invaded the Soviet Union, opening the largest and bloodiest theatre of war in history. Soviet war casualties accounted for the highest proportion of the conflict in the effort of acquiring the upper hand over Axis forces at intense battles such as Stalingrad and Kursk; the territories overtaken by the Red Army became satellite states of the Soviet Union.
The post-war division of Europe into capitalist and communist halves would lead to increased tensions with the United States-led Western Bloc, known as the Cold War. Stalin died in 1953 and was succeeded by Nikita Khrushchev, who in 1956 denounced Stalin and began the de-Stalinization; the Cuban Missile Crisis occurred during Khrushchev's rule, among the many factors that led to his downfall in 1964. In the early 1970s, there was a brief détente of relations with the United States, but tensions resumed with the Soviet–Afghan War in 1979. In 1985, the last Soviet premier, Mikhail Gorbachev, sought to reform and liberalize the economy through his policies of glasnost and perestroika, which caused political instability. In 1989, Soviet satellite states in Eastern Europe overthrew their respective communist governments; as part of an attempt to prevent the country's dissolution due to rising nationalist and separatist movements, a referendum was held in March 1991, boycotted by some republics, that resulted in a majority of participating citizens voting in favor of preserving the union as a renewed federation.
Gorbachev's power was diminished after Russian President Boris Yeltsin's high-profile role in facing down a coup d'état attempted by Communist Party hardliners. In late 1991, Gorbachev resigned and the Supreme Soviet of the Soviet Union met and formally dissolved the Soviet Union; the remaining 12 constituent republics emerged as independent post-Soviet states, with the Russian Federation—formerly the Russian SFSR—assuming the Soviet Union's rights and obligations and being recognized as the successor state. The Soviet Union was a powerhouse of many significant technological achievements and innovations of the 20th century, including the world's first human-made satellite, the first humans in space and the first probe to land on another planet, Venus; the country had the largest standing military in the world. The Soviet Union was recognized as one of the five nuclear weapons states and possessed the largest stockpile of weapons of mass destruction, it was a founding permanent member of the United Nations Security Council as well as a member of the Organization for Security and Co-operation in Europe, the World Federation of Trade Unions and the leading member of the Council for Mutual Economic Assistance and the Warsaw Pact.
The word "Soviet" is derived from a Russian word сове́т meaning council, advice, harmony and all deriving from the proto-Slavic verbal stem of vět-iti, related to Slavic věst, English "wise", the root in "ad-vis-or", or the Dutch weten. The word sovietnik means "councillor". A number of organizations in Russian history were called "council". For example, in the Russian Empire the State Council, which functioned from 1810 to 1917, was referred to as a Council of Ministers after the revolt of 1905. During the Georgian Affair, Vladimir Lenin envisioned an expression of Great Russian ethnic chauvinism by Joseph Stalin and his supporters, calling for these nation-states to join Russia as semi-independent parts of a greater union, which he named as the Union of Soviet Republics of Europe and Asia. Stalin resisted the proposal, but accepted it, although with Lenin's agreement changed the name of the newly proposed sta
Saint Petersburg is Russia's second-largest city after Moscow, with 5 million inhabitants in 2012, part of the Saint Petersburg agglomeration with a population of 6.2 million. An important Russian port on the Baltic Sea, it has a status of a federal subject. Situated on the Neva River, at the head of the Gulf of Finland on the Baltic Sea, it was founded by Tsar Peter the Great on 27 May 1703. During the periods 1713–1728 and 1732–1918, Saint Petersburg was the capital of Imperial Russia. In 1918, the central government bodies moved to Moscow, about 625 km to the south-east. Saint Petersburg is one of the most modern cities of Russia, as well as its cultural capital; the Historic Centre of Saint Petersburg and Related Groups of Monuments constitute a UNESCO World Heritage Site. Saint Petersburg is home to the Hermitage, one of the largest art museums in the world. Many foreign consulates, international corporations and businesses have offices in Saint Petersburg. An admirer of everything German, Peter the Great named the city, Sankt-Peterburg.
