Many applications of fractional calculus amount to replacing the time derivative in a given evolution equation by a derivative of fractional-order.
In hopes of enticing, or forcing, residents to abandon the scent of freshly cut grass, cities in this parched region have offered homeowners ever-increasing amounts to replace their lawns with drought-resistant plants; those who keep their grass face tough watering restrictions and fines for leaky sprinklers.
The product ϕ r 1, i 3 ( 1 ) ϕ r 2, i 3 ( 2 ) in (57) can be replaced by f i 3, r 1, r 2, which amounts to replace the allocation matrices Φ(1) and Φ(2) by the third‐order allocation tensor F ∈ C I 3 × R 1 × R 2, the matrix F = Φ ( 1 ) ◇ Φ ( 2 ) T ∈ C I 3 × R 1 R 2 being equivalent to F I 3 × R 1 R 2 ∈ C I 3 × R 1 R 2, i.e., a mode‐1 flat matrix unfolding of the allocation tensor.
A court in Beijing sentenced Mr. Liu to 11 years in prison in December 2009 after he helped organize Charter 08, a petition calling for wide-ranging political changes in China that would have amounted to replacing Communist Party rule with a multiparty democracy.
It amounts to replacing part of the host image by the logo image.
Indeed, if we substitute,,, respectively, for in (2.1), this amounts to replacing by in (2.3).
For instance the translation of operator Y (the past version of X) simply amounts to replacing n−1 by n+1 in the definition of the reducer for X.
Formally, this amounts to replacing the equation governing Xi with a new equation Xi = xi, substituting for this new value of Xi in all the equations in which Xi occurs but leaving the other equations themselves unaltered.
With this formulation, including contact separation in the analysis amounts to replacing a call to a linear equation solver by a call to an LCP solver, a modification of only two steps of the procedure.
