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Monotone (other)
Monotone refers to a sound, for example music or speech, that has a single unvaried tone. See: pure tone and monophony. Monotone or monotonicity may also refer to: In economics * Monotone preferences, a property of a consumer's preference ordering. *Monotonicity (mechanism design), a property of a social choice function. * Monotonicity criterion, a property of a voting system. *Resource monotonicity, a property of resource allocation rules and bargaining systems. In mathematics *Monotone class theorem, in measure theory * Monotone convergence theorem, in mathematics *Monotone polygon, a property of a geometric object * Monotonic function, a property of a mathematical function *Monotonicity of entailment, a property of some logical systems *Monotonically increasing, a property of number sequence Other uses * Monotone (software), an open source revision control system *Monotonic orthography Greek orthography has used a variety of diacritics starting in the Hellenistic perio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Tone
Pure may refer to: Computing * A pure function * A pure virtual function * PureSystems, a family of computer systems introduced by IBM in 2012 * Pure Software, a company founded in 1991 by Reed Hastings to support the Purify tool * Pure-FTPd, FTP server software * Pure (programming language), functional programming language based on term rewriting * Pure Storage, a company that makes datacenter storage solutions * Pure (CRIS), a research information system bought by Elsevier. Companies and products * Pure (app), dating app * Pure (restaurant chain), a British fast food chain * Pure Insurance, Privilege Underwriters Reciprocal Exchange * Pure Trading, a Canadian electronic communication network operated by CNQ * Pure Digital, a UK consumer electronics company specialising in DAB radios * Pure Oil, a U.S. chain of gas stations * Propulsion Universelle et Récuperation d'Énergie (PURE), a motorsport engineering company * Pure FM (Portsmouth), a university radio station based i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonicity Of Entailment
Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment is monotone if and only if the rule is admissible. Logical systems with this property are occasionally called ''monotonic logics'' in order to differentiate them from non-monotonic logics. Weakening rule To illustrate, consider the natural deduction sequent: Γ \vdash C That is, on the basis of a list of assumptions Γ, one can prove C. Weakening, by adding an assumption A, allows one to conclude: Γ, A \vdash C For example, the syllogism "All men are mortal. Socrates is a man. Therefore Socrates is mortal." can be weakened by adding a premise: "All men are mortal. Socrates is a man. Cows produce milk. Therefore Socrates is mortal." The validity of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yoasobi
Yoasobi (stylized in all caps) is a Japanese music superduo formed by Sony Music Entertainment Japan, composed of Vocaloid producer Ayase, and singer-songwriter Ikura. Represented by the slogan "novel into music", the duo has released songs based on novels posted on , a novel-centered social media operated by their label, which is also from various media like novels written by professional authors, books, and letters. After going viral on social media, Yoasobi's 2019 debut single, "Yoru ni Kakeru", gave them their breakthrough by reaching atop the ''Billboard'' Japan Hot 100 for six non-consecutive weeks and the 2020 year-end chart, and becoming the first song to be certified diamond for streaming by Recording Industry Association of Japan (RIAJ). It was followed by other successful singles, such as '' Blue Period''-inspired " Gunjō", and ''Beastars'' second season themes " Kaibutsu" and " Yasashii Suisei". The group's first two EPs, '' The Book'' and '' The Book 2'' (both 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Quantifier
In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases. For example, the generalized quantifier ''every boy'' denotes the set of sets of which every boy is a member: \ This treatment of quantifiers has been essential in achieving a compositional semantics for sentences containing quantifiers. Type theory A version of type theory is often used to make the semantics of different kinds of expressions explicit. The standard construction defines the set of types recursively as follows: #''e'' and ''t'' are types. #If ''a'' and ''b'' are both types, then so is \langle a,b\rangle #Nothing is a type, except what can be constructed on the basis of lines 1 and 2 above. Given this definition, we have the simple types ''e'' and ''t'', but also a countable infinity of complex types, some of which include: \langle e,t\rangle;\qquad \langle t,t\rangle;\qquad \langle\langle e,t\rangle, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Monotones
