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Reciprocity (Canadian Politics)
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 *** Concealed_carry_in_the_United_States#Reciprocity, Concealed carry reciprocity ** Occupational licensing, which in some jurisdictions provides for it * Traffic violations reciprocity where non-resident drivers are treated like residents * Quid pro quo#Common law, 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 exch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity (electrical Networks)
Reciprocity in electrical networks is a property of a circuit that relates voltages and currents at two points. The reciprocity theorem states that the current at one point in a circuit due to a voltage at a second point is the same as the current at the second point due to the same voltage at the first. The reciprocity theorem is valid for almost all Passivity (engineering), passive networks. The reciprocity theorem is a feature of a more general principle of Reciprocity (electromagnetism), reciprocity in electromagnetism. Description If a electric current, current, I_\text , injected into port (circuit theory), port A produces a voltage, V_\text , at port B and I_\text injected into port B produces V_\text at port A, then the network is said to be reciprocal. Equivalently, reciprocity can be defined by the dual situation; applying voltage, V_\text , at port A producing current I_\text at port B and V_\text at port B producing current I_\text at port A. In general, Passi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity Relation
In multivariate calculus, a differential or differential form is said to be exact or perfect (''exact differential''), as contrasted with an inexact differential, if it is equal to the general differential dQ for some differentiable function Q in an orthogonal coordinate system (hence Q is a multivariable function whose variables are independent, as they are always expected to be when treated in multivariable calculus). An exact differential is sometimes also called a ''total differential'', or a ''full differential'', or, in the study of differential geometry, it is termed an exact form. The integral of an exact differential over any integral path is path-independent, and this fact is used to identify state functions in thermodynamics. Overview Definition Even if we work in three dimensions here, the definitions of exact differentials for other dimensions are structurally similar to the three dimensional definition. In three dimensions, a form of the type A(x, y, z ... [...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 In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credit .... The term "reciprocity law (mathematics), 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 Gotthold Eisenstein, Eisenstein and Ernst Kummer, Kummer to David Hilbert, Hilbert's product formula for the Hilbert symbol, 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 Adelic algebraic group, idèle class group ... [...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 Ei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Reciprocity
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence ''x''3 ≡ ''p'' (mod ''q'') is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if ''p'' and ''q'' are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence ''x''3 ≡ ''p'' (mod ''q'') is solvable if and only if ''x''3 ≡ ''q'' (mod ''p'') is solvable. History Sometime before 1748 Euler made the first conjectures about the cubic residuacity of small integers, but they were not published until 1849, 62 years after his death. Gauss's published works mention cubic residues and reciprocity three times: there is one result pertaining to cubic residues in the Disquisitiones Arithmeticae (1801). In the introduction to the fifth and sixth proofs of quadratic reciprocity (1818) he said that he was publishing these proofs because their techniques ( Gauss ... [...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 ref ... [...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] |
Antenna (radio)
In radio-frequency engineering, an antenna (American English) or aerial (British English) is an electronic device that converts an alternating current, alternating electric current into radio waves (transmitting), or radio waves into an electric current (receiving). It is the interface between radio waves Radio propagation, propagating through space and electric currents moving in metal Electrical conductor, conductors, used with a transmitter or receiver (radio), receiver. In transmission (telecommunications), transmission, a radio transmitter supplies an electric current to the antenna's Terminal (electronics), terminals, and the antenna radiates the energy from the current as electromagnetic radiation, electromagnetic waves (radio waves). In receiver (radio), reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplifier, amplified. Antennas are essential components ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocity Theorem (other)
Reciprocity theorem may refer to: *Quadratic reciprocity, a theorem about modular arithmetic **Cubic reciprocity **Quartic reciprocity **Artin reciprocity ** Weil reciprocity for algebraic curves * Frobenius reciprocity theorem for group representations * Stanley's reciprocity theorem for generating functions * Reciprocity (engineering), theorems relating signals and the resulting responses ** including Reciprocity (electrical networks), a theorem relating voltages and currents in a network *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-invarian ..., theorems relating sources and the resulting fields in classical electromagnetism * Tellegen's theorem, a theorem about the transfer function of passive networks *Reciprocity law for Dedekind sums * Betti's theorem i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Screw Theory
Screw theory is the algebraic calculation of pairs of Vector (mathematics and physics), vectors, also known as ''dual vectors'' – such as Angular velocity, angular and linear velocity, or forces and Moment (physics), moments – that arise in the kinematics and Dynamics (mechanics), dynamics of Rigid body, rigid bodies. Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw axis, screw axes of spatial movement and the Line of action, lines of action of forces. The pair of vectors that form the Plücker coordinates of a line define a unit screw, and general screws are obtained by multiplication by a pair of real numbers and Vector addition, addition of vectors. Important theorems of screw theory include: the ''transfer principle'' proves that geometric calculations for points using vectors have parallel geometric calculations for lines obtained by replacing vectors with screws; Chasles' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
