Inhomogeneous simultaneous

The equations just derived are inhomogeneous simultaneous linear equations in 3N unknowns, the three cartesian components of each relative velocity V — ft . As such, they have the solution... 

This is a set of linear inhomogeneous simultaneous equations in m and b. We write them in the form... 

To consider the possibility of automatic convergence, suppose first that it is desired to solve a set of inhomogeneous simultaneous equations... 

Cramer s rule is a systematic method for solving linear inhomogeneous simultaneous equations. Consider the set of two linear inhomogeneous equations ... 

T.M. Habashy, W.C. Chew, and E.Y. Chow, Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab, Radio Sci., 1986,21,... 

Pullerits T, Visscher K J, Hess S, Sundstrom V, Freiberg A, Timpmann K and Van Grondelle R 1994 Energy-transfer in the inhomogeneously broadened core antenna of purple bacteria-a simultaneous fit of low-intensity picosecond absorption and fluorescence kinetics Biophys. J. 66 236-48... 

In reality, the adsorption of gas particles on a real surface can be simultaneously influenced by inhomogeneity of the surface and interaction between absorbed particles. Presumably, it is the nature of a specific absorbate-adsorbent pair that controls the major mechanism in each case. 

Despite the fact that the structure of the interface between a metal and an electrolyte solution has been the subject of numerous experimental and theoretical studies since the early days of physical chemistry," our understanding of this important system is still incomplete. One problem has been the unavailability (until recently) of experimental data that can provide direct structural information at the interface. For example, despite the fact that much is known about the structure of the ion s solvation shell from experimental and theoretical studies in bulk electrolyte solutions, " information about the structure of the adsorbed ion solvation shell has been mainly inferred from the measured capacity of the interface. The interface between a metal and an electrolyte solution is also very complex. One needs to consider simultaneously the electronic structure of the metal and the molecular structure of the water and the solvated ions in the inhomogeneous surface region. The availability of more direct experimental information through methods that are sensitive to the microscopic... 

The resolution of an FPD is theoretically limited by the number of channels (512-2048). In practice, it is even less because the image suffers some broadening as it passes from the first MCP to the photodiode array (Fig. 4.63). Therefore, instruments with FPD can normally be switched from FPD to SEM detection, e.g., by vertical electrostatic deflection of the ion beam (Finnigan MAT900). Furthermore, quadrupole lenses or an inhomogeneous ESA behind the magnet are employed to achieve variable dispersion, i.e., to zoom the m/z range of simultaneous... 

When <0, the bifurcation diagram is as in Fig. 13. There exists a subcritical region in which three stable steady-state solutions may coexist simultaneously the thermodynamic branch and two inhomogeneous solutions. It must be pointed out that the latter are necessarily located at a finite distance from the thermodynamic branch. As a result, their evaluation cannot be performed by the methods described here. The existence of these solutions is, however, ensured by the fact that in the limit B->0, only the thermodynamic solution exists whereas for B Bc it can be shown that the amplitude of all steady-state solutions remains bounded. 

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