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We consider the solution of the Korteweg-de Vries (KdV) equationwhere C, A, k, µ, and β are constants. The solution is shown to be uniformly bounded for all small ε, and a formal expansion is constructed for the solution via the method of multiple scales. By using the energy method, we show that for any given number T > 0, the difference between the true solution v(x, t; ε) and the Nth partial sum of the asymptotic series is bounded by ε N +1 multiplied by a constant depending on T and N, for all −∞ < x < ∞, 0 ≤ t ≤ T /ε, and 0 ≤ ε ≤ ε 0 .

Electronic transport properties in an Al cluster are investigated theoretically in this paper. We propose a possible illustration of Coulomb blockade based on variable electrostatic potential (ESP). Density functional theory (DFT) was used to achieve the global minimum structure and wave function for analyzing the ESP and density of states (DOS) of Al 68 in different charged states. Al 68 is able to contain multiple electrons. According to the calculation of systematic energy and surface ESP, respectively, the surface of Al 68 presents a 0-6.33 eV ESP barrier after electron injection, which is 0 eV at first. The probability density of flow of electrons was calculated under onedimensional model with double barriers. Expected results were obtained, containing a nonlinear relationship between J and V and flow density steps. Moreover, an assumption is proposed associated with nonlinear conductance phenomenon of zero-dimensional nanomaterials. Significantly, Al films with different thicknesses were prepared by the low vacuum physical vapor deposition (LVPVD) method, exhibiting novel fluorescent behaviors. In addition, the I-V curve of a 25-nm Al film exhibited two steps at 7 and 27 V, respectively, which meant that the step effect was caused by Coulomb blockade, in accordance with the theoretical calculation.

It is often interest of comparing two pharmacodynamics (PD) profiles in drug development. Currently the common practice is borrowing the bioequivalence (BE) rule in pharmacokinetics analysis for pharmacodynamics comparison in terms of the area under the effect curve (AUEC) of the pharmacodynamics profile. However, this may not be a feasible and sensitive enough approach since the bioequivalence approach is based on the summarized parameter of the pharmacodynamics profile rather than on directly comparison of the whole pharmacodynamics profile. In this paper, a simple but efficient and pragmatic pharmacodynamics comparability index is proposed to evaluate the comparability of pharmacodynamics profiles by comparing the whole pharmacodynamics profiles directly. Different biological products have different variability and the CV% can be in a very large range. The PD comparability index can take account of the reference knowledge into consideration in assessment but the AUEC BE type approach ignores the reference variability. The good properties of the proposed approach are illustrated through simulated data and a real dataset.Citation: Liao JJZ, Li Y, Jiang X (2017) Comparability of Pharmacodynamics Profiles with an Application to a Biosimilar Study. J Biom Biostat 8: 345.