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Reciprocity
Reciprocity may refer to: Law and trade * Reciprocity (Canadian politics), free trade with the United States of America ** Reciprocal trade agreement, entered into in order to reduce (or eliminate) tariffs, quotas and other trade restrictions on items traded between the signatories * Interstate reciprocity, recognition of sibling federated states' laws: ** In the United States specifically: *** Full Faith and Credit Clause, which provides for it ** Occupational licensing, which in some jurisdictions provides for it * Traffic violations reciprocity where non-resident drivers are treated like residents * Quid pro quo, a legal concept of the exchange of good or services, each having value Social sciences and humanities * Norm of reciprocity, social norm of in-kind responses to the behavior of others * Reciprocity (cultural anthropology), way of defining people's informal exchange of goods and labour * Reciprocity (evolution), mechanisms for the evolution of cooperation * Reciproc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Reciprocity
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard statement is: This law, together with its supplements, allows the easy calculation of any Legendre symbol, making it possible to determine whether there is an integer solution for any quadratic equation of the form x^2\equiv a \bmod p for an odd prime p; that is, to determine the "perfect squares" modulo p. However, this is a non-constructive result: it gives no help at all for finding a ''specific'' solution; for this, other methods are required. For example, in the case p\equiv 3 \bmod 4 using Euler's criterion one can give an explicit formula for the "square roots" modulo p of a quadratic residue a, namely, :\pm a^ indeed, :\left (\pm a^ \right )^2=a^=a\cdot a^\equiv a\left(\frac\right)=a \bmod p. This formula only works if it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity Law
In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f(x) with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irreducible polynomial f(x) = x^2 + ax + b splits into linear terms when reduced mod p. That is, it determines for which prime numbers the relationf(x) \equiv f_p(x) = (x-n_p)(x-m_p) \text (\text p)holds. For a general reciprocity lawpg 3, it is defined as the rule determining which primes p the polynomial f_p splits into linear factors, denoted \text\. There are several different ways to express reciprocity laws. The early reciprocity laws found in the 19th century were usually expressed in terms of a power residue symbol (''p''/''q'') generalizing the quadratic reciprocity symbol, that describes when a prime number is an ''n''th power residue modulo another prime, and gave a relation between (''p''/''q'') and (''q''/''p''). Hilbert re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norm Of Reciprocity
The norm of reciprocity requires that we repay in kind what another has done for us.Whatley, M, A., Rhodes, A., Smith, R. H., Webster, J. M. (1999) ''The Effect of a Favor on Public and Private Compliance: How Internalized is the Norm of Reciprocity?''. Basic and Applied Social Psychology, 21(3), 251–259 It can be understood as the expectation that people will respond favorably to each other by returning benefits for benefits, and responding with either indifference or hostility to harms. The social norm of reciprocity often takes different forms in different areas of social life, or in different societies. All of them, however, are distinct from related ideas such as gratitude, the Golden Rule, or mutual goodwill. See reciprocity (social and political philosophy) for an analysis of the concepts involved. The norm of reciprocity mirrors the concept of reciprocal altruism in evolutionary biology. However, evolutionary theory and therefore sociobiology was not well received by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity (social And Political Philosophy)
The social norm of reciprocity is the expectation that people will respond to each other in similar ways—responding to gifts and kindnesses from others with similar benevolence of their own, and responding to harmful, hurtful acts from others with either indifference or some form of retaliation. Such norms can be crude and mechanical, such as a literal reading of the eye-for-an-eye rule lex talionis, or they can be complex and sophisticated, such as a subtle understanding of how anonymous donations to an international organization can be a form of reciprocity for the receipt of very personal benefits, such as the love of a parent. The norm of reciprocity varies widely in its details from situation to situation, and from society to society. Anthropologists and sociologists have often claimed, however, that having some version of the norm appears to be a social inevitability. Reciprocity figures prominently in social exchange theory, evolutionary psychology, social psychology, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity (electromagnetism)
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints. Reciprocity is closely related to the concept of symmetric operators from linear algebra, applied to electromagnetism. Perhaps the most common and general such theorem is Lorentz reciprocity (and its various special cases such as Rayleigh-Carson reciprocity), named after work by Hendrik Lorentz in 1896 following analogous results regarding sound by Lord Rayleigh and light by Helmholtz (Potton, 2004). Loosely, it states that the relationship between an oscillating current and the resulting electric field is unchanged if one interchanges the points where the current is placed and where the field is measured. For the specific case of an electrical network, it is sometimes phrased as the stateme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity (photography)
