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Xi (letter)
Xi ( or ; uppercase Ξ, lowercase ξ; ) is the fourteenth letter of the Greek alphabet, representing the voiceless consonant cluster . Its name is pronounced in Modern Greek. In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh . Xi is distinct from the letter chi, which gave its form to the Latin letter X. Greek Both in classical Ancient Greek and in Modern Greek, the letter Ξ represents the consonant cluster /ks/. In some archaic local variants of the Greek alphabet, this letter was missing. Instead, especially in the dialects of most of the Greek mainland and Euboea, the cluster /ks/ was represented by Χ (which in classical Greek is chi, used for ). Because this variant of the Greek alphabet was used in Magna Graecia (the Greek colonies in Sicily and the southern part of the Italian peninsula), the Latin alphabet borrowed Χ rather than Ξ as the Latin letter that represented the /ks/ cluster that was also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triple Bar
Triple is used in several contexts to mean "threefold" or a " treble": Sports * Triple (baseball), a three-base hit * A basketball three-point field goal * A figure skating jump with three rotations * In bowling terms, three strikes in a row * In cycling, a crankset with three chainrings Places * Triple Islands, an uninhabited island group in Nunavut, Canada * Triple Island, British Columbia, Canada * Triple Falls (other), four waterfalls in the United States & Canada * Triple Glaciers, in Grand Teton National Park, Wyoming * Triple Crossing, Richmond, Virginia, believed to be the only place in North America where three Class I railroads cross * Triple Bridge, a stone arch bridge in Ljubljana, Slovenia Transportation * Kawasaki triple, a Japanese motorcycle produced between 1969 and 1980 * Triumph Triple, a motorcycle engine from Triumph Motorcycles Ltd * A straight-three engine * A semi-truck with three trailers Science and technology * Triple (mathematics) ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grand Canonical Ensemble
In statistical mechanics, the grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that are in thermodynamic equilibrium (thermal and chemical) with a reservoir. The system is said to be open in the sense that the system can exchange energy and particles with a reservoir, so that various possible states of the system can differ in both their total energy and total number of particles. The system's volume, shape, and other external coordinates are kept the same in all possible states of the system. The thermodynamic variables of the grand canonical ensemble are chemical potential (symbol: ) and absolute temperature (symbol: . The ensemble is also dependent on mechanical variables such as volume (symbol: , which influence the nature of the system's internal states. This ensemble is therefore sometimes called the ensemble, as each of these three quantitie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Function (statistical Mechanics)
In physics, a partition function describes the statistics, statistical properties of a system in thermodynamic equilibrium. Partition functions are function (mathematics), functions of the thermodynamic state function, state variables, such as the temperature and volume. Most of the aggregate thermodynamics, thermodynamic variables of the system, such as the energy, total energy, Thermodynamic free energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular Thermodynamic free energy, free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the Environment (systems), environment at fixed temperature, volume, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Xi Baryon
Xi (letter), Xi is the 14th letter of the Greek alphabet. Xi may refer to: Arts and entertainment * Xi (alternate reality game), ''Xi'' (alternate reality game), a console-based game * Xi, Japanese name for the video game ''Devil Dice'' * ''Saw XI'', an upcoming film in the ''Saw'' franchise Phonetics * Xi, a List of Latin digraphs#X, Latin digraph used in British English to write the sound People *Xi (surname), any of several Chinese surnames **Xi Jinping, General Secretary of the Chinese Communist Party since 2012 Places *Xi (state), an ancient Chinese state during the Shang and Zhou Dynasties *Xi County, Henan, China *Xi County, Shanxi, China *Xi River, western tributary of the Pearl River in southern China Other uses * Xi (business), a Chinese form of business organization * Xi baryon, a range of baryons with one up or down quark and two heavier quarks * Xi, a brand name for the 4G LTE mobile telecommunications service operated by NTT DoCoMo in Japan * Xi (apartment), a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable, that is, '' holomorphic functions''. The concept can be extended to functions of several complex variables. Complex analysis is contrasted with real analysis, which dea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. * Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. *Additive numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrix (mathematics), matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The algebraic objects amenable to such a description include group (mathematics), groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the group representation, representation theory of groups, in which elements of a group are represented by invertible matrices such that the group operation is matrix multiplication. Representation theory is a useful method because it reduces problems in abstract algebra to problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis, spectral analysis, and neuroscience. The term "harmonics" originated from the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are integer multiples of one another, as are the freq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Alphabet
The Russian alphabet (, or , more traditionally) is the script used to write the Russian language. The modern Russian alphabet consists of 33 letters: twenty consonants (, , , , , , , , , , , , , , , , , , , ), ten vowels (, , , , , , , , , ), a semivowel / consonant (), and two modifier letters or "signs" (, ) that alter pronunciation of a preceding consonant or a following vowel. History Russian alphabet is derived from the Cyrillic script, which was invented in the 9th century to capture accurately the phonology of the first Slavic literary language, Old Church Slavonic. The early Cyrillic alphabet was adapted to Old East Slavic from Old Church Slavonic and was used in Kievan Rus' from the 10th century onward to write what would become the modern Russian language. The last major reform of Russian orthography took place in 1917–1918. Letters : An alternative form of the letter De () closely resembles the Greek letter delta (). : An alternative form of the l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
