Sentence examples for by replacing the integer from inspiring English sources

(ii) The different equations above can be fractionalized by replacing the integer derivatives either in space or time by fractional derivatives.

Therefore, it is very necessary for us to consider the anomalous diffusion equation which is obtained from the standard diffusion equation by replacing the integer derivative with a fractional derivative of order (qin (0,1)).

Replacing the integer N by any complex number α, we relax the definition of the multiple Hurwitz-Lerch zeta function, and we generalize the formulas (8), (10) and (11).

Replacing the integer n by any number (beta inmathbb{C}), (operatorname{Re}(beta )>0), we define the left-fractional conformable integral operator by _{a}^{beta}mathfrak{I}^{alpha}f(x)= frac{1}{Gamma(beta)} int_{a}^{x} biggl( frac{(x-a)^{alpha}- t-a)^{alpha}- t-aha} biggr) ^{alpha}- t-a frac{dt}{(t-a)^{alpha}a}{alpha}.

Several applications replacing the integer temporal operator by an operator of fractional order are presented in [1 11].

We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver.

OptORF is formulated as a single level mixed integer linear program (MILP) by replacing the inner maximization problem with its optimality conditions as constraints.

By replacing the zero entries of (mathcal {A}) with (-frac{1}{k}), where k is a positive integer, we see that the Z-tensor (mathcal{A}_{k}) is irreducible.

One of the possible generalizations of a Langevin equation is to replace the integer-order derivative by a fractional-order derivative in it.

The usual way to use this tool is to replace the integer-order derivatives of the partial differential equation that describes one specific phenomenon by a derivative of non-integer order.

The best single-scattering fits were further refined using multiple-scattering parameters to account for EXAFS arising from the imidazole side chain of histidine ligands, by replacing integer numbers of N/O donors in the single-scattering fits with imidazoles (see Tables S1 S9 of the Supporting Information).