Indeterminacies

We might also mention that, for this rule, the region of color-indeterminacy, somewhat arbitrarily defined as the set of sites having. 4 < W <. 6, takes on a sirail2urly regular band-pattern. 

The mass transfer term in this equation is indeterminate since ki 00 and a — Ug 0. The indeterminacy is overcome by using Equation (11.5). Thus,... 

There is an indeterminacy in the term oligotroph, and the dilemma is exacerbated by the fact that it may be impossible to isolate obligate oligotrophs by established procedures. The application of DNA probes should, however, contribute to an understanding of the role of these noncultivable organisms. Oligotrophic bacteria in the marine environment are able to utilize low substrate concentrations, and they may be important in pristine environments. 

It was suggested [35,45] that the indeterminacy of the CSchE could be removed by replacing in it the 3- and the A-RDM s by their corresponding approximations evaluated within the SRHformalism. After this replacement is performed, the matrix equation can be solved with the help of relation (10) and... 

In the PARAF AC model, the three loading matrices A, B, C are not necessarily orthogonal [56]. The solution of the PARAF AC model, however, is unique and does not suffer from the indeterminacy that arises in principal components and factor analysis. 

One possible solution is to obtain new experimental data, which is independent of co/pH curves. The zeta potential is of course a possibility, but it suffers from the intrinsic indeterminacy of the exact location in the double layer where it occurs. Another possibility is the surface potential, Vo, which will be defined below. Variations of Vo can be measured by using electrolyte/insulator/semiconductor structures. It has been shown by Bousse et al. (14) that the Vo/pH characteristics are determined mainly by the number of charged but uncomplexed surface sites, and are insensitive to complex-ation. This means that combined consideration of tro/pH and Vo/pH characteristics should lead to a more complete and reliable determination of model parameters. 

Heisenberg s principle of uncertainty (or indeterminacy) was based in the Dirac-Jordan transformation theory (see Kragh, Dirac, 44) P. A. M. Dirac, "The Physical Interpretation of the Quantum Dynamics,"... 

Whereas many early-twentieth-century physicists were inclined to regard conventionalism, complementarity, and indeterminacy as concessions of failure in their traditional philosophical enterprise, chemists were not surprised that a simple, "logical" account of the behavior of electrons and atoms, like that of molecules and people, often gives way to the inconsistencies and uncertainties of empiricism. This is a point of view they taught physicists to accept, among them, Richard Feynman ... 

At Oak Ridge, the focus was to develop specific-sequence DNA to improve the diffraction quality of NCP crystals. The positioning of the DNA on the histone core has to be precise so that all the NCPs are identical. A project was undertaken to understand the DNA sequence effects on nucleosome phasing [25]. Second, a DNA palindrome was developed to extend the two-fold symmetry of the histone core to the DNA. The objective was to eliminate the two-fold disorder caused by the indeterminacy of packing of an asymmetric particle into the crystal lattice. A palindrome based on one-half of the primary candidate sequence was constructed and methods were developed to produce the palindrome fragment in large quantities for reconstitution of NCPs. 

VI. An Exact Formal Solution to the Contracted Schrodinger Equation s Indeterminacy... 

The dependence of the 2-CSE on the 3- and 4-RDMs renders indeterminate this equation [18, 52]. This is the reason why the interest in this equation was initially lost. However, after the encouraging results obtained in the construction of the 2-RDM in terms of the 1-RDM [19], the possibility arose of constmcting good approximations of the high-order RDMs in terms of the lower-order ones. This permitted one to remove the indeterminacy and opened the way to build an iterative method for solving the 2-CSE. 

As has been mentioned earlier, the indeterminacy of the 2-CSE may be removed by approximating the 3- and 4-RDMs in terms of the 1- and 2-RDMs. These... 

VI. AN EXACT FORMAL SOLUTION TO THE CONTRACTED SCHRODINGER EQUATION S INDETERMINACY... 

The indeterminacy of the 2-CSE had caused this equation to be overlooked for many years. In 1992 Valdemoro proposed a method to approximate the 2-RDM in terms of the 1-RDM [108], which was extended in order to approximate the 3- and 4-RDMs in terms of the lower-order matrices [46, 47] and in 1994 Colmenero and Valdemoro [48] applied these approximate constructing algorithms to avoid the indeterminacy problem and solve iteratively the 2-CSE. Since then, the smdy of improved constructing algorithms as well as alternative strategies in the iterative procedure have been proposed [1,6, 15, 18, 36, 49-57, 59, 60, 62-65, 68, 70, 71, 79-85, 109-111]. Also, good results of several calculations have been reported [6, 49-52, 55, 56, 68, 70, 88, 109, 111]. 

As can be seen, the 2-CSE depends not only on the 2-RDM but also on the 3- and 4-RDMs. This fact lies at the root of the indeterminacy of this equation [63, 107]. As already mentioned, in the method proposed by Colmenero and Valdemoro [46 8] and in those further proposed by Nakatsuji and Yasuda [49, 51] and by Mazziotti [52, 111], a set of algorithms for approximating the higher-order ROMs in terms of the lower-order ones [46, 47, 108] allows this equation to be solved iteratively until converging to a self-consistent solution. In the approach considered in this work, the spin-adapted 2-CSE has been used. This equation is obtained by coupling the 2-CSE with the second-order contracted spin equation [50]. 

Since diagonal elements of S enter into the expression for rTu, the indeterminacy of 7>(S) introduces a corresponding indeterminacy in T. The constraint 7>(S) = 0 is unaffected by the various rotations and translations of the coordinate systems used in the course of the analysis. 

Remove all indeterminacy that is, the planes should have nonzero intercepts. Find intercepts along three axes of the crystal system. 

In the case of second-order transitions, A F and AS have zero values, and equation (4.3) will have a 0/0 indeterminacy. We can, however, derive analogues of the Clausius-Clapeyron equation for these transitions, such as equation (4.4) ... 

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