Reciprocity method

In evaluation of kinetic parameters, the double reciprocal method is used for linearisation of the Michaelis-Menten equation (5.7.3). 

The purpose of the second edition is to meet the need for a ready-to-use text on the validation of aseptic pharmaceutical production and to provide general information and guidelines. It is a compilation of various theories, sterilization variables, and engineering and microbial studies that can be used independently or in combination to validate equipment and processes. The concepts and methods presented in this edition are not intended to serve as a final rule. Reciprocal methods for achieving this purpose exist and should also be reviewed and consulted, if applicable. 

B.A. Davis, P.J. Gramann, J.C. Maetzig, and T.A. Osswald. The dual-reciprocity method for heat transfer in polymer processing. Engineering Analysis withBoundary Elements, 13 249-261, 1994. 

W.F. Florez. Multi-domain dual reciprocity method for the solution of nonlinear flow problems. PhD thesis, University of Wales, Wessex Institute of Technology, Southampton, 2000. 

Molecular recognitions of amino acids. The binding constant is a measure of recognition interactions of different amino acids with metallohematoporphyrin. It can be estimated by Benesi-Hildebrand equation (the double-reciprocal method) ... 

This equation shows that a plot of R versus R/[S] should result in a line that has a slope of — Ki and an intercept of fe2[E],. A plot of this type is known as an Eadie—Hofstee plot, and it is illustrated graphically in Figure 6.7. The methods of data analysis that are based on Eqs. (6.29) and (6.33) are called single reciprocal methods. 

BEM) or using dual reciprocity method (which requires a set of additional collocation points defined in the solution domain). 

The responses in Fig. 3.8 are calibrated results by two methods of the sensor calibration. One is a calibration method by NIST, as illustrated in Fig. 3.10 (Breckenridge 1982). A large steel block of 90 cm diameter and 43 cm deep was employed. As a step-function impulse, a glass capillary source was employed, and elastic waves were detected by a capacitive transducer and by a sensor under test. The calibration curve was obtained as a ratio of the response of the sensor to that of the eapacitive transducer. The capacitive transducer (sensor) could record a Lamb s solution due to surface pulse as discussed in Chapter 7. It is reasonably assumed that the capacitive transducer detect the vertical displacement at the surface due to a step-function force. The other is known as a reciprocity method, which Hatano and Watanabe (Hatano Watanabe 1997) suggested to use, and confirmed an agreement with the NIST methods. As seen in Fig. 3.8, it is demonstrated that both method can provide similar calibration curves. 

Hatano and Moro [1976] suggested the use of a reciprocity method, where sensors are coupled onto a steel plate. This approach uses Rayleigh waves. Other methods described in the literature suggest using a laser-vibrometer to measure the displacement of the free surface of the sensor, or a network analyzer (Weiler and Grosse 1995 Grosse 1996). 

The BEM has been applied in scanning electrochemical microscopy applications by Fisher and Denuault [169] to examine the influence of probe and substrate surface topography. In addition, time-dependent phenomena have been assessed in oil droplets [170, 171] and a range of microelectrode geometries using the dual reciprocity method (DRM) [172] closely related to the BEM [173]. 

A way of eliminating the domain integral in Eq. 8.81 is based on the well-known idea of combining a particular solution to a complementary solution of a homogeneous problem. This idea was discussed in Buzbee et al. (1971), who named the method the capacitance matrix method. Brebbia and Nardini (1986) have applied the concept to boundary element method and called it the dual reciprocity method (DRM). Henry and Banerjee (1988) have also proposed a related method in the name of the particular integral method. Now, let us consider a particular solution T that satisfies... 

In practice, illuminating material samples over the entire hemisphere is the reciprocal method for determining transmittance for a given FOV and any scattering profile. Therefore, the light source and photodetector in Fig. 2 can be reversed in order to construct a diffuse/normal (d/0°) measuring instrument (Fig. 4). 

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