On 1 September 1914, after the outbreak of World War I, the Imperial government renamed the city Petrograd, meaning "Peter's city", in order to expunge the German name Sankt and Burg. On 26 January 1924, shortly after the death of Vladimir Lenin, it was renamed to Leningrad, meaning "Lenin's City". On 6 September 1991, Sankt-Peterburg, was returned. Today, in English the city is known as "Saint Petersburg". Local residents refer to the city by its shortened nickname, Piter; the city's traditional nicknames among Russians are the Window to Europe. Swedish colonists built Nyenskans, a fortress at the mouth of the Neva River in 1611, in what was called Ingermanland, inhabited by Finnic tribe of Ingrians; the small town of Nyen grew up around it. At the end of the 17th century, Peter the Great, interested in seafaring and maritime affairs, wanted Russia to gain a seaport in order to trade with the rest of Europe, he needed a better seaport than the country's main one at the time, on the White Sea in the far north and closed to shipping during the winter.
On 12 May 1703, during the Great Northern War, Peter the Great captured Nyenskans and soon replaced the fortress. On 27 May 1703, closer to the estuary 5 km inland from the gulf), on Zayachy Island, he laid down the Peter and Paul Fortress, which became the first brick and stone building of the new city; the city was built by conscripted peasants from all over Russia. Tens of thousands of serfs died building the city; the city became the centre of the Saint Petersburg Governorate. Peter moved the capital from Moscow to Saint Petersburg in 1712, 9 years before the Treaty of Nystad of 1721 ended the war. During its first few years, the city developed around Trinity Square on the right bank of the Neva, near the Peter and Paul Fortress. However, Saint Petersburg soon started to be built out according to a plan. By 1716 the Swiss Italian Domenico Trezzini had elaborated a project whereby the city centre would be located on Vasilyevsky Island and shaped by a rectangular grid of canals; the project is evident in the layout of the streets.
In 1716, Peter the Great appointed Frenchman Jean-Baptiste Alexandre Le Blond as the chief architect of Saint Petersburg. The style of Petrine Baroque, developed by Trezzini and other architects and exemplified by such buildings as the Menshikov Palace, Kunstkamera and Paul Cathedral, Twelve Collegia, became prominent in the city architecture of the early 18th century. In 1724 the Academy of Sciences and Academic Gymnasium were established in Saint Petersburg by Peter the Great. In 1725, Peter died at the age of fifty-two, his endeavours to modernize Russia had met with opposition from the Russian nobility—resulting in several attempts on his life and a treason case involving his son. In 1728, Peter II of Russia moved his seat back to Moscow, but four years in 1732, under Empress Anna of Russia, Saint Petersburg was again designated as the capital of the Russian Empire. It remained the seat of the Romanov dynasty and the Imperial Court of the Russian Tsars, as well as the seat of the Russian government, for another 186 years until the communist revolution of 1917.
In 1736–1737 the city suffered from catastrophic fires. To rebuild the damaged boroughs, a committee under Burkhard Christoph von Münnich commissioned a new plan in 1737; the city was divided into five boroughs, the city centre was moved to the Admiralty borough, situated on the east bank between the Neva and Fontanka. It developed along three radial streets, which meet at the Admiralty building and are now one street known as Nevsky Prospekt, Gorokhovaya Street and Voznesensky Prospekt. Baroque architecture became dominant in the city during the first sixty years, culminating in the Elizabethan Baroque, represented most notably by Italian Bartolomeo Rastrelli with such buildings as the Winter Palace. In the 1760s, Baroque architecture was succeeded by neoclassical architecture. Established in 1762, the Commission of Stone Buildings of Moscow and Saint Petersburg ruled that no structure in the
Société mathématique de France
The Société Mathématique de France is the main professional society of French mathematicians. The society was founded in 1872 by Émile Lemoine and is one of the oldest mathematical societies in existence, it publishes several academic journals: Annales Scientifiques de l'École Normale Supérieure, Astérisque, Bulletin de la Société Mathématique de France, Gazette des mathématiciens, Mémoires de la Société Mathématique de France, Panoramas et Synthèses, Revue d'histoire des mathématiques. European Mathematical Society Centre International de Rencontres Mathématiques List of mathematical societies Webpage of the society
In control systems theory, the describing function method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, extended by Ralph Kochenburger is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, the approximation of the non-linear system under investigation by a linear time-invariant transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is linear. Thus, this dependence on amplitude generates a family of linear systems that are combined in an attempt to capture salient features of the non-linear system behavior; the describing function is one of the few applicable methods for designing nonlinear systems, is widely used as a standard mathematical tool for analyzing limit cycles in closed-loop controllers, such as industrial process controls and electronic oscillators.
