Sentence examples for mapping functions defined from inspiring English sources

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).

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 �� 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}).

In particular, (Delta^{-v}) maps functions defined on (mathbb{N} _{a} ) to functions defined on (mathbb{N} _{a+v}), where (mathbb{N} _{t}={t,t+1,t+2,ldots}).

The coefficients of the expansion (sampling matrix) map functions defined on ℋ into the N th-dimensional complex space ℂ N × 1.

(iii) The nabla left fractional difference ∇ a α maps functions defined on N a to functions defined on N a + n. (iv) The nabla right fractional difference ∇ α b maps functions defined on N b to functions defined on N b − n.