Algorithm for

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. 

Clearly, in designs different from those in Figs. 16.13 and 16.14 when streams are split to satisfy the CP inequality, this might create a problem with the number of streams at the pinch such that Eqs. (16.3) and (16.4) are no longer satisfied. This would then require further stream splits to satisfy the stream number criterion. Figure 16.15 presents algorithms for the overall approach. ... 

Algorithm for Heat Exchanger Capital Cost Target... 

As in the case of infrared, progress in computing and the development of powerful algorithms for Fourier transforms has made the development of pulse NMR possible. 

The evaluation of the proposed algorithms for the classification of ultrasonic resonance spectra clearly indicated that an adequate classifier can in many practical cases be obtained by... 

A. Rougee, K.M. Hanson, and D. Saint-Felix Comparison of 3D Tomographic Algorithms for Vascular Reconstruction. SPIE Vol. 914 Medical Imaging II, 1988, pp. 397-405. 

The adaptive estimation of the pseudo-inverse parameters a n) consists of the blocks C and E (Fig. 1) if the transformed noise ( ) has unknown properties. Bloek C performes the restoration of the posterior PDD function w a,n) from the data a (n) + (n). It includes methods and algorithms for the PDD function restoration from empirical data [8] which are based on empirical averaging. Beeause the noise is assumed to be a stationary process with zero mean value and the image parameters are constant, the PDD function w(a,n) converges, at least, to the real distribution. The posterior PDD funetion is used to built a back loop to block B and as a direct input for the estimator E. For the given estimation criteria f(a,d) an optimal estimation a (n) can be found from the expression... 

Nielsen, S.A. Borum, K.K. and Gundtoft, H.E (1995). Verifying an ultrasonic reconstruction algorithm for non-destructive tomography. Proc. of 1st World Congress on Ultrasonics, Berlin, Vol. 1, 446-450. 

Grangeat P. Description of a 3-D reconstruction algorithm for diverging X-ray beam., Radiol. Soc. North. America Conf Proc., Nov.1985. 

Simulations about Eddy Current Distributions and Crack Detection Algorithms for a SQUID Based NDE System. 

A. Mohammad-Djafari H. Carfantan and. 1. Idier. A single site update algorithm for non linear diffraction tomography. ICASSP, 4, 1997. 

THE ALGORITHM FOR SIZING OF CRACKS WITH COMPLEX CROSS-SECTIONS... 

The algorithm for sizing of eraeks with complex cross-sections and unknown shapes based on the method was used in for sizing of cracks oriented perpendicularly to the applied field. This algoritlim is presented in Fig.3. In this paper, the same algorithm is applied readily to sizing of cracks with non-perpendicular orientation with respect to the applied field. 

Fig.3 The algorithm for sizing of cracks with complex cross-sections and unknown shapes. The five minimisation procedures are numbered consecutively.

Table 1. Computed results from the algorithm for sizing of the cracks from Fig.4a, Fig.4b, and Fig.4c and orientation angles d)=0°, 0=30° and 0=45°, and true values of the eorresponding crack parameters.

The results of both experiments showed that the analysis in the frequency domain provides new technological possibilities of testing characteristics of austenitic steels. Using known phase-frequency characteristics of structural noises it is possible to construct algorithms for separation of useful signal from the defect, even through amplitude values of noise and signal are close in value. 

Bennett C H 1977 Molecular dynamics and transition state theory the simulation of infrequent events Algorithms for Chemical Computation (ACS Symposium Series No 46) ed R E Christofferson (Washington, DC American Chemical Society)... 

Alexander M H and Manolopoulos D E 1987 A stable linear reference potential algorithm for solution of the quantum close-coupled equations in molecular scattering theory J. Chem. Phys. 86 2044-50... 

Doolittle L R 1986 A semiautomatic algorithm for Rutherford backscattering analysis Nucl. Instrum. Methods B 15 227... 

Olsen J, Roes B, J0rgensen P and Jensen H J Aa 1988 Determinant based eonfiguration interaetion algorithms for eomplete and restrieted eonfiguration interaetion spaees J. Chem. Phys. 89 2185-92... 

Nesbet, R K 1965 Algorithm for diagonalization of large matriees J. Chem. Rhys. 43 311-12... 

Watson S C and Carter E A 2000 Linear-scaling parallel algorithms for the first principles treatment of metals Comp. Pbys. Common. 128 67-92... 

The Boltzmaim weight appears implicitly in the way the states are chosen. The fomi of the above equation is like a time average as calculated in MD. The MC method involves designing a stochastic algorithm for stepping from one state of the system to the next, generating a trajectory. This will take the fomi of a Markov chain, specified by transition probabilities which are independent of the prior history of the system. 

Andersen H C 1983 RATTLE a velocity version of the SHAKE algorithm for molecular dynamics calculations J. Comput. Phys. 52 24-34... 

Perram J W, Petersen H G and DeLeeuw S W 1988 An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles Moi Phys. 65 875-93... 

Greengard L and Rokhlin V 1987 A fast algorithm for particle simulations J. Comput. Phys. 73 325—48... 

Tuckerman M, Berne B J, Martyna G J and Klein M L 1993 Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals J. Chem. Phys. 99 2796-808... 

Heermann D W and Burkitt A N 1995 Parallel algorithms for statistical physics problems The Monte Carlo Method In Condensed Matter Physios vol 71 Toplos In Applied Physios ed K Binder (Berlin Springer) pp 53-74... 

Neuhauser D and Rabitz H 1993 Paradigms and algorithms for controlling molecular motion Acc. Chem. Res. 26 496... 

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