Consider feedback around a discontinuous nonlinearity cascaded with a slow stable linear system. The continuous region in which the feedback is presented to the nonlinearity depends on the amplitude of the output of the linear system; as the linear system's output amplitude decays, the nonlinearity may move into a different continuous region. This switching from one continuous region to another can generate periodic oscillations; the describing function method attempts to predict characteristics of those oscillations by assuming that the slow system acts like a low-pass or bandpass filter that concentrates all energy around a single frequency. If the output waveform has several modes, the method can still provide intuition about properties like frequency and amplitude. Using this low-pass assumption, the system response can be described by one of a family of sinusoidal waveforms; this SIDF is a modification of the transfer function H used to characterize linear systems. In a quasi-linear system, when the input is a sine wave, the output will be a sine wave of the same frequency but with a scaled amplitude and shifted phase as given by H.
Many systems are quasi-linear in the sense that although the response to a sine wave is not a pure sine wave, most of the energy in the output is indeed at the same frequency ω as the input. This is because such systems may possess intrinsic low-pass or bandpass characteristics such that harmonics are attenuated, or because external filters are added for this purpose. An important application of the SIDF technique is to estimate the oscillation amplitude in sinusoidal electronic oscillators. Other types of describing functions that have been used are DFs for level inputs and for Gaussian noise inputs. Although not a complete description of the system, the DFs suffice to answer specific questions about control and stability. DF methods are best for analyzing systems with weak nonlinearities. In addition the higher order sinusoidal input describing functions, describe the response of a class of nonlinear systems at harmonics of the input frequency of a sinusoidal input; the HOSIDFs are an extension of the SIDF for systems where the nonlinearities are significant in the response.
Although the describing function method can produce reasonably accurate results for a wide class of systems, it can fail badly for others. For example, the method can fail; such examples have been presented by Tzypkin for bang–bang systems. A similar example is a closed-loop oscillator consisting of a non-inverting Schmitt trigger followed by an inverting integrator that feeds back its output to the Schmitt trigger's input; the output of the Schmitt trigger is going to be a square waveform, while that of the integrator is going to have a triangle waveform with peaks coinciding with the transitions in the square wave. Each of these two oscillator stages lags the signal by 90 degrees. If one were to perform DF analysis on this circuit, the triangle wave at the Schmitt trigger's input would be replaced by its fundamental, which passing through the trigger would cause a phase shift of less than 90 degrees so the system would appear not to oscillate in the same way. In the case where the conditions for Aizerman's or Kalman conjectures are fulfilled, there are no periodic solutions by describing function method, but counterexamples with periodic solutions are well known.
Therefore, the application of the describing function method requires additional justification. Electrical Engineering Encyclopedia: Describing Functions
Crimea is a peninsula on the northern coast of the Black Sea in Eastern Europe, completely surrounded by both the Black Sea and the smaller Sea of Azov to the northeast. It is located south of the Ukrainian region of Kherson, to which it is connected by the Isthmus of Perekop, west of the Russian region of Kuban, from which it is separated by the Strait of Kerch though linked by the Crimean Bridge; the Arabat Spit is located to the northeast, a narrow strip of land that separates a system of lagoons named Sivash from the Sea of Azov. Across the Black Sea to its west is Romania and to its south Turkey. Crimea has been at the boundary between the classical world and the Pontic–Caspian steppe, its southern fringe was colonised by the Greeks, the Persians, the Romans, the Byzantine Empire, the Crimean Goths, the Genoese and the Ottoman Empire, while at the same time its interior was occupied by a changing cast of invading steppe nomads and empires, such as the Cimmerians, Sarmatians, Alans, Huns, Kipchaks and the Golden Horde.
