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Formal Distribution
In mathematics, a formal distribution is an infinite sum of powers of a formal variable, usually denoted z in the theory of formal distributions. The coefficients of these infinite sums can be many different mathematical structures, such as vector spaces or rings, but in applications most often take values in an algebra over a field. These infinite sums are allowed to have infinitely many positive and negative powers, and are not required to converge, and so do not define functions of the formal variable. Rather, they are interpreted as distributions, that is, linear functionals on an appropriate space of test functions. They are closely related to formal Laurent series, but are not required to have finitely many negative powers. In particular, this means even if the coefficients are ring-valued, it is not necessarily possible to multiply two formal distributions. They are important in the study of vertex operator algebras, since the vertex operator playing a central role in the th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z 1, Z 1^{-1}, \cdots, Z N, Z N^{-1}
Z, or z, is the twenty-sixth and last letter of the Latin alphabet. It is used in the modern English alphabet, in the alphabets of other Western European languages, and in others worldwide. Its usual names in English are ''zed'' (), which is most commonly used in British English, and ''zee'' (), most commonly used in American English, with an occasional archaic variant ''izzard'' ()."Z", ''Oxford English Dictionary,'' 2nd edition (1989); ''Merriam-Webster's Third New International Dictionary of the English Language, Unabridged'' (1993); "zee", ''op. cit''. Name In most English-speaking countries, including Australia, Canada, India, Ireland, New Zealand, South Africa and the United Kingdom, the letter's name is ''zed'' , reflecting its derivation from the Greek letter ''zeta'' (this dates to Latin, which borrowed Y and Z from Greek), but in American English its name is ''zee'' , analogous to the names for B, C, D, etc., and deriving from a late 17th-century English dialecta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
