Representative, definition

The development of a quantitative theory of a free-radical copolymerization implies the derivation of equations for the rate of the monomers depletion and the statistical characteristics of the chemical structure of macromolecules present in the reaction system at the given conversion p of monomers. Elaborating such a theory one should take into account a highly important peculiarity inherent to any free-radical copolymerization. This peculiarity is that the characteristic time of a macroradical life is appreciably less than the time of the process duration. Consequently, its products represent definitely... 

By contrast, the ellipses in the previous diagrams are action types representing definitions of all the interactions that can take place. The actors they link are types of object each type describes a role that specific instances can play. (We don t always put arrows on the actions at this stage, because each action may represent a sequence of smaller interactions between the participants there may be several alternative sequences, each of which has a different initiator. We ll see shortly how we distinguish who does the teaching and who gets taught.)... 

Constitutional formulae were designed "on paper", primarily to be "in harmony" with known chemical properties and without pretension to "represent the symmetrical or spatial arrangement of the atom in a compound" [22], Not only was this stipulation gradually relaxed to represent three-dimensional structures, but the connecting lines were also soon after assumed to represent definite electronic links between atoms. This assumption opened the door for the introduction of semi-empirical quantum-mechanical characterization of chemical bonds. It is important to realize that chemical bonds have never been observed in any experiment and that they only exist as conjectures to interpret primitive molecular graphs. Their value as heuristic aids in the study of chemical change and composition is beyond dispute, but as a basis for the theoretical understanding of chemical cohesion they are of little value. 

You should be able to interpret chemical equations, and appreciate that they represent definite quantities of materiab reacting together. You should be familiar with the concepts of exothermic and endothermic reactions. 

In the two special cases of isothermalj reversible expansion considered above, the work done, as given by equations (8.3) and (8.4) or (8.5), is evidently a definite quantity depending only on the initial and final states, e.g., pressure or volume, at a constant temperature. Since there is always an exact relationship between P and F, it follows from equation (8.2) that the work done in any isothermal, reversible expansion must have a definite value, irrespective of the nature of the system. For an isothermal, reversible process in which the work performed is exclusively work of expansion, it is apparent, therefore, from equation (7.2), that both W and Q will be determined by the initial and final states of the system only, and hence they will represent definite quantities. Actually, this conclusion is applicable to any isothermal, reversible change (cf. 25a), even if work other than that of expansion is involved. 

Resonance is an important concept in chemistry. Though we represent definite Lewis structures of molecules, in actuality the electrons are not localized. They are shared and delocalized by atoms in such a way as to be in the most stable electron distribution. This is called resonance. 

In mathematical terms in Equations I and 2 the functions representing definite molecular properties are linearly dependent, whereas in Equations 3 and 4 they are linearly independent of each other. The essential differences between the Equations 1-4 are that in (1) symmetry arguments are applicable. 

Important note T and P are numbers, and Tti represents definition of phases (gas or liquid or solid). The ehange of Aifj with T or jr, (effect of P is usually negligible except for processes at very high pressure) can be obtained from the change of enthalpies with T or jr,-. Suppose that the heat of reaction of a certain reaction is given at T°, P°, and tt and is represented by AHr(T°, P°,7t°i). We want to compute the heat of reaction at T, P°, and Jti this can be achieved through the fact that... 

It should be emphasized that capital cost estimates using installation factors are at best crude and at worst highly misleading. When preparing such an estimate, the designer spends most of the time on the equipment costs, which represent typically 20 to 40 percent of the total installed cost. The bulk costs (civil engineering, labor, etc.) are factored costs which lack definition. At best, this type of estimate can be expected to be accurate to 30 percent. 

Specifications represent, as indicated in dictionaries, the definition of the characteristics that a construction, a material, a product, etc., must have. The specifications for industrial products, such as petroleum products, are thus lists of terms and conditions that the products must meet. There are many types of specifications for petroleum products ... 

