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Because of mathematical complexity, however, very few works have been reported for substitutional alloys.
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The ion buffer capacity of heterogeneous (two-phase) systems has been studied relatively well only for the pH buffers (Pfendt 1995; Dougherty et al. 2006), partly because slow reactions make experimental studies difficult, partly because of the mathematical complexity of the theoretical calculations.
These items are essential in the formulation of the boundary element method (BEM); their evaluation has remained a subject of interest because of the mathematical complexity.
However, no analytical results for the SEP, or outage probability have been derived because of the mathematical complexity.
The network method solves problems of great mathematical complexity in a versatile and efficient way.
The very best passages of Hemingway have the mathematical complexity of a fractal: a seemingly simple formula that, in its recurrence, causes slight but crucial changes over time.
However, it is not in a practical form from an engineering perspective because of the appearance of partial derivative terms, which bring unnecessary mathematical complexity and obscure physical interpretation of mechanical boundary conditions in the shell modeling.
Studies of more complex but realistic stress states were based on prebuckling analyses using either membrane theory or linear bending theory because even these involved considerable mathematical complexity.
Traditionally, the mathematical complexity of master Eqn 2 has been avoided by setting ΔCi = 0, so that ΔCB = Δ[HCO3-].
The mathematical complexity of Friedrich's model is such that finding solutions analytically or numerically is, in general, impractical.
Reduction of mathematical model complexity is achievable by different methods [ 2].
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