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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] |
Laplace Operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a Scalar field, scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the Del, nabla operator), or \Delta. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical coordinates, cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian of a function at a point measures by how much the average value of over small spheres or balls centered at deviates from . The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics: the Laplacian of the gravitational potential due to a given mass density distributio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uncertainty Principle
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known. More formally, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as position, ''x'', and momentum, ''p''. Such paired-variables are known as complementary variables or canonically conjugate variables. First introduced in 1927 by German physicist Werner Heisenberg, the formal inequality relating the standard deviation of position ''σx'' and the standard deviation of momentum ''σp'' was derived by Earle Hesse Kennard later that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential (mathematics)
In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. Introduction The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if ''x'' is a variable, then a change in the value of ''x'' is often denoted Δ''x'' (pronounced ''delta x''). The differential ''dx'' represents an infinitely small change in the variable ''x''. The idea of an infinitely small or infinitely slow change is, intuitively, extremely useful, and there are a number of ways to make the notion mathematically precise. Using calculus, it is possible to relate the infinitely small changes of various variables to each other mathematically us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delta Baryon
The Delta baryons (or baryons, also called Delta resonances) are a family of subatomic particle made of three up or down quarks (u or d quarks), the same constituent quarks that make up the more familiar protons and neutrons. Properties Four closely related baryons exist: (constituent quarks: uuu), (uud), (udd), and (ddd), which respectively carry an electric charge of , , , and . The baryons have a mass of about ; their third component of isospin \; I_3 = \pm\tfrac ~\mathsf~ \pm\tfrac\;; and they are required to have an intrinsic spin of or higher (half-integer units). Ordinary nucleons (symbol N, meaning either a proton or neutron), by contrast, have a mass of about , and both intrinsic spin and isospin of . The (uud) and (udd) particles are higher-mass spin-excitations of the proton (, uud) and neutron (, udd), respectively. The and , however, have no direct nucleon analogues: For example, even though their charges ... [...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] |
Ancient Greek
Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek Dark Ages, Dark Ages (), the Archaic Greece, Archaic or Homeric Greek, Homeric period (), and the Classical Greece, Classical period (). Ancient Greek was the language of Homer and of fifth-century Athens, fifth-century Athenian historians, playwrights, and Ancient Greek philosophy, philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Homeric Greek, Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek. From the Hellenistic period (), Ancient Greek was followed by Koine Greek, which is regar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De (Cyrillic)
De (Д д; italic: ''Д д'') is a letter of the Cyrillic script. It commonly represents the voiced dental stop , like the pronunciation of in " door", except closer to the teeth. De is usually Romanized using the Latin letter D. History The Cyrillic letter De was derived from the Greek letter Delta (Δ δ). In the Early Cyrillic alphabet its name was (''dobro''), meaning "good". In the Cyrillic numeral system, De had a value of 4. Form The major graphic difference between De and its modern Greek equivalent lies in the two descenders ("feet") below the lower corners of the Cyrillic letter. The descenders were borrowed from a Byzantine uncial shape of uppercase Delta. De, like the Cyrillic letter El, has two typographical variants: an older variant where its top is pointed (like Delta), and a modern one (first used in mid-19th-century fonts) where it is square. Nowadays, almost all books and magazines are printed with fonts with the second variant of the letter ... [...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] |
Dalet (letter)
Dalet (, also spelled Daleth or Daled) is the fourth letter of the Semitic abjads, including Phoenician ' 𐤃, Hebrew , Aramaic ' 𐡃, Syriac ' ܕ, and Arabic (in abjadi order; 8th in modern order). Its sound value is the voiced alveolar plosive (). It is also related to the Ancient North Arabian 𐪕, South Arabian , and Ge'ez . The letter is based on a glyph of the Proto-Sinaitic script, probably called ' (''door'' in Modern Hebrew is delet), ultimately based on a hieroglyph depicting a door: O31 Arabic ''dāl'' The letter is named (), and is written in several ways depending on its position in the word: The letter represents a sound. Phoenician The Phoenician dālet gave rise to the Greek delta (Δ), Latin D, and the Cyrillic letter Д. Aramaic Hebrew dalet Hebrew spelling: The letter is ''dalet'' in the modern Israeli Hebrew pronunciation (see Tav (letter)). ''Dales'' is still used by many Ashkenazi Jews and ''daleth'' by some Jews of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant coefficient'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Romanization Of Greek
Romanization of Greek is the transliteration ( letter-mapping) or transcription (sound-mapping) of text from the Greek alphabet into the Latin alphabet. History The conventions for writing and romanizing Ancient Greek and Modern Greek differ markedly. The sound of the English letter B () was written as in ancient Greek but is now written as the digraph , while the modern sounds like the English letter V () instead. The Greek name became Johannes in Latin and then John in English, but in modern Greek has become ; this might be written as Yannis, Jani, Ioannis, Yiannis, or Giannis, but not Giannes or Giannēs as it would be for ancient Greek. The word might variously appear as Hagiοs, Agios, Aghios, or Ayios, or simply be translated as " Holy" or "Saint" in English forms of Greek placenames. Traditional English renderings of Greek names originated from Roman systems established in antiquity. The Roman alphabet itself was a form of the Cumaean alphabet derived f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
