|
Reciprocal
Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another polynomial by reversing its coefficients * Reciprocal rule, a technique in calculus for calculating derivatives of reciprocal functions * Reciprocal spiral, a plane curve * Reciprocal averaging, a statistical technique for aggregating categorical data In science and technology * Reciprocal aircraft heading, 180 degrees (the opposite direction) from a stated heading * Reciprocal lattice, a basis for the dual space of covectors, in crystallography * Reciprocal length, a measurement used in science * Reciprocating engine or piston engine * Reciprocating oscillation in physical wave theory Life sciences and medicine * Hybrid (biology), in genetics, the result of a reciprocal pair of crossings, forming ''reciprocal hybrids'' * Reciprocal altr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Lattice
In physics, the reciprocal lattice represents the Fourier transform of another lattice (group) (usually a Bravais lattice). In normal usage, the initial lattice (whose transform is represented by the reciprocal lattice) is a periodic spatial function in real space known as the ''direct lattice''. While the direct lattice exists in real space and is commonly understood to be a physical lattice (such as the lattice of a crystal), the reciprocal lattice exists in the space of spatial frequencies known as reciprocal space or k space, where \mathbf refers to the wavevector. In quantum physics, reciprocal space is closely related to momentum space according to the proportionality \mathbf = \hbar \mathbf, where \mathbf is the momentum vector and \hbar is the Planck constant. The reciprocal lattice of a reciprocal lattice is equivalent to the original direct lattice, because the defining equations are symmetrical with respect to the vectors in real and reciprocal space. Mathematically, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Altruism
In evolutionary biology, reciprocal altruism is a behaviour whereby an organism acts in a manner that temporarily reduces its fitness while increasing another organism's fitness, with the expectation that the other organism will act in a similar manner at a later time. The concept was initially developed by Robert Trivers to explain the evolution of cooperation as instances of mutually altruistic acts. The concept is close to the strategy of "tit for tat" used in game theory. In 1987 Trivers told a symposium on reciprocity that he had originally submitted his article under the title "The Evolution of Delayed Return Altruism", but reviewer W. D. Hamilton suggested that he change the title to "The Evolution of Reciprocal Altruism". Trivers changed the title, but not the examples in the manuscript, which has led to confusion about what were appropriate examples of reciprocal altruism for the last 50 years. In their contribution to that symposium, Rothstein and Pierotti (1988) ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Public License
The Reciprocal Public License (RPL) is a copyleft software license released in 2001. Version 1.5 of the license was published on July 15, 2007, and was approved by the Open Source Initiative as an open-source license. Description The RPL was authored in 2001 by Scott Shattuck, a software architect for Technical Pursuit Inc. for use with that company's TIBET product line. The RPL was inspired by the GNU General Public License (GPL) and authored to explicitly remove what the RPL's authors have referred to as the GPL's "privacy loophole". The GPL privacy loopholes allows recipients of GPL'd code to: #make changes to source code which are never released to the open source community (by virtue of not deploying "to a third party"), and #derive financial or other business benefit from that action, violating what some might consider a simple concept of "fairness". Because of its " viral" nature, the RPL is often found in dual-licensing models in which it is paired with more traditio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a rational number, fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the Function (mathematics), function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an Involution (mathematics), involution). Multiplying by a number is the same as Division (mathematics), dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Construction
A reciprocal construction (abbreviated ) is a grammatical pattern in which each of the participants occupies both the role of agent and patient with respect to the other. An example is the English sentence ''John and Mary criticized each other'': John criticized Mary, and Mary criticized John. Reciprocal constructions can be said to express mutual relationships. Many languages, such as Semitic languages, Altaic languages or Bantu languages, have special reciprocal affixes in verbs. Other languages, including English, use reciprocal pronouns such as ''"each other"'' to indicate a mutual relation. Latin uses the preposition ''inter'' and its reflexive pronoun ''inter se'' (between themselves) when the verb is third person. Most Indo-European languages do not have special reciprocal affixes on verbs, and mutual relations are expressed through reflexive constructions or other mechanisms. For example, Russian reciprocal constructions have the suffix -sja (-ся, 'self'), which a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Determinism
Reciprocal determinism is the theory set forth by psychologist Albert Bandura which states that a person's behavior both influences and is influenced by personal factors and the social environment. Bandura accepts the possibility that an individual's behavior may be conditioned through the use of consequences. At the same time he asserts that a person's behavior (and personal factors, such as cognitive skills or attitudes) can impact the environment. Bandura was able to show this when he created the Bandura's Box experiment. As an example, Bandura's reciprocal determinism could occur when a child is acting out in school. The child doesn't like going to school; therefore, they act out in class. This results in teachers and administrators of the school disliking having the child around. When confronted by the situation, the child admits they hate school and other peers don't like them. This results in the child acting inappropriately, forcing the administrators who dislike having t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sherrington's Law Of Reciprocal Innervation
