Formal representation

Despite having a simple physical interpretation, it is clear that quantum states generally have very complex formal representations. 

Is this vision effectively and correctly transformed into design criteria for the formal representation of a curriculum (are the criteria valid, precise and complete transformation 1) ... 

Cheung, J. T.-Y., Representation and extraction of trends from process data. Sc.D. Thesis, Massachusetts Institute of Technology, Dept. Chem. Eng., Cambridge, MA (1992). Cheung, J. T.-Y., and Stephanopoulos, G., Representation of process trends. Part I. A formal representation framework. Comput. Chem. Eng. 14, 495-510 (1990). 

The final aim is to construct a formalized representation of the decision process. Decision trees and structured system analysis are possibilities. Some types of expert systems can derive their own rules from examples. These are described in Chapters 18 and 33. 

The latent information of the measuring sample is transferred via an energetic carrier into analytical information which is manifested by signals. Their parameters correspond to the coding (encoding) process in information systems. For the formal representation of the analytical coding the following analytical quantities are introduced ... 

In all the ligno-celluloslc boards, the logarithm of the rate of Isothermal heat evolution decreased approximately linearly with reaction time. A formal representation according to a first order reaction type is ... 

Figure 3. The modeling relation, as adapted from J. L. Casti [90] The encoding operation provides the link between a natural system (real world) and its formal representation (mathematical world). A set of rules and computational methods allows to infer properties (theorems) of the formal system. Using a decoding relation, we can interpret those theorems in terms of the behavior of the natural system. In this sense, the inferred properties of the formal system become predictions about the natural system, allowing us to verify the consistency of the encoding. The modeling process needs to provide the appropriate encoding/decoding relations that translate back and forth between thereal world and the mathematical world.

Certainly, Eq. (16) is only a formalized representation of the function X(e) representing in a simplified form the non-constancy of viscosity (see Sect. 2.2.6 for details) however, it provides a possibility to assess the tendency of extension wedge form variation. According to estimations 100at X / const, the wedge deviates from the exponential one, it becomes more sharp for X increasing with e and more smooth for decreasing viscosity (see Fig. 25). 

A Formal Representation of Chemical Genomics Problems 2.1. Pharmacogenomics of Gene Expression... 

This formal representation helps to provide a framework for investigating two questions ... 

We shall now start with the formal representation of the solution of equations (4.2), which, first of all, is conveniently written in the form... 

Figure 7. Formal representation of the interaction of an external EM field with the dissipative subsystem in the Frohlich vibrational model (n is the nonlinear coupling parameter (Equation 17) the other quantities have the same meaning as...

The general model developed for sweet and bitter compounds leads to a sweet-bitter receptor, which can be given formal representation as a hydrophobic pocket with a bipolar system (Fig. 

Fig. 3.2. Formal representation of mechanisms of size change in particulate processes [6].

All the foregoing information allows one to state that the formation of C-dihydrotoxiferine I from hemidihydrotoxiferine I (LXVIII) in acetic acid involves the condensation of two molecules of LXVIII, with the loss of two molecules of water and with the disappearance of the aldehyde and >Na—H functions. Evidence for such a condensation is provided by the fact that a mixture of equivalent amounts of norhemidihydrotoxiferine I and hemidihydrotoxiferine I in acetic acid gives a reaction product containing nordihydrotoxiferine I, its mono-Ab-metho salt, and C-dihydrotoxiferine I (86). The formation of toxiferine I from hemitoxiferine I (LXVII) must be strictly analogous, and the only structures which can be written to accommodate the above evidence are LXXI (R = H) or LXXII (R = H) for C-dihydrotoxiferine I and LXXI (R = OH) or LXXII (R = OH) for toxiferine I. Structure LXXIII can be written as a formal representation of the intermediate in both condensation and fission reactions. Of these alternatives, the structures LXXI were at first preferred (86, 31), mainly because of the striking similarity between the UV-spectra of the two alkaloids and those of simple a-methyleneindolines. The above chemical evidence allows of no distinction between formulas LXXI and LXXII. 

Figure 16-27 Two extreme formal representations of the bonding of a 1,3-butadiene group to a metal atom (a) implies that there are two more or less independent monoolefin metal interactions (b) depicts cr bonds to C-l and C-4 coupled with a monoolefin metal interaction to C-2 and C-3.

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