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Dirac Comb
In mathematics, a Dirac comb (also known as shah function, impulse train or sampling function) is a periodic function with the formula \operatorname_(t) \ := \sum_^ \delta(t - k T) for some given period T. Here ''t'' is a real variable and the sum extends over all integers ''k.'' The Dirac delta function \delta and the Dirac comb are tempered distributions. The graph of the function resembles a comb (with the \deltas as the comb's ''teeth''), hence its name and the use of the comb-like Cyrillic letter sha (Ш) to denote the function. The symbol \operatorname\,\,(t), where the period is omitted, represents a Dirac comb of unit period. This implies \operatorname_(t) \ = \frac\operatorname\ \!\!\!\left(\frac\right). Because the Dirac comb function is periodic, it can be represented as a Fourier series based on the Dirichlet kernel: \operatorname_(t) = \frac\sum_^ e^. The Dirac comb function allows one to represent both continuous and discrete phenomena, such as sampling and al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyrillic Script
The Cyrillic script ( ), Slavonic script or the Slavic script, is a writing system used for various languages across Eurasia. It is the designated national script in various Slavic languages, Slavic, Turkic languages, Turkic, Mongolic languages, Mongolic, Uralic languages, Uralic, Caucasian languages, Caucasian and Iranian languages, Iranic-speaking countries in Southeastern Europe, Eastern Europe, the Caucasus, Central Asia, North Asia, and East Asia. , around 250 million people in Eurasia use Cyrillic as the official script for their national languages, with Russia accounting for about half of them. With the accession of Bulgaria to the European Union on 1 January 2007, Cyrillic became the third official script of the European Union, following the Latin script, Latin and Greek alphabet, Greek alphabets. The Early Cyrillic alphabet was developed during the 9th century AD at the Preslav Literary School in the First Bulgarian Empire during the reign of tsar Simeon I of Bulgar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tate–Shafarevich Group
In arithmetic geometry, the Tate–Shafarevich group of an abelian variety (or more generally a group scheme) defined over a number field consists of the elements of the Weil–Châtelet group that become trivial in all of the completions of (i.e. the -adic fields obtained from , as well as its real and complex completions). Thus, in terms of Galois cohomology, it can be written as :\bigcap_v\mathrm\left(H^1\left(G_K,A\right)\rightarrow H^1\left(G_,A_v\right)\right). This group was introduced by Serge Lang and John Tate and Igor Shafarevich. Cassels introduced the notation , where is the Cyrillic letter " Sha", for Shafarevich, replacing the older notation or . Elements of the Tate–Shafarevich group Geometrically, the non-trivial elements of the Tate–Shafarevich group can be thought of as the homogeneous spaces of that have -rational points for every place of , but no -rational point. Thus, the group measures the extent to which the Hasse principle fails to ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shcha
Shcha (Щ щ; italics: ), Shta or Sha with descender is a letter of the Cyrillic script. In Russian, it represents the voiceless alveolo-palatal fricative , similar to the pronunciation of in ''sheep'' (but longer). In Ukrainian and Rusyn, it represents the consonant cluster . In Bulgarian, it represents the consonant cluster . Other non-Slavic languages written in Cyrillic use this letter to spell the few loanwords that use it or foreign names; it is usually pronounced and is often omitted when teaching those languages. In English, Shcha is romanized as or (with háčeks) or occasionally as , all reflecting the historical Russian pronunciation of the letter (as a combined ''Ш'' and ''Ч''). English-speaking learners of Russian are often instructed to pronounce it in this way although it is no longer the standard pronunciation in Russian (it still is in Ukrainian and Rusyn, as above). The letter Щ in Russian and Ukrainian corresponds to ШЧ in related words in Bel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shcha
Shcha (Щ щ; italics: ), Shta or Sha with descender is a letter of the Cyrillic script. In Russian, it represents the voiceless alveolo-palatal fricative , similar to the pronunciation of in ''sheep'' (but longer). In Ukrainian and Rusyn, it represents the consonant cluster . In Bulgarian, it represents the consonant cluster . Other non-Slavic languages written in Cyrillic use this letter to spell the few loanwords that use it or foreign names; it is usually pronounced and is often omitted when teaching those languages. In English, Shcha is romanized as or (with háčeks) or occasionally as , all reflecting the historical Russian pronunciation of the letter (as a combined ''Ш'' and ''Ч''). English-speaking learners of Russian are often instructed to pronounce it in this way although it is no longer the standard pronunciation in Russian (it still is in Ukrainian and Rusyn, as above). The letter Щ in Russian and Ukrainian corresponds to ШЧ in related words in Bel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Igor Shafarevich
Igor Rostislavovich Shafarevich (russian: И́горь Ростисла́вович Шафаре́вич; 3 June 1923 – 19 February 2017) was a Soviet and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised socialism and other books which were (controversially) described as anti-semitic. Mathematics From his early years, Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry. In particular, in algebraic number theory, the Shafarevich–Weil theorem extends the commutative reciprocity map to the case of Galois groups, which are central extensions of abelian groups by finite groups. Shafarevich was the first mathematician to give a completely self-contained formula for the Hilbert pairing, thus initiating an important branch of the study of explicit formulas in number theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shin (letter)
