Symbolic representation

The study of chemistry deals essentially with three main aspects the macroscopic approach, the representational/symbolic dimension and the submicroscopic level of thinking (Johnstone, 1991, 2007). This chapter considers the role of the macroscopic component, taking also into account the other two levels. 

Figure 9 A second way to represent the molecular structure of CaTiOj. (a) Common representation (b) stereoscopic representation. Symbols as in Figure 8...

Region Feature Physical representation Symbolism in equivalent circuif... 

Figure 17.2 Traditional representation of impedance data for the Randles circuit presented as Figure 17.1(a) with a as a parameter, a) complex-impedance-plane or Nyquist representation (symbols are used to designate decades of frequency.) b) Bode representation of the magnitude of the impedance and c) Bode representation of the phase angle. (Taken from Orazem et al. ° and reproduced with permission of The Electrochemical Society.)...

Representational symbols, formulae, equations, molarities, tables and graphs... 

It is important that even the variables themselves allow more than one representation. Symbol p stands for pressure and quantifies the force per unit area exerted by the vapor T performs likewise for temperature and determines the direction of heat flow if the system is placed in contact with another. In an intriguing way, both quantities are eqnivalent to differential functions ... 

TABLE 6.5 Summary of the representation symbols in nonlinear molecule point groups. 

The ROSDAL syntax is characterized by a simple coding of a chemical structure using alphanumeric symbols which can easily be learned by a chemist [14]. In the linear structure representation, each atom of the structure is arbitrarily assigned a unique number, except for the hydrogen atoms. Carbon atoms are shown in the notation only by digits. The other types of atoms carry, in addition, their atomic symbol. In order to describe the bonds between atoms, bond symbols are inserted between the atom numbers. Branches are marked and separated from the other parts of the code by commas [15, 16] (Figure 2-9). The ROSDAL linear notation is rmambiguous but not unique. 

To code the configuration of a molecule various methods are described in Section 2.8. In particular, the use of wedge symbols clearly demonstrates the value added if stereodescriptors are included in the chemical structure information. The inclusion of stereochemical information gives a more realistic view of the actual spatial arrangement of the atoms of the molecule imder consideration, and can therefore be regarded as between the 2D (topological) and the 3D representation of a chemical structure. 

A structure descriptor is a mathematical representation of a molecule resulting from a procedure transforming the structural information encoded within a symbolic representation of a molecule. This mathematical representation has to be invariant to the molecule s size and number of atoms, to allow model building with statistical methods and artificial neural networks. 

A structure descriptor is a mathematical representation of a molecule resulting from a procedure transforming the structural information encoded within a symbolic representation of a molecule. 

Shorthand Notation for Electrochemical Cells Although Figure 11.5 provides a useful picture of an electrochemical cell, it does not provide a convenient representation. A more useful representation is a shorthand, or schematic, notation that uses symbols to indicate the different phases present in the electrochemical cell, as well as the composition of each phase. A vertical slash ( ) indicates a phase boundary where a potential develops, and a comma (,) separates species in the same phase, or two phases where no potential develops. Shorthand cell notations begin with the anode and continue to the cathode. The electrochemical cell in Figure 11.5, for example, is described in shorthand notation as... 

In this representation the X indicates the substituent other bonds involve only hydrogens. This formalism also applies to 1,1-disubstituted ethylenes in whicli the substituents are different. With these symbols, the isotactic, syndiotactic, and atactic structures shown in Fig. 1.2 are represented by structures [VI]-[VIII], respectively ... 

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

Figure 6.15 Circuit symbols and electrical representation of a basic triode or power transistor (BJT)...

Fig. 14. Schematic representation of a (5.5) tubule growing on the corresponding catalyst particle. The decomposition of acetylene on the same catalyst particle is also represented. The catalyst contains many active sites but only those symbolized by grey circles are directly involved in the (5,5) tubule growth.

Guthrie and Guthrie and Jencks have proposed an alternative mechanistic symbolism that is capable of more detailed description than the Ingold system, although at the expense of greater complexity. This system may be useful for the computer representation of reaction mechanisms. 

The Laplace transformation converts a function of t, F(t), into a function of s, f s), where s is the transform variable. The quantity/(s) is called the Laplace transform of F(t). Equation (3-66) shows several equivalent symbolic representations of the Laplace transform of the function y = F(t). 

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