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 simplified to The problem is simplified to a two-dimensional scattering problem, and the existence and uniqueness of solutions are discussed by an integral equation approach. As the order is 1, the result here is simplified to that of first order differential equation. A theoretical model, sufficiently simplified to allow analytical solution, is developed and evaluated to provide a first approximation of the potential and current distributions in the electrolyte and steel band. Methods for the determination of dipole moments and Kerr constants in solution can be simplified to a considerable extent for those compounds for which the additivity scheme was applied to calculate the molar volumes. The driving force acting on the pile-top is simplified to a triangular impact force. For isomers, the equation is simplified to a two-parameter equation and the correlations between retention indices, total solubility parameters and molar volume are excellent. The second advantage of it is using dual representation, of the target's facet surface, in which the illuminated part is treated as bicubic patches for RCS calculation, and is simplified to flat facet when ray tracing is done. When the system is designed for uniformity coefficient equal or more than 70%, the water application in the field can be expressed as a normal distribution and further simplified to a linear distribution. These theories can be easily simplified to account for plates, cylinders, beams, etc. However, by using difference measure, the BSS problem is furthermore simplified to a standard symmetric eigenproblem. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems. The result will be simplified to the boundary element method of dynamic problem. Under some certain assumptions, the physical model of the air combustion system was simplified to a laminar flame system. The interaction between the spins and their surroundings is described by the usual spin-Hamiltonian which is, however, simplified to a spin 1/2 particle (instead of the triplet state). The gravitational interaction is treated perturbatively and by choosing an appropriate orthonormal gauge the equations of motion are simplified to a large extent. However, the objective function is usually simplified to represent the weight, disregarding the fabrication and erection costs of the structure. The theory is simplified to yield a Boussinesq-like set of governing equations. In case the signal only contains power-law noise, the MLE computations can be simplified to a $${\mathcal{O}}(N\log N)$$ process where N is the number of observations. Based on the local similarity of the flow field the two-dimensional Navier-Stokes equations are simplified to a one-dimensional approximation for the stagnation streamline. 114, 711-717 (1969)] has been simplified to eliminate centrifugation and transfer steps and both the selectivity and the sensitivity have been increased.

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