Dependent matrix

S. Olive, U. Grafe, I. Steinbach. The modelling of Ostwald-ripening during non-isothermal heat treatments resulting in temperature dependent matrix solubihty of the precipitate forming elements a further development of the LSW-theory. Comput Mater Sci 7. 94, 1996. 

Xu, X. Mei, H. Wang, S. Zhou, Q. Wang, G. et ah A study of common discovery dosing formulation components and their potential for causing time-dependent matrix effects in high-performance liquid chromatography tandem mass... 

An alternative to quantitative analysis by ICP-MS is semiquantitative analysis, which is generally considered as a rapid multielement survey tool with accuracies in the range 30-50%. Semiquantitative analysis is based on the use of a predefined response table for all the elements and a computer program that can interpret the mass spectrum and correct spectral Interferences. This approach has been successfully applied to different types of samples. The software developed to perform semiquantitative analysis has evolved in parallel with the instrumentation and, today, accuracy values better than 10% have been reported by several authors, even competing with typical ones obtained by quantitative analysis. The development of a semiquantitative procedure for multielemental analysis with ICP-MS requires the evaluation of the molar response curve in the ICP-MS system (variation of sensitivity as a function of the mass of the measured isotope) [17]. Additionally, in the development of a reliable semiquantitative method, some mathematical approaches should be employed in order to estimate the ionisation conditions in the plasma, its use to correct for ionisation degrees and the correction of mass-dependent matrix interferences. 

Exercise. Let A(t) be a time-dependent matrix. Write explicitly the first five terms of... 

Using these coordinate values we may now evaluate the matrix elements of Eq. (14.12) by substituting for the dipole moments the dipole matrix elements between the initial and final states. This procedure yields explicitly time dependent matrix elements VAB(r). It is particularly interesting to consider the (0,0) resonances, for two reasons. First, the (0,0) resonances have no further splitting due to the spin orbit interaction and are therefore good candidates for detailed experimental study. Second, since these resonances only involve the matrix... 

C) Subspaces, Linear (In)dependence, Matrix Inverse and Bases... 

The tunneling Hamiltonian includes rr-dependent matrix elements, considered in linear approximation... 

Consider now a single-level molecule (a = 0) and extend our system, including two additional states from the left (a = l) and right (a = r) sides of a molecule, which are coupled to the central state through rr-dependent matrix elements, and to the leads in a usual way through C l(r)- Then the Hamiltonian is of linear electron-vibron type... 

The direct (Kronecker) product of the SU (2) matrices representing the q- and p-pararotations acts in this space with the notion that the q-dependent matrix eq. (3.48) acts on the states of the first particle and the p-dependent one on the states of the second particle in the product state. Then we form linear combinations of the above states, which correspond to specific values of the total spin and desired spatial symmetry. The combination which corresponds to the zero total spin of two particles transforms as a scalar i.e. (singlet) s-function. Those which correspond to the total spin equal to unity form the basis in the three-dimensional (triplet) space of />functions. The coordinate (x-, y-, and z-) functions are obtained as the following combinations of the states with the definite spin projections (the above product states) ... 

Ross, B.S., and Hieftje, G.M. (1991) Alteration of the ion-optic lens configuration to eliminate mass-dependent matrix interference effects in inductively coupled plasma-mass spectrometry Spectrochim. Acta 46B, 1263-1273. 

The simplest approach to the book-keeping problem of calculating all the nuclear spin-dependent matrix elements is first to evaluate all the terms in the primitive basis set, leaving only J, I and F as variables. We therefore construct the following 6x6 matrix, using the functions listed in (8.353). The rotational levels are widely spaced compared with the hyperfine terms, so that we also confine attention to matrix elements diagonal in J. The required 6x6 matrix is as follows. 

X, Xn, H. Mei, S. Wang, Q. Zhon, G. Wang, L. Broske, A. Pena, and W. A. Korfmacher, A stndy of common discovery dosing formnlation components and their potential for cansing time-dependent matrix effects in high-performance liqnid chromatography tandem mass spectrometry assays. Rapid Commun. Mass Spectrom. 19 (2005), 2643-2650. 

In all cases the X[Pg.133]

Main Distance-Dependent Matrix 4D Molecular Similarity Analysis... 

Then, the Main Distance-Dependent Matrix (MDDM), for each pair of Interaction Pharmacophore Elements (IPEs) is estimated. The IPEs are specific and independent groups representing molecule functionality (Table Numerical Entriesl). The seventh IPE type (HS) encodes information about the overall molecular shape since all the nonhydrogen atoms are considered. From the MDDM estimated for the HS-HS pair, a similarity measure with respect to the whole molecule is obtained. 

The GF EA and IP theories were derived from consideration of the following time-dependent matrix elements ... 

It should be noted that Eq. (26) does not contain an -dependent matrix element on its left-hand side as do the MPn EOM equations (Eq. (14)) or the equivalent GE equations. This is because the EOM-CC equations are usually not subjected to the operator-space partitioning that the GF and MPn-based EOM theories commonly employ. It should also be noted that the operators appearing on the left-hand side of Eq. (26) produce non-Hermitian matrices. As a result, there arise non-orthogonal left- and right-eigenvectors in solving Eq. (26). As discussed in Refs. [34,35], it is important to compute both sets of eigenvectors if one wishes to compute, e.g. photo-electron intensities. 

This sort of interference effect (resulting in an e//-dependent matrix element in the symmetrized basis) can occur via HROT only between two A < 1 0 = levels. 

The pressure- and PM loading-dependence matrix of Table 5a reveals several trends ... 

Moreover, when constructing the geometry-dependent matrix D one is not restricted to consider only atoms. One can introdnce any number of geometric points along chemical bond and in this way obtain sequences... 

G. Morscher, Stress-dependent Matrix Cracking in 2D Woven SiC-fiber Reinforced Melt-infiltrated Sic Matrix Composites, Compos. ScL Techno ., 64 [9] I311-9 (2004). 

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