Standards also give definitions for the characteristics of a material or product, or they provide the means and methods to implement quality tests for them. The difference lies in their method of preparation, therefore, in their legal status. A standard is the result of a consensus between all parties concerned. These parties represent the manufacturers of the product or material, the consumers who are the industries or user services or, ultimately, consumer associations, as well as, finally, governments. 

Finally, each coefficient were standardized by the division of the sum of all coefficients(2). This definition allows also to regard as the co-occurrence matrix as a function of probability distribution, it can be represented by an image of KxK dimensions. 

Figure 2 represents the main view of the model, including all the objects and relationships, the detailed definition of which is given in the standard draft ( 8.2.1 - cf table I). fhe object groups of figure 1 have also been represented on figure 2, for an easier comprehension. This main view is common to all the NDT methods. 

A third definition of surface mobility is essentially a rheological one it represents the extension to films of the criteria we use for bulk phases and, of course, it is the basis for distinguishing states of films on liquid substrates. Thus as discussed in Chapter IV, solid films should be ordered and should show elastic and yield point behavior liquid films should be coherent and show viscous flow gaseous films should be in rapid equilibrium with all parts of the surface. 

Let us consider the consequence of mechanics for the ensemble density. As in subsection A2.2.2.1. let D/Dt represent differentiation along the trajectory in F space. By definition,... 

The traditional definition of a zeolite refers to microporous, crystalline, hydrated aluminosilicates with a tliree-dimensional framework consisting of comer-linked SiO or AlO tetrahedra, although today the definition is used in a much broader sense, comprising microporous crystalline solids containing a variety of elements as tetrahedral building units. The aluminosilicate-based zeolites are represented by the empirical fonmila... 

These new wave functions are eigenfunctions of the z component of the angular momentum iij = —with eigenvalues = +2,0, —2 in units of h. Thus, Eqs. (D.l 1)-(D.13) represent states in which the vibrational angular momentum of the nuclei about the molecular axis has a definite value. When beating the vibrations as harmonic, there is no reason to prefer them to any other linear combinations that can be obtained from the original basis functions in... 

The intensity of shading at any point represents the magnitude of 1, i.e. the probability of finding the electron at that point. This may also be called a spherical charge-cloud . In helium, with two electrons, the picture is the same, but the two electrons must have opposite spins. These two electrons in helium are in a definite energy level and occupy an orbital in this case an atomic orbital. 

Using the electron transfer definition, many more reactions can be identified as redox (reduction-oxidation) reactions. An example is the displacement of a metal from its salt by a more reactive metal. Consider the reaction between zinc and a solution of copper(If) sulphate, which can be represented by the equation... 

Besides the expressions for a surface derived from the van der Waals surface (see also the CPK model in Section 2.11.2.4), another model has been established to generate molecular surfaces. It is based on the molecular distribution of electronic density. The definition of a Limiting value of the electronic density, the so-called isovalue, results in a boundary layer (isoplane) [187]. Each point on this surface has an identical electronic density value. A typical standard value is about 0.002 au (atomic unit) to represent electronic density surfaces. 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

The explicit definition of water molecules seems to be the best way to represent the bulk properties of the solvent correctly. If only a thin layer of explicitly defined solvent molecules is used (due to hmited computational resources), difficulties may rise to reproduce the bulk behavior of water, especially near the border with the vacuum. Even with the definition of a full solvent environment the results depend on the model used for this purpose. In the relative simple case of TIP3P and SPC, which are widely and successfully used, the atoms of the water molecule have fixed charges and fixed relative orientation. Even without internal motions and the charge polarization ability, TIP3P reproduces the bulk properties of water quite well. For a further discussion of other available solvent models, readers are referred to Chapter VII, Section 1.3.2 of the Handbook. Unfortunately, the more sophisticated the water models are (to reproduce the physical properties and thermodynamics of this outstanding solvent correctly), the more impractical they are for being used within molecular dynamics simulations. 

Lead structure According to Valler and Green s definition a lead structure is a representative of a compound series with sufficient potential (as measured by potency, selectivity, pharmacokinetics, physicochemical properties, absence of toxicity and novelty) to progress to a full drug development program [12]. 

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