The Monotones were a six-member American doo-wop vocal group in the 1950s. They are considered a one-hit wonder, as their only hit single was " The Book of Love", which peaked at No. 5 on the Billboard Top 100 in 1958. Biography The Monotones formed in 1955 when the seven original singers, all residents of the Baxter Terrace housing project in Newark, New Jersey, began performing covers of popular songs. They were: * Lead singer Charles Howard Patrick (September 11, 1938 - September 11, 2020) * First Warren Davis (born March 1, 1939 - April 17, 2016) * Second tenor George Malone (January 5, 1940 – October 5, 2007) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Orthography
Greek orthography has used a variety of diacritics starting in the Hellenistic period. The more complex polytonic orthography ( el, πολυτονικό σύστημα γραφής, translit=polytonikó sýstīma grafī́s), which includes five diacritics, notates Ancient Greek phonology. The simpler monotonic orthography ( el, μονοτονικό σύστημα γραφής, translit=monotonikó sýstīma grafīs), introduced in 1982, corresponds to Modern Greek phonology, and requires only two diacritics. Polytonic orthography () is the standard system for Ancient Greek and Medieval Greek. The acute accent (), the circumflex (), and the grave accent () indicate different kinds of pitch accent. The rough breathing () indicates the presence of the sound before a letter, while the smooth breathing () indicates the absence of . Since in Modern Greek the pitch accent has been replaced by a dynamic accent (stress), and was lost, most polytonic diacritics have no phonetic signi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotone (software)
Monotone is an Open-source software, open source software tool for distributed revision control. Monotone tracks revisions to files, groups sets of revisions into changesets, and tracks history across renames. The focus of the project is on integrity over performance. Monotone is designed for distributed operation, and makes heavy use of cryptographic primitives to track file revisions (via the SHA-1 Cryptographic hash function, secure hash) and to authenticate user actions (via RSA (algorithm), RSA Digital signature, cryptographic signatures). History Milestones Monotone version 0.26 introduced major changes to the internal database structures, including a new structure known by Monotone developers as a ''roster''. Monotone databases created with version 0.26 can not exchange revisions with older Monotone databases. Older databases must first be upgraded to the new format. The new netsync protocol is incompatible with earlier versions of Monotone. As Git inspiration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequences
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infinit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonically Increasing Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infinit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monophony
In music, monophony is the simplest of musical textures, consisting of a melody (or "tune"), typically sung by a single singer or played by a single instrument player (e.g., a flute player) without accompanying harmony or chords. Many folk songs and traditional songs are monophonic. A melody is also considered to be monophonic if a group of singers (e.g., a choir) sings the same melody together at the unison (exactly the same pitch) or with the same melody notes duplicated at the octave (such as when men and women sing together). If an entire melody is played by two or more instruments or sung by a choir with a fixed interval, such as a perfect fifth, it is also said to be monophony (or "monophonic"). The musical texture of a song or musical piece is determined by assessing whether varying components are used, such as an accompaniment part or polyphonic melody lines (two or more independent lines). In the Early Middle Ages, the earliest Christian songs, called plainchant (a we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotone Polygon
In geometry, a polygon ''P'' in the plane is called monotone with respect to a straight line ''L'', if every line orthogonal to ''L'' intersects the boundary of ''P'' at most twice. Similarly, a polygonal chain ''C'' is called monotone with respect to a straight line ''L'', if every line orthogonal to ''L'' intersects ''C'' at most once. For many practical purposes this definition may be extended to allow cases when some edges of ''P'' are orthogonal to ''L'', and a simple polygon may be called monotone if a line segment that connects two points in ''P'' and is orthogonal to ''L'' lies completely in ''P''. Following the terminology for monotone functions, the former definition describes polygons strictly monotone with respect to ''L''. Properties Assume that ''L'' coincides with the ''x''-axis. Then the leftmost and rightmost vertices of a monotone polygon decompose its boundary into two monotone polygonal chains such that when the vertices of any chain are being traversed in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
