Sentence examples for maps functions defined from inspiring English sources
The fractional sum (Delta^{-nu}) maps functions defined on (mathbb{N}_{a}) to functions defined on (mathbb{N}_{a+nu}).
The fractional sum (Delta^{-alpha}) maps functions defined on (mathbb {N}_{a}) to the functions defined on (mathbb{N}_{a+alpha}).
The fractional Caputo-like difference operator (^{C} Delta^{mu}) maps functions defined on (mathbb{N}_{a}) to the functions defined on (mathbb {N}_{a+m-mu}).
(i) The delta left fractional difference Δ a α maps functions defined on N a to functions defined on N a + ( n − α ).
(ii) The delta right fractional difference Δ α b maps functions defined on N b to functions defined on N b − ( n − α ).
(7) One should note that the left q-fractional integral (_{q}nabla^{-alpha}_{a}) maps functions defined on (mathbb{T}_{q}) to functions defined on (mathbb{T}_{q}).
The coefficients of the expansion (sampling matrix) map functions defined on ℋ into the N th-dimensional complex space ℂ N × 1.
The important characteristic of these operators is that they map functions defined on the oscillating domains Ω 1 ε and Ω 2 ε into functions defined on the fixed domains Ω × Y 1 and Ω × Y 2 respectively.
where exp· and log· are the pair of exponential and logarithm mapping functions defined in (2) and (3) under log-Euclidean metric and m is the index for the current iteration.
To decrease the intensity values of the high-illumination pixels and increase the intensity values of the low-illumination pixels simultaneously, the intensity image is treated with enhancement and compression processes, respectively, using a specifically designed nonlinear sine intensity mapping function defined in [6] as T I in x, y = sin 2 π 2 I in x, y q, I in x, y ∈ 0, 1 (3).
