Questions on IBM kernel functions (11.4.2.4)

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Should the 1D kernels, given by Eqs. (11.34)-(11.36), be expressed as functions of $x/\Delta x$ as in Peskin's paper? Although it is commonly assumed that $\Delta x = 1$ in LBM, would it be more appropriate to represent the kernels as functions of $x/\Delta x$, which also agrees well with the $x$-axis in Fig. 11.11?