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Wave Function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter), psi, respectively). Wave functions are complex number, complex-valued. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density function, probability density of measurement in quantum mechanics, measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called ''normalization''. Since the wave function is complex-valued, only its relative phase and relative magnitud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as well as consonants. In Archaic Greece, Archaic and early Classical Greece, Classical times, the Greek alphabet existed in Archaic Greek alphabets, many local variants, but, by the end of the 4th century BC, the Ionia, Ionic-based Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard throughout the Greek-speaking world and is the version that is still used for Greek writing today. The letter case, uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , , , , , , , The Greek alphabet is the ancestor of several scripts, such as the Latin script, Latin, Gothic alphabet, Gothic, Coptic script, Coptic, and Cyrillic scripts. Throughout antiquity, Greek had only a single uppercas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ef (Cyrillic)
Ef or Fe (Ф ф; italics: ) is a Cyrillic letter, commonly representing the voiceless labiodental fricative , like the pronunciation of in ''fill'', ''flee'' or ''fall''. The Cyrillic letter Ef is romanized as . History The Cyrillic letter Ef was derived from the Greek letter Phi (Φ φ). It merged with and eliminated the letter Fita (Ѳ) in the Russian alphabet in 1918. The name of Ef in the Early Cyrillic alphabet is ( or ), in later Church Slavonic and Russian form it became (). In the Cyrillic numeral system, Ef has a value of 500. Appearance and usage in Slavic languages The Slavic languages have almost no native words containing . This sound did not exist in Proto-Indo-European (PIE). It arose in Greek and Latin from PIE (which yielded Slavic ). In some instances in Latin, it represented historical th-fronting and derived from Proto-Indo-European . In the Germanic languages, the f sound arose from PIE via Grimm's law, which remained unchanged in Slavic. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Phase
Three-phase electric power (abbreviated 3ϕ) is a common type of alternating current (AC) used in electricity generation, transmission, and distribution. It is a type of polyphase system employing three wires (or four including an optional neutral return wire) and is the most common method used by electrical grids worldwide to transfer power. Three-phase electrical power was developed in the 1880s by several people. In three-phase power, the voltage on each wire is 120 degrees phase shifted relative to each of the other wires. Because it is an AC system, it allows the voltages to be easily stepped up using transformers to high voltage for transmission and back down for distribution, giving high efficiency. A three-wire three-phase circuit is usually more economical than an equivalent two-wire single-phase circuit at the same line-to-ground voltage because it uses less conductor material to transmit a given amount of electrical power. Three-phase power is mainly used dir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is a numeral system, system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal number (linguistics), ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal number (linguistics), cardinal numbers, however, modern Greece uses Arabic numerals. History The Minoans, Minoan and Mycenaean civilizations' Linear A and Linear B alphabets used a different system, called Aegean numerals, which included number-only symbols for powers of ten: = 1, = 10, = 100, = 1000, and = 10000. Attic numerals composed another system that came into use perhaps in the 7th century BC. They were acrophonic, derived (after the initial one) from the first letters of the names of the numbers represented. They ran = 1, = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koine Greek
Koine Greek (, ), also variously known as Hellenistic Greek, common Attic, the Alexandrian dialect, Biblical Greek, Septuagint Greek or New Testament Greek, was the koiné language, common supra-regional form of Greek language, Greek spoken and written during the Hellenistic period, the Roman Empire and the early Byzantine Empire. It evolved from the spread of Greek following the conquests of Alexander the Great in the fourth century BC, and served as the lingua franca of much of the Mediterranean region and the Middle East during the following centuries . It was based mainly on Attic Greek, Attic and related Ionic Greek, Ionic speech forms, with various admixtures brought about through dialect levelling with other varieties. Koine Greek included styles ranging from conservative literary forms to the spoken vernaculars of the time. As the dominant language of the Byzantine Empire, it developed further into Medieval Greek, which then turned into Modern Greek. Literary Koine was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Greek
Modern Greek (, or , ), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the language sometimes referred to as Varieties of Modern Greek#Standard Modern Greek, Standard Modern Greek. The end of the Medieval Greek period and the beginning of Modern Greek is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic features of the modern language arose centuries earlier, having begun around the fourth century AD. During most of the Modern Greek period, the language existed in a situation of diglossia, with regional spoken dialects existing side by side with learned, more archaic written forms, as with the vernacular and learned varieties (''Dimotiki'' and ''Katharevousa'') that co-existed in Greece throughout much of the 19th and 20th centuries. Variet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single Phase
In electrical engineering, single-phase electric power (abbreviated 1φ) is the distribution of alternating current electric power using a system in which all the voltages of the supply vary in unison. Single-phase distribution is used when loads are mostly lighting and heating, with few large electric motors. A single-phase supply connected to an alternating current electric motor does not produce a rotating magnetic field; single-phase motors need additional circuits for starting (capacitor start motor), and such motors are uncommon above 10 kW in rating. Because the voltage of a single phase system reaches a peak value twice in each cycle, the instantaneous power is not constant. Standard frequencies of single-phase power systems are either 50 or 60 Hz. Special single-phase traction power networks may operate at 16.67 Hz or other frequencies to power electric railways. History Single phase power transmission took many years to develop. The earliest developments ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after the commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is divided into a wide range of different fields, including computer engineering, systems engineering, power engineering, telecommunications, radio-frequency engineering, signal processing, instrumentation, photovoltaic cells, electronics, and optics and photonics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations including hardware engineering, power electronics, Electromagnetism, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Phase
A polyphase system (the term coined by Silvanus Thompson) is a means of distributing alternating-current (AC) electrical power that utilizes more than one AC phase, which refers to the phase offset value (in degrees) between AC in multiple conducting wires; ''phases'' may also refer to the corresponding terminals and conductors, as in color codes. Polyphase systems have two or more energized electrical conductors carrying alternating currents with a defined phase between the voltage waves in each conductor. Early systems used 4 wire two-phase with a 90° phase angle, but modern systems almost universally use three-phase voltage, with a phase angle of 120° (or 2π/3 radians). Polyphase systems are particularly useful for transmitting power to electric motors which rely on alternating current to rotate. Three-phase power is used for industrial applications and for power transmission. Compared to a single-phase, two-wire system, a three-phase three-wire system transmits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a Set (mathematics), set with an Binary operation, operation that combines any two elements of the set to produce a third element within the same set and the following conditions must hold: the operation is Associative property, associative, it has an identity element, and every element of the set has an inverse element. For example, the integers with the addition, addition operation form a group. The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry, groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of the object, and the transformations of a given type form a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclotomic Polynomial
In mathematics, the ''n''th cyclotomic polynomial, for any positive integer ''n'', is the unique irreducible polynomial with integer coefficients that is a divisor of x^n-1 and is not a divisor of x^k-1 for any Its roots are all ''n''th primitive roots of unity e^ , where ''k'' runs over the positive integers less than ''n'' and coprime to ''n'' (and ''i'' is the imaginary unit). In other words, the ''n''th cyclotomic polynomial is equal to : \Phi_n(x) = \prod_\stackrel \left(x-e^\right). It may also be defined as the monic polynomial with integer coefficients that is the minimal polynomial over the field of the rational numbers of any primitive ''n''th-root of unity ( e^ is an example of such a root). An important relation linking cyclotomic polynomials and primitive roots of unity is :\prod_\Phi_d(x) = x^n - 1, showing that x is a root of x^n - 1 if and only if it is a ''d''th primitive root of unity for some ''d'' that divides ''n''. Examples If ''n'' is a prim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
