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Dyadic
Dyadic describes the interaction between two things, and may refer to: *Dyad (sociology), interaction between a pair of individuals **The dyadic variation of Democratic peace theory *Dyadic counterpoint, the voice-against-voice conception of polyphony *People who are not intersex (see also endosex) Mathematics *Dyadic, a relation or function having an arity of two in logic, mathematics, and computer science *Dyadic decomposition, a concept in Littlewood–Paley theory *Dyadic distribution, a type of probability distribution *Dyadic fraction, a mathematical group related to dyadic rationals * Dyadic solenoid, a type of dyadic fraction *Dyadic transformation The dyadic transformation (also known as the dyadic map, bit shift map, 2''x'' mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation) : T: , 1) \to , 1)^\infty : x \mapsto (x_0, x_1, x_2, ... *Dyadics, tensor math (including dyadic products) *A synonym for binary rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyadic Solenoid
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number. The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted \Z tfrac12/math>. In advanced mathematics, the dyadic rational numbers are central to the cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyadic Fraction
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number. The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted \Z tfrac12/math>. In advanced mathematics, the dyadic rational numbers are central to the cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyadics
In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product returns a pseudovector. Both of these have various significant geometric interpretations and are widely used in mathematics, physics, and engineering. The dyadic product takes in two vectors and returns a second order tensor called a ''dyadic'' in this context. A dyadic can be used to contain physical or geometric information, although in general there is no direct way of geometrically interpreting it. The dyadic product is distributive over vector addition, and associative with scalar multiplication. Therefore, the dyadic product is linear in both of its operands. In general, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic. However, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyadic Transformation
The dyadic transformation (also known as the dyadic map, bit shift map, 2''x'' mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation) : T: , 1) \to [0, 1)^\infty : x \mapsto (x_0, x_1, x_2, \ldots) (where [0, 1)^\infty is the set of sequences from [0, 1)) produced by the rule : x_0 = x : \text n \ge 0,\ x_ = (2 x_n) \bmod 1. Equivalently, the dyadic transformation can also be defined as the iterated function map of the piecewise linear function : T(x)=\begin2x & 0 \le x < \frac \\2x-1 & \frac \le x < 1. \end The name ''bit shift map'' arises because, if the value of an iterate is written in notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a "one", replacing it with a zero. The dyadic transform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Democratic Peace Theory
The democratic peace theory posits that democracies are hesitant to engage in armed conflict with other identified democracies. Among proponents of the democratic peace theory, several factors are held as motivating peace between democratic states. Variations of the democratic peace theory emphasize that liberal and republican forms of democracies are less likely to go to war with one another. Variations of the democratic peace hold its "monadic" (democracies are in general more peaceful in their international relations); "dyadic" (democracies do not go to war with other democracies); and "systemic" (more democratic states in the international system makes the international system more peaceful). In terms of norms and identities, it is hypothesized that democratic publics are more dovish in their interactions with other democracies, and that democratically elected leaders are more likely to resort to peaceful resolution in disputes (both in domestic politics and international ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyad (sociology)
In sociology, a dyad is a group of two people, the smallest possible social group. As an adjective, "dyadic" describes their interaction.Macionis, John J., and Linda Marie Gerber. Sociology. 7th ed. Toronto: Pearson Prentice Hall, 2011. 153-54. Print. The pair of individuals in a dyad can be linked via romantic interest, family relation, interests, work, partners in crime, and so on. The relation can be based on equality, but may be based on an asymmetrical or hierarchical relationship (master–servant). The strength of the relationship is evaluated on the basis of time the individuals spend together, as well as on the emotional intensity of their relationship. The term dyad is from . A dyad can be unstable because both persons must cooperate to make it work. If one of the two fails to complete their duties, the group would fall apart. Because of the significance of marriages in society, their stability is very important. For this reason marital dyads are often enforced through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Endosex
