Inductive theory

Scientific theories themselves can be distinguished as deductive or inductive in nature, according to the underlying character of their premises. In a deductive theory, the fundamental premises are axioms or postulates that are neither questionable nor explainable within the theory itself. Outstanding examples of deductive theories include Euclidean geometry (based on Euclid s five axioms) and quantum mechanics (based on Schrodinger s prescription for converting classical trajectory equations into wave equations). An inductive theory, on the other hand, is based on universal laws of experience that express what has always been found to be true in the past, and may therefore be reasonably expected to hold in the future. Thermodynamics is the pre-eminent example of an inductive theory. 

Kobozev s inductive theory of active ensembles (168,169,171,172a,b) postulates that the carrier of catalytic activity is a phase present in high dilution on the support. This phase, which is in the amorphous precrystalline state, consists of a number of cells separated by geometrical barriers (microfissures) which are impenetrable to molecules for movement from one group of cells to another. Thus there is no exchange of catalyst atoms, reactant molecules or catalyst poisons between these cells. The smallest group of catalytically active atoms in the cells form an ensemble which constitutes the carrier of the catalytic activity and to... 

According to the association-induction theory proposed by Ling (1962), fixed charges on macromolecules and their associated counterions constrain water molecules to form a matrix of polarized multilayers having restricted motion, compared with pure water. The monolayer of water molecules absorbed on the polar sorption site of the molecule is almost immobilized and thus behaves, in many respects, like part of the solid or like water in ice. It has different properties than additional water layers defined as multilayers have. The association-induction theory has been shared by many researchers for many years. Unfortunately, elucidation of the nature of individual layers of water molecules has been less successful, due to the complexity of the system and lack of appropriate techniques. 

This chapter describes the operating principle, fabrication, and application of a variety of sensors made of magnetic materials and based on the principle of electromagnetic induction. To well describe these systems, fundamental magnetic principles, such as magnetic induction theory and material properties, are also briefly described along with representative examples of these sensors and their applications, with a focus on the area of biomedical engineering. 

Eisenhardt (1989) describes the process of inducting theory using case studies from specifying the research questions to reaching closure. She argues that this research approach is especially appropriate in new topic areas, and the resultant theory is often novel, testable, and empirically valid. 

Some induction schemes for ct, n, and 5 orbital basis sets on C y sites of polyhedral complexes are to be found in Appendix D. In addition to the Frobenius theorem, there is also a stronger result for induction theory based on the concept of a fiber bundle. This requires the coupling of representations and will be considered in Sect. 6.9. 

This is precisely the set of fluorine displacements that we constructed in Sect. 4.8 in order to describe the vibrational modes of UFe. One remarkable result of induction theory is that the mechanical representation can also be obtained as the direct product of the positional representation and the translational representation, T u, this is the representation of the three displacements of the centre of the cluster. 

The absolute infrared absorption intensities of the two translational mode lines at 68 and 114 cm i were calculated by Ron and Schnepp (1967) using the quadrupole induction theory. These authors also found the predicted intensities to be in order-of-magnitude type agreement witlh rough measurements. Brown and King (1970) and Kuan (1969) made... 

We note that the complex conjugate non-degenerate irreps, F1 and F2, directly generate the sextuple representation. According to induction theory, this process will yield at once the six eigenvectors in monomial form [25], where we use the sixfold axis as cyclic coset generator. 

---