Crimea and adjacent territories were united in the Crimean Khanate during the 15th to 18th century. In 1783, Crimea became a part of the Russian Empire as the result of the Russo-Turkish War. Following the Russian Revolution of 1917, Crimea became an autonomous republic within the Russian Soviet Federative Socialist Republic in the USSR. During World War II, Crimea was downgraded to the Crimean Oblast after its entire indigenous population, the Crimean Tatars, were deported to Central Asia, an act recognized as a genocide. In 1954, it was transferred to the Ukrainian SSR from the Russian SFSR. With the collapse of the Soviet Union, Ukraine was formed as an independent state in 1991 and most of the peninsula was reorganized as the Autonomous Republic of Crimea, while the city of Sevastopol retained its special status within Ukraine; the 1997 Partition Treaty on the Status and Conditions of the Black Sea Fleet partitioned the former Soviet Black Sea Fleet and allowed Russia to continue basing its fleet in Crimea: both the Ukrainian Naval Forces and Russian's Black Sea Fleet were to be headquartered in Sevastopol.
Ukraine extended Russia's lease of the naval facilities under the 2010 Kharkiv Pact in exchange for further discounted natural gas. In February 2014, following the 2014 Ukrainian revolution that ousted the Ukrainian President, Viktor Yanukovych, pro-Russian separatists and Russian Armed Forces took over the territory. A controversial Crimea-wide referendum, unconstitutional under the Ukrainian and Crimean constitutions, was held on the issue of reunification with Russia which official results indicated was supported by a large majority of Crimeans. Russia formally annexed Crimea on 18 March 2014, incorporating the Republic of Crimea and the federal city of Sevastopol as the 84th and 85th federal subjects of Russia; the classical name Tauris or Taurica is from the Greek Ταυρική, after the peninsula's Scytho-Cimmerian inhabitants, the Tauri. Strabo and Ptolemy refer variously to the Strait of Kerch as the Κιμμερικὸς Βόσπορος, its easternmost part as the Κιμμέριον Ἄκρον (Kimmerion Akron, Roman name: Promontorium Cimmerium, as well as to the city of Cimmerium and whence the name of the Kingdom of the Cimmerian Bosporus.
The earliest recorded use of the toponym “Crimea” for the peninsula occurred between 1315-1329 AD by the Arab writer Abū al-Fidā where he recounts a political fight in 1300-1301 AD resulting in a rival's decapitation and having “sent his head to the Crimea”. The Crimean Tatar name of the peninsula is Qırım and so for the city of Krym, now called Stary Krym which served as a capital of the Crimean province of the Golden Horde; some sources hold that the name of the capital was extended to the entire peninsula at some point during Ottoman suzerainty. The origin of the word Qırım is uncertain. Suggestions argued in various sources: a corruption of Cimmerium. A derivation from the Turkic term qirum, from qori-. Other suggestions either unsupported or contradicted by sources based on similarity in sound, include: a derivation from the Greek Cremnoi. However, Herodotus identifies the port not in Crimea, but as being on the west coast of the Sea of Azov. No evidence has been identified that this name was in use for the peninsula.
The Turkic term is related to the Mongolian appellation kerm "wall", but sources indicate that the Mongolian appellation of the Crimean peninsula of Qaram is phonetically incompatible with kerm/kerem and therefore deriving from another original term. The name "Crimea" is the Italian form, i.e. la Crimea, since at least the 17th century and the "Crimean peninsula" becomes current during the 18th century replacing the classical name of Tauric Peninsula in the course of the 19th century. In English usage since the early modern period the Crimean Khanate is referred to as Crim Tartary; the omission of the definite article in English became common during the 20th century. The classical name was used in 1802 in the name of the Russian