Kramer’s equation

Kramer s Equation—Kramer (1935) made a series of measurements of flume traction in which the important variables (including particle-size) were carefully controlled. Kramer s equation of the critical tractive force was as follows ... 

Enzyme Kinetics. The change in the number-average molecular weight of gelatin with time was determined as follows. Measurements of viscosity at known concentrations were extrapolated to infinite dilution to obtain the intrinsic viscosity r from Huggins and Kramer s equations,... 

The theoretical solution for a viscoelastic fluid in dynamic squeezing flow is based on the equations of Kramer (8). Kramer s equations for a viscoelastic fluid in small amplitude sinusoidal squeezing flow are ... 

The background continuum of the fluorescence spectrum can be modeled by fitting a curve derived from Kramer s equation, which has the general form ... 

Barcilon, V, Singular Perturbation Analysis of the Fokker-Planck Equation Kramer s Underdamped Problem, SIAM Journal of Applied Mathematics 56, 446, 1996. 

Making use of Kramer s rule, we should identify (derive ) the system characteristic equation ... 

An example is the S = 2 spectrum from a mononuclear high-spin Fe site in the protein desulfoferrodoxin given in Figure 5.14. A relatively sharp effective feature is observed from within the ms = 2 non-Kramer s doublet, but the z-value is shifted from the axial g = 8 value (cf. Equation 5.39) to a higher g-value (i.e., lower field). Also, an extremely broad feature from the ms = 1 doublet, expected at gz > gN = 4, extends over the whole field range of the figure. 

Christov, S. G. Two types of Kramers rate equations for reactions in condensed media, IntJ.Quantum Chem., 52(1994), 1219-1228... 

The modern resurgence in interest in capillary wave hydrodynamics, which started in the early 1950s, centers around the damping effects and the presence of a viscoelastic film between two fluids [37,49-56]. All are more or less similar, in the assumptions invoked and the hydrodynamic theory used. The Lucassen-Reynders-Lucassen [55] and Kramer s [56] dispersion equations are essentially identical except Kramer ignores the gravity wave at the outset which is consistent with the wave vector range often used experimentally, and this is seen in Fig. 3. 

The driving force behind the liquid transport has been determined by Kramer and Bubeck to be capillary pressure [17]. The velocity of liquid flow V is expressed by Darcy s equation... 

In the FKKE proposed by Barkai and Silbey [30] in contrast, the memory or fractional derivative term is supposed to act only on the dissipative part of the normal Klein-Kramers operator, so that Barkai and Silbey s equation [where, however, rotational quantities (angle [Pg.373]

Equation 11.16 forms a system of M linear nonhomogeneous equations for the M unknowns a L=, m and can be solved by using any of the standard methods (e.g., Kramer s rule). In matrix notation, the solution is... 

Solving a system of n equations analytically is generally cumbersome and one may have to use Kramer s rule or analyze an inverse of H instead, see Bernstein and Federgruen (2000) for an example. The only way to avoid this... 

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