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Longer titles found: Almost periodic function (view), Doubly periodic function (view), Mean-periodic function (view), Quasiperiodic function (view)

searching for Periodic function 80 found (184 total)

alternate case: periodic function

Elliptic hypergeometric series (1,299 words) [view diff] exact match in snippet view article find links to article

function of n, and basic hypergeometric series where the ratio is a periodic function of the complex number n. They were introduced by Date-Jimbo-Kuniba-Miwa-Okado

exponential (eiθ), where the variable θ is the phase of a wave or other periodic function. The phase factor is a unit complex number, i.e. a complex number

(pp. 52–53) describes the finite Fourier transform as a "continuous periodic function" and the discrete Fourier transform (DFT) as "a set of samples of

1938, he submitted his PhD thesis "Some Generalization of Almost Periodic Function" under the supervision of Naum Akhiezer. He then defended the habilitation

power p ( t ) = | s ( t ) | 2 {\textstyle p(t)=|s(t)|^{2}} is also a periodic function of period T {\displaystyle T} . The peak power is simply defined by:

obtained by treating the duration of the segment as one period of a periodic function and computing the Fourier series coefficients. Sine and cosine transforms:

extension with cyclic Galois group Graph theory: Cyclic function, a periodic function Cycle graph, a connected, 2-regular graph Cycle graph (algebra), a

differential equation that is a special case of Hill's equation with the periodic function given as a square wave. There are many ways to write the Meissner

functional equation for a given f(x), then so is F(x)+C(x) for any periodic function C(x) with period 1. Therefore, each indefinite sum actually represents

of a motion Penup Phase (waves) – Elapsed fraction of a cycle of a periodic function Pitch (handwriting) Polar distribution – Type of probability distributionPages

boundedness over the entire real axis of the integral of an almost-periodic function. The ultimate form of this inequality was given by Jean Favard; the

e^{-i2\pi fTn}.} This Fourier series (in frequency) is a continuous periodic function, whose periodicity is the sampling frequency 1 / T {\displaystyle

e^{-i2\pi fTn}.} This Fourier series (in frequency) is a continuous periodic function, whose periodicity is the sampling frequency 1 / T {\displaystyle

approximation theory. The term was coined by Sergei Bernstein. Let f be a 2π-periodic function. Then f is α-Hölder for some 0 < α < 1 if and only if for every natural

(x)|^{2}dx\right]^{\frac {1}{2}}=1.} The Fourier series is a method of expressing a periodic function in terms of sinusoidal basis functions. Taking C[−π,π] to be the space

}|f(t)-f(t+\varepsilon )|} Notice that we consider here f to be a periodic function, e.g. if t = 0 and ε is negative then we define f(ε) = f(2π + ε).

samples of one cycle. If the original sequence is one cycle of a periodic function, the DFT provides all the non-zero values of one DTFT cycle. The DFT

of multiple dimensions, such as images. The Fourier transform of a periodic function, s P ( t ) , {\displaystyle s_{_{P}}(t),} with period P , {\displaystyle

The energy of a periodic function is the same in the time and frequency domain.

Tent map Triangular distribution Triangle wave, a piecewise linear periodic function Trigonometric functions "Basic properties of splines and B-splines"

Wiener, Norbert (1942). "On the oscillation of the derivatives of a periodic function". Trans. Amer. Math. Soc. 52 (2): 249–256. doi:10.1090/s0002-9947-1942-0007169-x

Press, 2006. Ch. 4, Sect. 4. Wilbraham, Henry (1848), "On a certain periodic function", The Cambridge and Dublin Mathematical Journal, 3: 198–201 Hewitt

stationary state solutions in the form of a plane wave multiplied by a periodic function u ( x ) {\displaystyle u(\mathbf {x} )} . The theorem arises as a

_{i}/2;\Lambda )} (see zeta function below). Also it is a "quasi-periodic" function, with the following property: σ ( z + 2 ω i ) = − e 2 η i ( z + ω

serve as activation functions. Usually the sinusoid is used, as any periodic function is decomposable into sinusoids by the Fourier transform. Quadratic

