Naturally valenced

A subset R of S is called naturally valenced if each element of R has finite valency. The present chapter starts with the observation that naturally valenced schemes give rise to quotient schemes over finite closed subsets. After the definition of quotient schemes we shall always assume S to be naturally valenced. 

For the remainder of this section, we shall now assume S to be naturally valenced. 

From Theorem 4.1.3(iii) together with Lemma 2.3.3 we obtain that S//T is naturally valenced for each finite closed subset T of S. 

In this section, S is assumed to be naturally valenced. The letter T stands for a finite closed subset of S. 

Water has been widely used as a probe molecule for the characterization of zeolites, especially of those with a high aluminium content [9]. Water adsorption on hydrophilic zeolites has been used to measure their pore volume, and it has been shown that the amount of water adsorbed is a linear function of the aluminium content [10]. Additionally, water adsorption is also highly sensitive to the nature, valence and accessibility of extra-framework cations [11]. Immersion calorimetry allows for the measurement of the degree of interaction between the zeolite and water, and this can be compared with the interaction between the zeolite and other molecules with different polarity. In this way, the polar character of the zeolite surface can be assessed. 

It should be noted the transitional elements in each period i Table II (10 elements) can be divided into two sub-groups, ne of four elements with high natural valency and the other of six elements with low natural valency, i.e. six elements which display low valencies in their naturally occurring compounds. 

Influence of Cation Nature, Valence, and Concentration on Adhesion. As... 

By summing all the formal bond orders to atom A, one can similarly determine the natural valency of atom A,... 

The natural valencies are found to closely resemble the classical valency values associated with position in the periodic table (Vh =1. = 4, Vn = 3, etc.). Similarly, the natural... 

Making several of the energy terms depend critically on calculations of bond orders for each atom is of central importance to describe variable atomic bonding. It is assumed that the bond order of any given atom can be calculated by evaluation of interatomic distances to neighbouring atoms and that all such contributions add up to a net bond order for each atom. In particular, this prevents otherwise pathological tendencies of the atoms to make bonds beyond their natural valency capabilities by inclusion of an overcoordination penalty. 

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