The transient nonlinear free surface problem of water waves is formulated assuming the potential theory and a higher-order boundary element method (HOBEM) is used to discretize Laplace's equation.
Horizontal and vertical diffusions are formulated assuming the random walk model, in which the probability density of the displacements is Gaussian distribution with (varGamma sqrt {2K_{text{h}} delta t}) for horizontal diffusion with (K_{text{h}}) = 4.0 × 103 m2/s and (varGamma sqrt {2K_{{{text{v}} }} delta t^{prime } }) for vertical diffusion.
Large efforts have been made in improving algorithm efficiency, which have resulted in an increasingly rapid convergence to the optimal solution and in reduced calculation time; robust algorithm have also been formulated, assuming stochastic behaviour for energy loads and prices.
However, as shown in the third column (Eqs. 3.2 8.2), all the double sampling estimators except PPS (Eq. 7.1) may be formulated assuming that the first-phase sample is a simple random sample that is smaller, usually much smaller, than the whole population; in these cases, the population size (N) is not necessarily known.
Equation 1 in the present study was formulated assuming that p t, the probability of entering first treatment, was independent of the era when a person's first heroin use began.
The stability conditions will be formulated assuming that we know the Cauchy solution (fundamental solution) of the unperturbed system.
In Section 2.1, the input output relationship of a multi-cell, SU-MIMO, and MU-MIMO DAS is formulated, assuming linear precoding and equalization, and the post-equalization SINR is derived.
A quantity for tumour response was formulated assuming that an effective treatment may decrease the cell proliferation rate (cytostatic) and/or increase the cell loss rate (cytotoxic) of the tumour.
These models are typically formulated assuming that the microstructure of the polycrystal is associated with a representation of microscopic crystals whose individual responses, on average, determine the macroscopic response of the polycrystal.
Unlike previous models that were formulated by assuming that the active materials and electrolyte are perfectly balanced according to the electrochemical reaction, the present model takes account of the fraction of the reaction products (Li2O2 and Li2O), the utilization of the onboard lithium metal, the utilization of the void volume of the porous cathode, and the onboard excess electrolyte.