(non-invertible) function Ψ(x) k(log Ψ(x)) is also a solution, for any periodic function k(x) with period log(s). All solutions of Schröder's equation are

to sampling), and Filter bank.) Sinusoids are an important type of periodic function, because realistic signals are often modeled as the summation of many

>0\\0,&{\mbox{otherwise}}.\end{cases}}} Let f {\displaystyle f} be a periodic function, thought of as being on the n-torus, T n {\displaystyle \mathbb {T}

P/T=N} to an integer value, resulting in an N {\displaystyle N} -periodic function: Discrete Fourier series s N [ n ] ≜ s ( n T ) = ∑ k = − ∞ ∞ S [ k

of rotation is a linear function of time, which modulo 360° is a periodic function. An example of this is the two-body problem with circular orbits.

formally stated as Ince's theorem: Ince's theorem—Define a basically periodic function as one satisfying y ( x + π ) = ± y ( x ) {\displaystyle y(x+\pi )=\pm

) {\displaystyle (q_{i},p_{i})} describes a closed function or a periodic function in q i {\displaystyle q_{i}} , the EBK procedure involves quantizing

representing a rotation by 1 radian. The complex exponential is thus a periodic function in the imaginary direction, with period 2πi and image 1 at points

appear as the voltage across the load resistor in the circuit are a periodic function of the applied magnetic flux with a period of Φ 0 {\displaystyle \Phi

{\displaystyle H(f)(x)=-i{\bigl (}F_{+}(x)+F_{-}(x){\bigr )}.} For a periodic function f the circular Hilbert transform is defined: f ~ ( x ) ≜ 1 2 π p

the array of the game. In electrical engineering, if the graph of a periodic function also has glide symmetries, it is called "half-wave symmetric". This

infinitely many parameters (for instance the Fourier modes of the periodic function f ( x ) − x {\displaystyle f(x)-x} ), the Virasoro group is infinite-dimensional

f} implies that if f {\displaystyle f} is two-to-one then it is a periodic function: f ( x ) = f ( y ) = f ( x ⊕ s ) . {\displaystyle f(x)=f(y)=f(x\oplus

function on an abelian variety, which may be regarded therefore as a periodic function of n complex variables, having 2n independent periods; equivalently

H_{n}} are the first-order harmonic numbers. The Dirichlet kernel is a periodic function which becomes the Dirac comb, i.e. the periodic delta function, in

two stable states. The degree of order is related to the amount of periodic function that it shows in the system response. When the periodic force is chosen

the oscillator's "natural" frequency and g {\displaystyle g} is a periodic function that yields the influence caused by the external oscillator. Note

equation as F. This now implies that Ψ(x) = −Ψ(x2) = Ψ(x4), so Ψ is a periodic function of loglog(1/x). Since dy (p.77) speaks of "another solution" and "plainly

described by Bloch's theorem. Bloch form A planewave multiplied by a periodic function Bloch state Bloch function Bloch potential Bloch wave Bloch wavefunction

Z_{\mathrm {L} }=0} ), the input impedance is purely imaginary and a periodic function of position and wavelength (frequency) Z i n ( ℓ ) = j Z 0 tan ⁡ (

(FM), generating a fringes interferometric signal. This signal is a periodic function of the phase Φ {\displaystyle \Phi } of the back-scattered field,

very long therapy, c ( t ) {\displaystyle c(t)} can be modeled as a periodic function (of period T {\displaystyle T} ) or (in case of continuous infusion

Nonhypotenuse number Parallelogram law Parseval's identity – The energy of a periodic function is the same in the time and frequency domain. Ptolemy's theorem –

The succeeding snapshots show summation of 1 to 5 terms in approximating a periodic function (blue) by finite sum of sine functions (red).

differentiability, and at jump points (the function x, considered as a periodic function, has a jump at π) converges to the average of the left and right limits

Discrete-time Fourier transform#Relation to Fourier Transform): which is a periodic function and its equivalent representation as a Fourier series, whose coefficients

give a unique solution, since it allows for multiplication by any periodic function g ( x ) {\displaystyle g(x)} with g ( x ) = g ( x + 1 ) {\displaystyle

u n k ( r ) {\displaystyle u_{n\mathbf {k} }(\mathbf {r} )} is a periodic function of r {\displaystyle \mathbf {r} } . Due to translational symmetry

powers of T, but since it is impossible for a polynomial to match a periodic function over all numbers, the difference in all such approximations will grow