René Descartes (1596–1650) was one of the first to conceive a model of reciprocal innervation (in 1626) as the principle that provides for the control of agonist and antagonist muscles. Reciprocal innervation describes skeletal muscles as existing in antagonistic pairs, with contraction of one muscle producing forces opposite to those generated by contraction of the other. For example, in the human arm, the triceps acts to extend the lower arm outward while the biceps acts to flex the lower arm inward. To reach optimum efficiency, contraction of opposing muscles must be inhibited while muscles with the desired action are excited. This reciprocal innervation occurs so that the contraction of a muscle results in the simultaneous relaxation of its corresponding antagonist. A common example of reciprocal innervation, is the effect of the nociceptive (or nocifensive) reflex, or defensive response to pain, otherwise commonly known as the withdrawal reflex; a type of involuntary act ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Polynomial
In algebra, given a polynomial :p(x) = a_0 + a_1x + a_2x^2 + \cdots + a_nx^n, with coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial,* denoted by or , is the polynomial :p^*(x) = a_n + a_x + \cdots + a_0x^n = x^n p(x^). That is, the coefficients of are the coefficients of in reverse order. They arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix. In the special case where the field is the complex numbers, when :p(z) = a_0 + a_1z + a_2z^2 + \cdots + a_nz^n, the conjugate reciprocal polynomial, denoted , is defined by, :p^(z) = \overline + \overlinez + \cdots + \overlinez^n = z^n\overline, where \overline denotes the complex conjugate of a_i, and is also called the reciprocal polynomial when no confusion can arise. A polynomial is called self-reciprocal or palindromic if . The coefficients of a self-reciprocal polynomial satisfy for all . Properties Reciprocal polynomials have several connec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid (biology)
In biology, a hybrid is the offspring resulting from combining the qualities of two organisms of different breeds, varieties, species or genera through sexual reproduction. Hybrids are not always intermediates between their parents (such as in blending inheritance), but can show hybrid vigor, sometimes growing larger or taller than either parent. The concept of a hybrid is interpreted differently in animal and plant breeding, where there is interest in the individual parentage. In genetics, attention is focused on the numbers of chromosomes. In taxonomy, a key question is how closely related the parent species are. Species are reproductively isolated by strong barriers to hybridisation, which include genetic and morphological differences, differing times of fertility, mating behaviors and cues, and physiological rejection of sperm cells or the developing embryo. Some act before fertilization and others after it. Similar barriers exist in plants, with differences in flowering tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Length
Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre (symbol: m−1), the reciprocal centimetre or inverse centimetre (symbol: cm−1). Quantities measured in reciprocal length include: *absorption coefficient or attenuation coefficient, in materials science *curvature of a line, in mathematics *gain, in laser physics *magnitude of vectors in reciprocal space, in crystallography *more generally any spatial frequency e.g. in cycles per unit length *optical power of a lens, in optics *rotational constant of a rigid rotor, in quantum mechanics *wavenumber, or magnitude of a wavevector, in spectroscopy *density of a linear feature in hydrology and other fields; see kilometre per square kilometre In optics, the dioptre is a unit equivalent to reciprocal metre. Measure of energy In some branches of ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Rule
In calculus, the reciprocal rule gives the derivative of the reciprocal of a function ''f'' in terms of the derivative of ''f''. The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents. Also, one can readily deduce the quotient rule from the reciprocal rule and the product rule. The reciprocal rule states that if ''f'' is differentiable at a point ''x'' and ''f''(''x'') ≠ 0 then g(''x'') = 1/''f''(''x'') is also differentiable at ''x'' and g'(x) = \frac \left(\frac \right) = -\frac. Proof This proof relies on the premise that f is differentiable at x, and on the theorem that f is then also necessarily continuous there. Applying the definition of the derivative of g at x with f(x) \ne 0 gives \begin g'(x) = \frac d \left(\frac \right) & = \lim_ \left (\frac \right )\\ & = \lim_ \left( \frac \right)\\ & = \lim_ \left( - \frac \cdot \frac 1 \right).\end The limit o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Cross
In genetics, a reciprocal cross is a breeding experiment designed to test the role of parental sex on a given inheritance pattern. All parent organisms must be true breeding to properly carry out such an experiment. In one cross, a male expressing the trait of interest will be crossed with a female not expressing the trait. In the other, a female expressing the trait of interest will be crossed with a male not expressing the trait. It is the cross that could be made either way or independent of the sex of the parents. For example, suppose a biologist wished to identify whether a hypothetical allele Z, a variant of some gene A, is on the male or female sex chromosome. They might first cross a Z-trait female with an A-trait male and observe the offspring. Next, they would cross an A-trait female with a Z-trait male and observe the offspring. Via principles of dominant and recessive alleles, they could then (perhaps after cross-breeding the offspring as well) make an inference as to w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
