Borel setIn mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel. For a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets (or, equivalently, all closed sets).
Matrix ringIn abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra.
Padé approximantIn mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating. The technique was developed around 1890 by Henri Padé, but goes back to Georg Frobenius, who introduced the idea and investigated the features of rational approximations of power series.
Émile BorelFélix Édouard Justin Émile Borel (bɔʁɛl; 7 January 1871 – 3 February 1956) was a French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Borel was born in Saint-Affrique, Aveyron, the son of a Protestant pastor. He studied at the Collège Sainte-Barbe and Lycée Louis-le-Grand before applying to both the École normale supérieure and the École Polytechnique. He qualified in the first position for both and chose to attend the former institution in 1889.
SchutzstaffelThe Schutzstaffel (SS; also stylized as ᛋᛋ with Armanen runes; ˈʃʊtsˌʃtafl̩; Protection Squadron) was a major paramilitary organization under Adolf Hitler and the Nazi Party in Nazi Germany, and later throughout German-occupied Europe during World War II. It began with a small guard unit known as the Saal-Schutz ("Hall Security") made up of party volunteers to provide security for party meetings in Munich. In 1925, Heinrich Himmler joined the unit, which had by then been reformed and given its final name.
Borel measureIn mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors require additional restrictions on the measure, as described below. Let be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of ; this is known as the σ-algebra of Borel sets. A Borel measure is any measure defined on the σ-algebra of Borel sets.
Russian spelling rulesIn Russian, the term spelling rule is used to describe a number of rules relating to the spelling of words in the language that would appear in most cases to deviate from a strictly phonetic transcription. All the spelling rules found in the Russian language dictate that certain consonants cannot be followed either under any circumstance or in an unstressed syllable by certain vowels. In most cases where spelling rules exist, they do not actually affect the pronunciation.
Declaration of State Sovereignty of the Russian Soviet Federative Socialist RepublicThe Declaration of State Sovereignty of the Russian SFSR (Декларация о государственном суверенитете РСФСР) was a political act of the Russian Soviet Federative Socialist Republic, then part of the Soviet Union, which marked the beginning of constitutional reform in Russia. The Declaration was adopted by the First Congress of People's Deputies of the Russian SFSR on 12 June 1990. It proclaimed the sovereignty of the Russian SFSR and the intention to establish a democratic constitutional state within a liberalized Soviet Union.
Andrey VoronikhinAndrey (Andrei) Nikiforovich Voronikhin (Андрей Никифорович Воронихин) (28 October 1759, Novoe Usolye, Perm Oblast – 21 February 1814, Saint Petersburg) was a Russian architect and painter. As a representative of classicism he was also one of the founders of the monumental Russian Empire style. Born a serf of the Stroganov family, he is best known for his work on Kazan Cathedral in Saint Petersburg. Andrey Voronikhin was born in the village of Novoa Usolye (now Perm Krai) to a family who were the serfs of count Alexander Sergeyevich Stroganov, a longtime President of the Imperial Academy of Arts.
Alexander KotsubinskyAlexander Petrovich Kotsubinsky (Александр Петрович Коцюбинский) is a Russian psychiatrist, a spokesman of St. Petersburg psychiatric school. Alexander Kotsubinsky graduated from Leningrad Pediatric Institute in 1964 and was in 1981 awarded the Candidate of Sciences degree for his dissertation The Peculiarities of Remissions in Faintly Progredient Schizophrenia (in Russian). He attained the M. D. degree in 2000. At present he is full professor in the Medical Academy of postgraduate education and head of the out-patient psychiatry department of the Bekhterev Psychoneurological Institute in St.
Alexander DvorkinAlexander Leonidovich Dvorkin (Алекса́ндр Леони́дович Дво́ркин; born 20 August 1955 in Moscow) is a Russian anti-cult activist. From 1999 to 2012 he was professor and head of the department of the study of new religious movements (cults) at Saint Tikhon's Orthodox University. He is currently professor of department of missiology at that university. Dvorkin received his secondary education at schools No. 25, 91 and 112 in Moscow. After graduation from school grade 10, in 1972, he became a student in the Faculty of Russian Language and Literature of Moscow Pedagogical Institute.
Ice shelfAn ice shelf is a large floating platform of ice that forms where a glacier or ice sheet flows down to a coastline and onto the ocean surface. Ice shelves are only found in Antarctica, Greenland, Northern Canada, and the Russian Arctic. The boundary between the floating ice shelf and the anchor ice (resting on bedrock) that feeds it is the grounding line. The thickness of ice shelves can range from about to . In contrast, sea ice is formed on water, is much thinner (typically less than ), and forms throughout the Arctic Ocean.
