quasidoubly periodic function - traduction vers russe
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quasidoubly periodic function - traduction vers russe

MATHEMATICAL FUNCTION
Quasi-periodic function
  • 2π}}+sin(''x'') satisfies the equation ''f''(''x''+2π)=''f''(''x'')+1, and is hence arithmetic quasiperiodic.

quasidoubly periodic function      
квазидвоякопериодическая функция
aperiodic         
FUNCTION THAT REPEATS ITS VALUES IN REGULAR INTERVALS OR PERIODS
Period length; Aperiodic; Periodic solution; Periodic functions; Aperiodic function; Periodic signal; Non-periodic; Period of a function; Periodic Waveform period; Period (mathematics); Periodical function; Antiperiodic function; Periodicity condition; Periodic Function; Period (math); Antiperiodic; Periodic solutions
апериодический, непериодический
periodic signal         
FUNCTION THAT REPEATS ITS VALUES IN REGULAR INTERVALS OR PERIODS
Period length; Aperiodic; Periodic solution; Periodic functions; Aperiodic function; Periodic signal; Non-periodic; Period of a function; Periodic Waveform period; Period (mathematics); Periodical function; Antiperiodic function; Periodicity condition; Periodic Function; Period (math); Antiperiodic; Periodic solutions

математика

периодический сигнал

Définition

aperiodic
¦ adjective chiefly Physics
1. not periodic; irregular.
2. damped to prevent oscillation or vibration.
Derivatives
aperiodicity noun

Wikipédia

Quasiperiodic function

In mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. A function f {\displaystyle f} is quasiperiodic with quasiperiod ω {\displaystyle \omega } if f ( z + ω ) = g ( z , f ( z ) ) {\displaystyle f(z+\omega )=g(z,f(z))} , where g {\displaystyle g} is a "simpler" function than f {\displaystyle f} . What it means to be "simpler" is vague.

A simple case (sometimes called arithmetic quasiperiodic) is if the function obeys the equation:

f ( z + ω ) = f ( z ) + C {\displaystyle f(z+\omega )=f(z)+C}

Another case (sometimes called geometric quasiperiodic) is if the function obeys the equation:

f ( z + ω ) = C f ( z ) {\displaystyle f(z+\omega )=Cf(z)}

An example of this is the Jacobi theta function, where

ϑ ( z + τ ; τ ) = e 2 π i z π i τ ϑ ( z ; τ ) , {\displaystyle \vartheta (z+\tau ;\tau )=e^{-2\pi iz-\pi i\tau }\vartheta (z;\tau ),}

shows that for fixed τ {\displaystyle \tau } it has quasiperiod τ {\displaystyle \tau } ; it also is periodic with period one. Another example is provided by the Weierstrass sigma function, which is quasiperiodic in two independent quasiperiods, the periods of the corresponding Weierstrass function.

Functions with an additive functional equation

f ( z + ω ) = f ( z ) + a z + b   {\displaystyle f(z+\omega )=f(z)+az+b\ }

are also called quasiperiodic. An example of this is the Weierstrass zeta function, where

ζ ( z + ω , Λ ) = ζ ( z , Λ ) + η ( ω , Λ )   {\displaystyle \zeta (z+\omega ,\Lambda )=\zeta (z,\Lambda )+\eta (\omega ,\Lambda )\ }

for a z-independent η when ω is a period of the corresponding Weierstrass ℘ function.

In the special case where f ( z + ω ) = f ( z )   {\displaystyle f(z+\omega )=f(z)\ } we say f is periodic with period ω in the period lattice Λ {\displaystyle \Lambda } .

Traduction de &#39quasidoubly periodic function&#39 en Russe