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Exact(11)
Furthermore, obviously, (g_{2} t,qs)) is an increasing function of the first argument t.
Firstly, we find the argument t in terms of x and ẋ.
Hereafter all variables are assumed to be functions of time t; however, the argument t is often omitted.
end{aligned} This implies that (g_{1} t,qs)) is an increasing function of the first argument t.
where τ, e ∈ C ( R, R ) are T-periodic, and g ∈ C ( R × R, R ) are T-periodic in the first argument, T > 0 is a constant.
where τ, e ∈ C ( R, R ) are T-periodic, and f, g ∈ C ( R × R, R ) are T-periodic in the first argument, T > 0 is a constant.
Similar(49)
The arguments (t), and (v) are shared by the syntax trees (2) and (3).
where Θ denotes the convolution for the LCT and ∗ denotes the conventional convolution for the FT. The WD of X M computed with arguments (u,v) is equal to the WD of x computed with arguments (t,ω): overline X (t,omega) = 2{e^{2iuv}}int_{- infty }^{+ infty} {{X_{M}} varepsilon X_{M}^(2u - varepsilon){e^{- 2ivvarepsilon}}dvarepsilon}.
Namely, we assume that the nearest neighbor (NN) hopping strengths are complex with alternating opposite arguments, (t exp (pm i phi)), i.e., the phase factors in the hopping strengths in the chain alternate as, +ϕ, −ϕ, +ϕ, −ϕ, +ϕ, −ϕ, … . Figure 1 1D chain of cavities coupled with complex NN hopping strengths.
Cubic Hermite splines are typically used for interpolation of numeric data specified at given argument values t 1, t 2,…, t n, to obtain a smooth continuous function.
implies oscillation of equation (1.2) for arbitrary (not necessarily non-decreasing) argument τ ( t ) ≤ t.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com