odd function

[′äd ‚fəŋk·shən]

(mathematics)

A function ƒ(x) is odd if, for every x, ƒ(-x) = -ƒ(x).

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References in classic literature ?

Indeed, except in respect of staring about him (a branch of the public service to which the pictorial cherub is much addicted), this domestic cherub discharged as many odd functions as his prototype; with the difference, say, that he performed with a blacking-brush on the family's boots, instead of performing on enormous wind instruments and double-basses, and that he conducted himself with cheerful alacrity to much useful purpose, instead of foreshortening himself in the air with the vaguest intentions.

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where [alpha] and [beta] are positive constants; [a.sub.ij] is the (i, j) element of A and [phi](*) is an odd function.

Consensus Control of Second-Order Multiagent Systems with Particle Swarm Optimization Algorithm

That is f is an odd function. Interchanging x with y in (16), we see that

A FUNCTIONAL EQUATION WITH RESTRICTED ARGUMENT RELATED TO COSINE FUNCTION

(a) Cross section of covariances [mathematical expression not reproducible] and [mathematical expression not reproducible] for even and odd function. Each covariance is similar to a sinc function centred at f = f', where a tip is added on top.

Fourier Spectroscopy: A Bayesian Way

If [F.sub.1](x) = [F.sub.11]([x.sub.1]) + [F.sub.12]([x.sub.2], ..., [x.sub.n]) is an odd function or [F.sub.11] ([x.sub.1]) = [[alpha].sub.1][x.sub.1], then [E.sub.1] = [x.sub.1] + [y.sub.1] can be made, where [[alpha].sub.1] is a real number.

A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems

I have indicated to our President and CEO that if there is anything I can do in the future, just reach out, so with that in mind I hope I keep running into you all at the odd function.

Exit stage left: a farewell from Bill Pearson

The gossip function f(x) is an odd function; thus f([x.sub.j](n) - [x.sub.j](n)) + f([x.sub.i](n) - [x.sub.j](n)) = 0.

Nonlinear gossip algorithms for wireless sensor networks

ii) Does any odd function contribute to the ground state?

Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation

It is easy to realize that [i.sub.nl](0) = 0 and, due to the circuit symmetry, [i.sub.nl](v) is an odd function of v.

Modeling, analysis, and experimental validation of frequency dividers with direct injection

[J.sub.xi](x) is a real odd function, and [J.sub.zi](x) is a real even function.

Efficient and accurate approximation of infinite series summation using asymptotic approximation and fast convergent series

We can verify this by substituting (11) into (10) and by using the fact that S'p(x)is an odd function such as [S'.sub.p] (x) = - [S'.sub.p] (-x) since the derivative of the even function becomes an odd function [19].

Optimal compensation of dual carrier frequency offsets for MISO-mode DVB-T2

On the other hand, the quadrature angles are the zeros of [p.sub.n+1] (x([theta])), where {[p.sub.k]}k[greater than or equal to]0 are the algebraic orthogonal polynomials with respect to the weight function (1.8); the functions {[p.sub.k] (x([theta]))} are indeed orthogonal in d[theta], but they are not all trigonometric polynomials, since [p.sub.k] is an odd function for k odd(cf.