Sentence examples for an imaginary unit from inspiring English sources
where is an imaginary unit.
In this paper, i will always denote an imaginary unit.
Here and in what follows, we denote by ω an imaginary unit.
To simplify notation, it is sometimes useful to express it in an imaginary unit of "utils".
A complex random variable (X=X_{1}+i X_{2}) is called symmetric α-stable (in short (Salpha S)) if the random vector ((X_{1},X_{2})) is (Salpha S) in (mathbb{R}^{2}), where i is an imaginary unit.
On the other hand, on approximation to complex Brownian motion, Bardina [8] considered the process (U_{n}^{theta}={U_{n}^{theta}(t), tin[0,infty)}) defined by U_{n}^{theta}(t)=sqrt{n} int_{0}^{2t}e^{itheta{N(ns)}},ds, quad tgeq0, where i is an imaginary unit.
where Δ p, A u = div ( | Δ u + i A ( x ) u | p ‒ 2 ( ‒ u + i A ( x ) u ) ), i is the imaginary unit, A ( x ) : R N → R N is a real vector potential, 1 < p < N, p * = N p / ( N ‒ p ) denotes the Sobolev critical exponent and N ≥ 3.
where Δ p, A u = div ( | ∇ u + i A ( x ) u | p − 2 ( ∇ u + i A ( x ) u ) ), i is the imaginary unit, A ( x ) : R N → R N is real vector potential, 1 < p < N, V ( x ) is a non-negative potential, p ∗ = N p / ( N − p ) denotes the Sobolev critical exponent for N ≥ 3 and K ( x ) is a bounded positive coefficient.
(I deliberately refer to an imaginary linear unit of sound, rather than using the highly-familiar units of "decibels". Decibels use a logarithmic scale, which would make the example less easily appreciated).
where λ is the length of the electromagnetic wave and I is the imaginary unit of a complex number1.
The set of complex numbers, i.e., numbers that can be written in the form for real numbers and where is the imaginary unit, form a vector space over the reals with the usual addition and multiplication: and for real numbers,,, and.
