Matrices partitioning

IC Information content of the distance matrix partitioned by frequency of occurrences of... 

However, Olgin employed a somewhat unwieldy matrix partition method to locate the surplus value term in the output multiplier matrix. An alternative derivation is suggested by substituting (A2.4) into (A2.1) such that... 

Di Muccio A, Ausili A, Dommarco R, et al. 1991. Solid-matrix partition for separation of organochlorine pesticide residues from fatty materials. J Chromatog 552 241-247. 

Philpotts A. R. (1979). Silicate immiscibility in tholeiitic basalts. J. Petrol, 20 99-118. Philpotts I A. and Schnetzler C. C. (1970). Phenocryst-matrix partition coefficients for K, Rb,... 

In flavor analysis, the most frequent use of volatile traps is in analyzing the flavor compounds in foods using purge-and-trap or dynamic headspace, followed by GC-MS or GCO. Additionally, the traps can be used to measure static headspace and air-matrix partition coefficients where air is pushed out of an equilibrated cell containing the sample onto a volatile trap (Chaintreau et al., 1995). Volatile traps have been also used for flavor release measurements during eating (Linforth and Taylor, 1993) or simulated eating (Roberts and Acree, 1995). 

In the simplest form, an aliquot of an aqueous solution is shaken with an equal volume of an immiscible organic solvent. This is an useful approach when the analyte of interest partitions itself in one layer and the interfering matrix partitions into the second layer. Because this rarely occurs, several physical and chemical factors can be changed to alter the partitioning. One approach is to add sodium chloride to the aqueous solvent to produce a saturated solution. 

Table 2.4. Crystal/matrix partition coefficients of noble gases in basaltic melts...

Philpotts, J. A., Schnetzler, C. C. Phenocryst-matrix partition coefficients forK, Rb, Sr and Ba with application to anorthosite and basalt genesis. Geochim. et Cosmochim. 

Liebman, M. N. (1982). Correlation of structure and function in biologically active small molecules and macromolecules by distance matrix partitioning. Griffin, J. F. and Duax, W. L. (eds). Mol. Struct. Biol. Act. Proc. Meet., Elsevier New York, pp. 193-212. [156]... 

C. Amovilli and R. McWeeny, A matrix partitioning approach to the calculation of intermolecular potentials. General theory and some examples, Cbem. Phys., 140 (1990) 343-361. 

Although SPME is mainly an equilibrium extraction technique, it has the ability to provide thorough extraction. If the coating/matrix partition coefficient, Ai,., is very large (i.e. K,J, F), the amount of analyte desorbed by the coating will be... 

This is an expression giving the eigenvalue of the original equation and the component of the vector corresponding to the first block of the full vector. Substitution of u, determined from Eq. (38), into Eq. (37) gives the unnormalized full vector. This matrix partitioning approach applied to the... 

The matrix (B —CM" C ) is called the partitioned orbital Hessian matrix because of its connection to matrix partitioning theory. While the matrix B is the matrix of second derivatives with respect to orbital rotations when the CSF mixing coefficients are held constant, the partitioned orbital Hessian matrix is the matrix of second derivatives with respect to orbital rotations when the CSF eoefficients relax optimally with the orbital changes. The matrix of Eq. (152), consisting of the partitioned orbital Hessian matrix and the orbital gradient vector, is called the augmented partitioned orbital Hessian matrix. 

The relation between the wavefunction corrections determined by the WSCI and PSCI methods and the corresponding Newton-Raphson methods may be determined using the matrix partitioning approach. For example, the solution to the PCI matrix eigenvalue equation is equivalent to the solution of the linear equation... 

This equation expresses the fact that the extended Green s function Q u>) is the projection of an operator resolvent onto a set of )U-orthonormal states [10]. Note that the matrix is hermitian if the Hamiltonian H of the many-body system is hermitian (which is assumed throughout this paper). By matrix partitioning we can write for the inverse of the Green s function... 

In the derivation of this term the solvent distribution is assumed to be uniform (but it is possible to extend the method to non uniform distributions, to describe e.g. dielectric saturation effects for cations [19], and electrostriction effects for supercritical liquids [20, 21]), and the response function is modeled in terms of a matrix partitioning approach to the calculation of intermolecular potentials [22]. With the aid of a formal re-elaboration of the whole model, and by introducing a few reasonable approximations, the related matrix is reduced to the following form ... 

The Dimension matrix can be partitioned into two matrices, one being a square matrix, that is, a matrix with the same number of rows as columns the other being the bulk, or remaining matrix elements. We define the square matrix as the Rank matrix and the remaining matrix as the Bulk matrix. Partitioning the above Dimension matrix gives... 

Enzyme Commission No. Enzyme Tissue Membrane/ matrix partition... 

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