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Wave Function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi, respectively). The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier t ... [...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 BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin during the modern era. Sound values and conventional transcriptions for some of ... [...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 . In some languages it is known as Fe. History The Cyrillic letter Ef was derived from the Greek letter Phi (Φ φ). It merged with an eliminated letter Fita (Ѳ) in the Russian alphabet in 1918. The name of Ef in the Early Cyrillic alphabet is (''fr̥tŭ'' or ''frĭtŭ''), in later Church Slavonic and Russian form it became ''фертъ'' (''fert''). In the Cyrillic numeral system, Ef has a value of 500. Appearance 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 , which remaine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Flux
In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber (Wb; in derived units, volt–seconds), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the measurement of magnetic flux. Description The magnetic interaction is described in terms of a vector field, where each point in space is associated with a vector that determines what force a moving charge would experience at that point (see Lorentz force). Since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines. The magnetic flux through some surface, in this simplified picture, is proportional to the num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Phase
Three-phase electric power (abbreviated 3φ) is a common type of alternating current 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 multiple people. Three-phase power works by the voltage and currents being 120 degrees out of phase on the three wires. As 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 directly to power large induction m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal numbers, however, modern Greece uses Arabic numerals. History The 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 comprised another system that came into use perhaps in the 7th century BCE. They were acrophonic, derived (after the initial one) from the first letters of the names of the numbers represented. They ran = 1, = 5, = 10, = 100, = 1,000, and = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archaic Greek
Archaic Greece was the period in Greek history lasting from circa 800 BC to the second Persian invasion of Greece in 480 BC, following the Greek Dark Ages and succeeded by the Classical period. In the archaic period, Greeks settled across the Mediterranean and the Black Seas, as far as Marseille in the west and Trapezus (Trebizond) in the east; and by the end of the archaic period, they were part of a trade network that spanned the entire Mediterranean. The archaic period began with a massive increase in the Greek population and of significant changes that rendered the Greek world at the end of the 8th century entirely unrecognisable from its beginning. According to Anthony Snodgrass, the archaic period was bounded by two revolutions in the Greek world. It began with a "structural revolution" that "drew the political map of the Greek world" and established the ''poleis'', the distinctively Greek city-states, and it ended with the intellectual revolution of the Classical period. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Greek
Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), 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 languages sometimes referred to as 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, beginning 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. Varieties Varieties of ... [...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 not greater 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 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 pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koine Greek
Koine Greek (; Koine el, ἡ κοινὴ διάλεκτος, hē koinè diálektos, the common dialect; ), also known as Hellenistic Greek, common Attic, the Alexandrian dialect, Biblical Greek or New Testament Greek, was the common supra-regional form of 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 and related 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 ... [...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 which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is now 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, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control, and electrical m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Totient Function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In other words, it is the number of integers in the range for which the greatest common divisor is equal to 1. The integers of this form are sometimes referred to as totatives of . For example, the totatives of are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, since and . Therefore, . As another example, since for the only integer in the range from 1 to is 1 itself, and . Euler's totient function is a multiplicative function, meaning that if two numbers and are relatively prime, then . This function gives the order of the multiplicative group of integers modulo (the group of units of the ring \Z/n\Z). It is also used for defining the RSA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