] {\displaystyle x[n]} sequence. This 2 π {\displaystyle 2\pi } -periodic function is the periodic summation of a Fourier transform, which makes it a

volume of the parallelepiped formed by the vectors {v1, ..., vn}. This periodic function is often referred to as the sampled spectrum and can be interpreted

this is identified through an alarm on an airflow monitor or through periodic function tests, are unsafe to use, and in some situations warrant padlocking

deviation from a pure sine wave, the deviation is in the form of a periodic function, and by definition, the voltage distortion contains harmonics. When

w_{kn}={\frac {|\eta |^{2}}{2\Omega ^{2}}}(1-\cos 2\Omega t)} which is a periodic function with frequency 2 Ω {\displaystyle 2\Omega } ; this function varies

function f is continuous on [-π,π]. We invoke the theorem that every periodic function on [-π,π] that is continuous is also bounded and uniformily continuous

pointwise almost everywhere, and defines a Λ {\displaystyle \Lambda } -periodic function on R d {\displaystyle \mathbb {R} ^{d}} , hence a function P s ( x

Vincent; Stehlé, Damien; Zimmermann, Paul (2007). "Worst Cases of a Periodic Function for Large Arguments". 18th IEEE Symposium on Computer Arithmetic.

external magnetic fields. The voltage across a SQUID is a nonlinear periodic function of the applied magnetic field, with a periodicity of one flux quantum

) {\displaystyle \Gamma (\psi )} is a 2 π {\displaystyle 2\pi } -periodic function representing the effect of the periodic external forcing on the oscillator

_{-}^{N}c_{-}r_{-}=e^{iN\phi }c_{+}r_{+}+e^{-iN\phi }c_{-}r_{-},} which represents a periodic function. The same matrices can also be used to calculate the evolution of

{\displaystyle n=1} , we have the one-particle density. For a crystal it is a periodic function with sharp maxima at the lattice sites. For a non-interacting gas

mathematician Henry Wilbraham (25 July 1825 – 13 February 1883) periodic function. Augustus De Morgan (1806–1871), mathematician; symbolic logic Sir

contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input. This allowed

{\displaystyle x\mapsto {\overline {(x+1)\cos(\pi x)}}} indicating the 2 periodic function coinciding with x ↦ ( x + 1 ) cos ⁡ ( π x ) {\displaystyle x\mapsto

}\varepsilon (n)nq^{\kappa n^{2}}} for a positive rational κ and an odd periodic function ε. (Any such theta series is a modular form of weight ⁠3/2⁠). The

{X} \right)} in the unit hyper-cube can be extended to a multiply periodic function and the multiple Fourier series expansion is f ( X 1 , X 2 , … , X

special emergency diesel generator (SEDG) failed to start during a periodic function test. The unit was started with compressed air but did not ignite

)+3\cos(4\zeta )}}.} It does change its shape during propagation, but it is a periodic function of z with period ζ = π / 2 {\displaystyle \zeta =\pi /2} . For soliton

(u,m)={\mathcal {E}}(u,m)-{\frac {E(m)}{K(m)}}u.} It is a singly periodic function which is meromorphic in u {\displaystyle u} , but not in m {\displaystyle

invariant such a model is power law growth, decorated with a log-periodic function. Fitting this model on the growth data (non-linear regression) allows

the brackets represents the cavity enhancement effect. This is a periodic function of 2 β L + ϕ 1 + ϕ 2 {\displaystyle 2\beta L+\phi _{1}+\phi _{2}}

moments. This process is wholly analogous to that used to decompose a periodic function into its Fourier sine & cosine components, the only difference being

f_{n}<0\qquad \qquad (3b)} The analytical solutions apply to any periodic function so long as each period, T {\textstyle T} can be represented as a series

{\displaystyle R_{\phi }} represents the Fourier transform of some periodic function κ ϕ {\displaystyle \kappa _{\phi }} . That is, FNO parameterizes the

combinatorial interpretation of the codenominator. The codiscriminant is a 2-periodic function. The Jimm (ج) function is defined on positive rational arguments via