Shin (also spelled Šin (') or Sheen) is the twenty-first letter of the Semitic abjads, including Phoenician Shin , Hebrew Shin , Aramaic Shin , Syriac Shin ܫ, and Arabic Shin (in abjadi order, 13th in modern order). Its sound value is a voiceless sibilant, or . The Phoenician letter gave rise to the Greek Sigma () (which in turn gave Latin and Cyrillic С), and the letter '' Sha'' in the Glagolitic and Cyrillic scripts (, ). The South Arabian and Ethiopian letter ''Śawt'' is also cognate. Origins The Proto-Sinaitic glyph, according to William Albright, was based on a "tooth" and with the phonemic value š "corresponds etymologically (in part, at least) to original Semitic ''ṯ'' (th), which was pronounced ''s'' in South Canaanite". The Phoenician letter expressed the continuants of two Proto-Semitic phonemes, and may have been based on a pictogram of a tooth (in modern Hebrew ''shen''). The Encyclopaedia Judaica, 1972, records that it originally represented a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serbo-Croatian
Serbo-Croatian () – also called Serbo-Croat (), Serbo-Croat-Bosnian (SCB), Bosnian-Croatian-Serbian (BCS), and Bosnian-Croatian-Montenegrin-Serbian (BCMS) – is a South Slavic language and the primary language of Serbia, Croatia, Bosnia and Herzegovina, and Montenegro. It is a pluricentric language with four mutually intelligible standard varieties, namely Serbian, Croatian, Bosnian, and Montenegrin. South Slavic languages historically formed a continuum. The turbulent history of the area, particularly due to expansion of the Ottoman Empire, resulted in a patchwork of dialectal and religious differences. Due to population migrations, Shtokavian became the most widespread dialect in the western Balkans, intruding westwards into the area previously occupied by Chakavian and Kajkavian (which further blend into Slovenian in the northwest). Bosniaks, Croats and Serbs differ in religion and were historically often part of different cultural circles, although a large part o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macedonian Language
Macedonian (; , , ) is an Eastern South Slavic language. It is part of the Indo-European language family, and is one of the Slavic languages, which are part of a larger Balto-Slavic branch. Spoken as a first language by around two million people, it serves as the official language of North Macedonia. Most speakers can be found in the country and its diaspora, with a smaller number of speakers throughout the transnational region of Macedonia. Macedonian is also a recognized minority language in parts of Albania, Bosnia and Herzegovina, Romania, and Serbia and it is spoken by emigrant communities predominantly in Australia, Canada and the United States. Macedonian developed out of the western dialects of the East South Slavic dialect continuum, whose earliest recorded form is Old Church Slavonic. During much of its history, this dialect continuum was called "Bulgarian", although in the 19th century, its western dialects came to be known separately as "Macedonian". Stan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glagolitic
The Glagolitic script (, , ''glagolitsa'') is the oldest known Slavic alphabet. It is generally agreed to have been created in the 9th century by Saint Cyril, a monk from Thessalonica. He and his brother Saint Methodius were sent by the Byzantine Emperor Michael III in 863 to Great Moravia to spread Christianity among the West Slavs in the area. The brothers decided to translate liturgical books into the contemporary Slavic language understandable to the general population (now known as Old Church Slavonic). As the words of that language could not be easily written by using either the Greek or Latin alphabets, Cyril decided to invent a new script, Glagolitic, which he based on the local dialect of the Slavic tribes from the Byzantine theme of Thessalonica. After the deaths of Cyril and Methodius, the Glagolitic alphabet ceased to be used in Moravia for political or religious needs. In 885, Pope Stephen V issued a papal bull to restrict spreading and reading Christian services ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coptic Alphabet
The Coptic alphabet is the script used for writing the Coptic language. The repertoire of glyphs is based on the Greek alphabet augmented by letters borrowed from the Egyptian Demotic and is the first alphabetic script used for the Egyptian language. There are several Coptic alphabets, as the Coptic writing system may vary greatly among the various dialects and subdialects of the Coptic language. History The Coptic alphabet has a long history, going back to the Hellenistic period, when the Greek alphabet was used to transcribe Demotic texts, with the aim of recording the correct pronunciation of Demotic. During the first two centuries of the Common Era, an entire series of spiritual texts were written in what scholars term Old Coptic, Egyptian language texts written in the Greek alphabet. A number of letters, however, were derived from Demotic, and many of these (though not all) are used in "true" form of Coptic writing. With the spread of Christianity in Egypt, by the late ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glagolitic Alphabet
The Glagolitic script (, , ''glagolitsa'') is the oldest known Slavic alphabet. It is generally agreed to have been created in the 9th century by Saint Cyril, a monk from Thessalonica. He and his brother Saint Methodius were sent by the Byzantine Emperor Michael III in 863 to Great Moravia to spread Christianity among the West Slavs in the area. The brothers decided to translate liturgical books into the contemporary Slavic language understandable to the general population (now known as Old Church Slavonic). As the words of that language could not be easily written by using either the Greek or Latin alphabets, Cyril decided to invent a new script, Glagolitic, which he based on the local dialect of the Slavic tribes from the Byzantine theme of Thessalonica. After the deaths of Cyril and Methodius, the Glagolitic alphabet ceased to be used in Moravia for political or religious needs. In 885, Pope Stephen V issued a papal bull to restrict spreading and reading Christian servic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