An ''endosex'' person is someone whose innate sex characteristics fit normative medical or social ideas for female or male bodies. The word ''endosex'' is an antonym of ''intersex''. Etymology and meaning The prefix '' endo-'' comes from the Ancient Greek (), meaning 'inner, internal', while the term ''sex'' is derived from Latin , meaning 'gender; gender traits; males or females; genitals'. The Latin term is derived from Proto-Indo-European ', from ', "to cut", thus meaning section or division into male and female. Surya Monro states that the term is used to "indicate a person born with sex characteristics that are seen as typically male or female at birth, therefore not medicalized as intersex". Janik Bastien-Charlebois uses the term to identify "people whose sexual development is considered normal by medicine and society". Origin An early English-language reference to the term ''endosex'' can be found in a symposium on intersex held at a European Federation of Sexology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Littlewood–Paley Theory
In harmonic analysis, a field within mathematics, Littlewood–Paley theory is a theoretical framework used to extend certain results about ''L''2 functions to ''L''''p'' functions for 1 1, then the sequence ''S''''n''''j'' converges almost everywhere. This was later superseded by the Carleson's theorem, Carleson–Hunt theorem showing that ''S''''n'' itself converges almost everywhere. Littlewood–Paley theory can also be used to prove the Marcinkiewicz multiplier theorem. References * * * * * * * * {{DEFAULTSORT:Littlewood-Paley theory Fourier analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyadic Distribution
A dyadic (or 2-''adic'') distribution is a specific type of discrete probability distribution that is of some theoretical importance in data compression. Definition A dyadic distribution is a probability distribution whose probability mass function In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete density function. The probability mass ... is :f(i) = 2^ where x_i is some whole number. It is possible to find a binary code defined on this distribution, which has an average code length that is equal to the entropy. Cover, T.M., Joy A. Thomas, J.A. (2006) ''Elements of information theory'', Wiley. References * Cover, T.M., Joy A. Thomas, J.A. (2006) ''Elements of information theory'', Wiley. {{DEFAULTSORT:Dyadic Distribution Types of probability distributions Data compression Discrete distributions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyphony
Polyphony ( ) is a type of musical texture consisting of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice, monophony, or a texture with one dominant melodic voice accompanied by chords, homophony. Within the context of the Western musical tradition, the term ''polyphony'' is usually used to refer to music of the late Middle Ages and Renaissance. Baroque forms such as fugue, which might be called polyphonic, are usually described instead as contrapuntal. Also, as opposed to the ''species'' terminology of counterpoint, polyphony was generally either "pitch-against-pitch" / "point-against-point" or "sustained-pitch" in one part with melismas of varying lengths in another. In all cases the conception was probably what Margaret Bent (1999) calls "dyadic counterpoint", with each part being written generally against one other part, with all parts modified if needed in the end. This point-against-point conception is opposed to " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indigenous Australians
Indigenous Australians or Australian First Nations are people with familial heritage from, and membership in, the ethnic groups that lived in Australia before British colonisation. They consist of two distinct groups: the Aboriginal peoples of the Australian mainland and Tasmania, and the Torres Strait Islander peoples from the seas between Queensland and Papua New Guinea. The term Aboriginal and Torres Strait Islander peoples or the person's specific cultural group, is often preferred, though the terms First Nations of Australia, First Peoples of Australia and First Australians are also increasingly common; 812,728 people self-identified as being of Aboriginal and/or Torres Strait Islander origin in the 2021 Australian Census, representing 3.2% of the total population of Australia. Of these indigenous Australians, 91.4% identified as Aboriginal; 4.2% identified as Torres Strait Islander; while 4.4% identified with both groups. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Relation
In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of elements in and in . It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element is ''related'' to an element , if and only if the pair belongs to the set of ordered pairs that defines the ''binary relation''. A binary relation is the most studied special case of an Finitary relation, -ary relation over sets , which is a subset of the Cartesian product X_1 \times \cdots \times X_n. An example of a binary relation is the "divides" relation over the set of prime numbers \mathbb and the set of integers \mathbb, in which each prime is related to each integer that is a Divisibility, multiple of , but not to an integer that is not a multiple of . In this relation, for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
