Divergence, definition

Chemoinfonnatics is a faiily new name for a discipline that, as we shall soon see, has been around for quite a while. Different people sometimes give rather divergent definitions of chemoinfoimatics. Before we discuss these different viewpoints, let us, for the time being, accept a rather broad and general definition ... 

Clearly the different methods described above may give rise to inconsistent measurements by different researchers. Besides the divergent definitions, there is the additional consideration that the criteria are somewhat subjective, are likely to be interpreted differently by different researchers, and their application will vary depending upon the resolution of the anatomical preparation. 

The following example for simplicity refers to a technically important ternary system, namely cellulose solutions in mixtures of the favorable solvent NMMO with the precipitant water. Fibers are formed as thin threads as homogeneous cellulose solutions are sptm into water. Figure 26 shows how experimental data for this ternary mixture compares with the modeling [68] on the basis of (60). On the theoretical side, it is important to take care of the fact that the information concerning the binary subsystems usually differs by a diverging definition of the size of a segment. 

Distillation, azeotropes, 6-177 to 195 Divergence, definition, A-68 to 74 DSC, definition, 12-1 to 4 DTA, definition, 12-1 to 4 Dubnium (element 105), 4-1 to 42,11-56 to 253 Dysprosium see also Elements electrical resistivity, 12-39 to 40 electron configuration, 1-18 to 19 heat capacity, 4-135 history, occurrence, uses, 4-1 to 42 ionization energy, 10-203 to 205 isotopes and their properties, 11-56 to 253 magnetic susceptibility, 4-142 to 147 molten, density, 4-139 to 141... 

Definitions. In addition to showing varying degrees of chemical purity, limestone assumes a number of widely divergent physical forms, including marble, travertine, chalk, calcareous mad, coral, shell, ooHtes, stalagmites, and stalactites. AH these materials are essentially carbonate rocks of the same approximate chemical composition as conventional limestone (2—4). 

One now wonders whether these two phenomena are to be observed also for the whole two-dimensional surface of a crystal non-locking of the crystal surface in spite of lattice periodicity, and divergence of the fluctuation-induced thickening of the interface (or crystal surface), and in consequence the absence of facets. The last seems to contradict experience crystals almost by definition have their charm simply due to the beautifully shining facets which has made them jewelry objects since ancient times. 

By definition, the Laplacian of U represents the divergence of the attraction field, and, correspondingly, its value characterizes the density of masses at same point. Now the following question arises. What does the Laplacian tells us about the behavior of the potential To answer this question we first consider the simplest case, when U depends on one argument, x, Fig. 1.7a. Then, we can represent the derivatives as ... 

In the case where a species has to be identified from an instrumental-analytical record like Fig. 3.8 with the help of a definite signal position, then the information content is determined according to Kullback s divergence measure of information (Kullback [1959] Eckschlager and Stepanek [1985] Eckschlager and Danzer [1994])... 

Given ng and 1(R, p), Eqs. (7.32a, b) can be integrated successively from r = R to a large value of r. By definition Z(R, p) = -y where yis the recombination probability in presence of scavenger. Only for the correct value of ydo the solutions of (7.32a, b) smoothly vanish asymptotically as r—-o° otherwise, they diverge. Thus, the mathematics is reduced to a numerical eigenvalue problem of finding the correct value of I(R, p). 

On the other hand, it is well known that there is a relationship between Lyapunov exponents and the divergence of the vector field deduced from the differential equations describing a dynamical system. This relation provides a test on the numerical values obtained from the simulation algorithm. This relationship is, according to the definition of Lyapunov exponents ... 

No divergences and dependence on the contact parameters Ti 2 remain in the form for r. It shows the transmittance function (at least in the weak-coupling limit) is indeed a well-defined molecular quantity. We can rewrite equation (38), taking into account the definition of 6 (see equation (35)) and the definition of the Chebyshev polynomials of the second kind U (cos 6) — sin[(n +l)0]/sin 6 as... 

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