Order, definition

A First-Order Definition of Multipolydispersity Example of Mass Distribution... 

Roy, B. and Vincke, P. H. (1987), Pseudo-Orders Definition, Properties, and Numerical Representation, Mathematical Social Sciences, Vol. 14, pp. 263-274. 

A second item of terminology is that I use the terms second order and first order not in the sense of properties of properties versus properties of individuals, but as follows a second-order property is a property that has a true definition in terms of having some other properties that meet a certain sort of condition. And a first-order property does not have such a true definition. A functional property is a special kind of second-order property in which the definition specifies causal relations to other properties and to inputs and outputs. I am supposing that the other properties quantified over in the second-order definition are themselves first-order properties. 

But perhaps we can do without that clause with the some in it We can just list the disjuncts. Suppose that there are exactly two first-order dormi-tive structures as a matter of physical law, Q2H12N2O3 and QsHyClNjO. However, if there were another first-order property that caused sleep, it would be dormitive, according to the second-order definition, without being one of the first-order disjuncts. And a similar point holds for the infinite disjunction. So, there is a modal difference. 

The calculations of local properties of metal-oxide electronic structure [571,581-583] were made in the cychc-cluster model, in the CNDO approximation. As in the CNDO approximation AOs are supposed to be orthogonalized by the Lowdin procedure (see Chap. 6), the definitions of local properties given in Sect. 9.1.1 for nonorthog-onal basis, have to be modified. In particular, the overlap population (9.9) becomes zero in the CNDO approximation, so that the electronic population is defined only by diagonal density matrix elements In (9.6) and in the bond-order definition... 

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