In photography, reciprocity is the inverse relationship between the intensity and duration of light that determines the reaction of light-sensitive material. Within a normal exposure range for film stock, for example, the reciprocity law states that the film response will be determined by the total exposure, defined as intensity × time. Therefore, the same response (for example, the optical density of the developed film) can result from reducing duration and increasing light intensity, and vice versa. The reciprocal relationship is assumed in most sensitometry, for example when measuring a Hurter and Driffield curve (optical density versus logarithm of total exposure) for a photographic emulsion. Total exposure of the film or sensor, the product of focal-plane illuminance times exposure time, is measured in lux seconds. History The idea of reciprocity, once known as Bunsen–Roscoe reciprocity, originated from the work of Robert Bunsen and Henry Roscoe in 1862. Deviation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity (social Psychology)
In social psychology, reciprocity is a social norm of responding to a positive action with another positive action, rewarding kind actions. As a social construct, reciprocity means that in response to friendly actions, people are frequently much nicer and much more cooperative than predicted by the self-interest model; conversely, in response to hostile actions they are frequently much more nasty and even brutal. Reciprocity makes it possible to build continuing relationships and exchanges. Francis Fukuyama states that “If the institutions of democracy and capitalism are to work properly, they must coexist within certain premodern cultural habits that ensure their proper functioning” (p. 11). He goes on to say “Law, contract, and economic rationality and prosperity…. must as well be leavened with reciprocity, moral obligation, duty toward community, and trust…. The latter are not anachronisms in a modern society but rather the sine qua non of the latter’s success� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity (cultural Anthropology)
In cultural anthropology, reciprocity refers to the non-market exchange of goods or labour ranging from direct barter (immediate exchange) to forms of gift exchange where a return is eventually expected (delayed exchange) as in the exchange of birthday gifts. It is thus distinct from the true gift, where no return is expected. When the exchange is immediate, as in barter, it does not create a social relationship. When the exchange is delayed, it creates both a relationship as well as an obligation for a return (i.e. debt). Hence, some forms of reciprocity can establish hierarchy if the debt is not repaid. The failure to make a return may end a relationship between equals. Reciprocal exchanges can also have a political effect through the creation of multiple obligations and the establishment of leadership, as in the gift exchanges (Moka) between Big Men in Melanesia. Some forms of reciprocity are thus closely related to redistribution, where goods and services are collected by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmholtz Reciprocity
The Helmholtz reciprocity principle describes how a ray of light and its reverse ray encounter matched optical adventures, such as reflections, refractions, and absorptions in a passive medium, or at an interface. It does not apply to moving, non-linear, or magnetic media. For example, incoming and outgoing light can be considered as reversals of each other,Hapke, B. (1993). ''Theory of Reflectance and Emittance Spectroscopy'', Cambridge University Press, Cambridge UK, , Section 10C, pages 263-264. without affecting the bidirectional reflectance distribution function (BRDF) outcome. If light was measured with a sensor and that light reflected on a material with a BRDF that obeys the Helmholtz reciprocity principle one would be able to swap the sensor and light source and the measurement of flux would remain equal. In the computer graphics scheme of global illumination, the Helmholtz reciprocity principle is important if the global illumination algorithm reverses light paths ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artin Reciprocity Law
The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from the quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result provided a partial solution to Hilbert's ninth problem. Statement Let L/K be a Galois extension of global fields and C_L stand for the idèle class group of L. One of the statements of the Artin reciprocity law is that there is a canonical isomorphism called the global symbol mapNeukirch (1999) p.391 : \theta: C_K/ \to \operatorname(L/K)^, where \text denotes the abelianization of a group. The map \theta is defined by assembling the maps called the local Artin symbol, the local reciprocity map or the norm resid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity (evolution)
Reciprocity in evolutionary biology refers to mechanisms whereby the evolution of cooperative or altruistic behaviour may be favoured by the probability of future mutual interactions. A corollary is how a desire for revenge can harm the collective and therefore be naturally deselected. Main types Three types of reciprocity have been studied extensively: * Direct reciprocity * Indirect * Network reciprocity Direct reciprocity Direct reciprocity was proposed by Robert Trivers as a mechanism for the evolution of cooperation. If there are repeated encounters between the same two players in an evolutionary game in which each of them can choose either to "cooperate" or "defect", then a strategy of mutual cooperation may be favoured even if it pays each player, in the short term, to defect when the other cooperates. Direct reciprocity can lead to the evolution of cooperation only if the probability, w, of another encounter between the same two individuals exceeds the cost-to-benefit ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartic Reciprocity
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence ''x''4 ≡ ''p'' (mod ''q'') is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence ''x''4 ≡ ''p'' (mod ''q'') to that of ''x''4 ≡ ''q'' (mod ''p''). History Euler made the first conjectures about biquadratic reciprocity. Gauss published two monographs on biquadratic reciprocity. In the first one (1828) he proved Euler's conjecture about the biquadratic character of 2. In the second one (1832) he stated the biquadratic reciprocity law for the Gaussian integers and proved the supplementary formulas. He saidGauss, BQ, § 67 that a third monograph would be forthcoming with the proof of the general theorem, but it never appeared. Jacobi presented proofs in his Königsberg lectures of 1836–37. The first published proofs were by Eis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
