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Fundamental pair of periods information


In mathematics, a fundamental pair of periods is an ordered pair of complex numbers that defines a lattice in the complex plane. This type of lattice is the underlying object with which elliptic functions and modular forms are defined.

Fundamental parallelogram defined by a pair of vectors in the complex plane.

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Fundamental pair of periods

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mathematics, a fundamental pair of periods is an ordered pair of complex numbers that defines a lattice in the complex plane. This type of lattice is the...

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Fundamental parallelogram

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Fundamental parallelogram may mean: Fundamental pair of periods on the complex plane Primitive cell on the Euclidean plane This disambiguation page lists...

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Fundamental domain

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poles and zeros on the boundary of the domain. Free regular set Fundamental polygon Brillouin zone Fundamental pair of periods Petersson inner product Cusp...

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Brillouin zone

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points. They can be found in the illustrations below. Fundamental pair of periods Fundamental domain "Topic 5-2: Nyquist Frequency and Group Velocity"...

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Weierstrass functions

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{\displaystyle \{\omega _{1},\omega _{2}\}} are a fundamental pair of periods. Through careful manipulation of the Weierstrass factorization theorem as it relates...

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Doubly periodic function

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functions Lemniscate elliptic functions Dixon elliptic functions Fundamental pair of periods Period mapping Jacobi, C. G. J. (1835). "De functionibus duarum...

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Free abelian group

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form. For more on the two-dimensional case, see fundamental pair of periods. Every set can be the basis of a free abelian group, which is unique up to group...

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Fundamental theorems of welfare economics

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There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

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Modular lambda function

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of the half-periods of Weierstrass's elliptic functions, let [ ω 1 , ω 2 ] {\displaystyle [\omega _{1},\omega _{2}]} be a fundamental pair of periods...

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Coprime integers

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{\displaystyle \mathbb {Z} /a\mathbb {Z} } of integers modulo a. Every pair of congruence relations for an unknown integer x, of the form x ≡ k (mod a) and x ≡ m...

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Pioneer plaque

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The Pioneer plaques are a pair of gold-anodized aluminum plaques that were placed on board the 1972 Pioneer 10 and 1973 Pioneer 11 spacecraft, featuring...

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Electron

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atomic orbitals in isolated atoms. A fundamental factor in these molecular structures is the existence of electron pairs. These are electrons with opposed...

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History of architecture

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also an essential element of change. Although many dwellings belonging to all prehistoric periods and also some clay models of dwellings have been uncovered...

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History of physics

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Nobel Prize in Physics). The Cooper pair was an early example of quasiparticles. Einstein deemed that all fundamental interactions in nature can be explained...

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Moduli stack of elliptic curves

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where the automorphism groups are of order 4, 6, respectively pg 170. One point in the Fundamental domain with stabilizer of order 4 {\displaystyle 4} corresponds...

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Headphones

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Headphones are a pair of small loudspeaker drivers worn on or around the head over a user's ears. They are electroacoustic transducers, which convert...

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Human bonding

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substances in a chemical equation. The term pair bond originated in 1940 in reference to mated pairs of birds; referring to a monogamous or relatively...

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Acid

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capable of either donating a proton (i.e. hydrogen ion, H+), known as a Brønsted–Lowry acid, or forming a covalent bond with an electron pair, known as...

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Conversation analysis

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initial hypotheses. While this kind of inductive analysis based on collections of data exhibits is basic to fundamental work in CA, it has been more common...

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Laser Interferometer Space Antenna

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the frequency domain: changes with periods of less than a day are signals of interest, while changes with periods of a month or more are irrelevant. This...

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Taplow Barrow

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between the church and the mound "raises fundamental questions about the mechanisms of conversion and the assertion of secular power in the conversion period...

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Craps

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Craps is a dice game in which players bet on the outcomes of the roll of a pair of dice. Players can wager money against each other (playing "street craps")...

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History of subatomic physics

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element was composed of a single, unique type of particle. Dalton and his contemporaries believed those were the fundamental particles of nature and thus named...

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