Relations deductive

To provide a sense of the value of some of these deviations from neutral taxation. Table 2 reports cumulative estimates over five years of selected energy-related tax expenditures. The Congressional Budget and Impoundment Control Act defines a tax expenditure as a revenue loss attributable to a special inclusion, exemption, or deduction from gross income or a special credit, preferential tax rate, or deferral of tax. 

A plausible deduction of the solubility product relation is the following. When excess of a sparingly soluble electrolyte, say silver chloride, is shaken up with... 

This is called Avogadro s theorem (1811) it appears here simply as a definition of molecular weighty and this is really the manner in which the relation is applied in chemistry. The kinetic theory of gases gives a new, and much deeper, significance to the statement by introducing the conception of the molecule this, however, does not concern us in thermodynamics, and since the molecular weights are purely relative numbers, the deductions made in this hook are equally strict whichever standpoint is adopted. 

In short, we may say that there is evidence that the deviations from the relations predicted by the characteristic equations may be due to chemical changes in the substances, which are not taken into consideration in the kinetic deduction of the equations. Weinstein loc. cit.) considers that it is possible to deduce an equation which takes account of these chemical changes as well. It will be sufficient here to re-einphasise the fact that there is at present no characteristic equation known which agrees accurately with the behaviour of a single substance, let alone various substances, over a wide range of temperature. 

The test of the validity of the theory of Arrhenius is not therefore to be found in the agreement between the values of i obtained from measurements of any properties of solutions which are conditioned by the osmotic pressure it is in quite another field—that of electrochemistry—that a comparison of known relations with the deductions from the theory may be instituted. 

The most intensively investigated dehydroxylation is probably the reaction of Mg(OH)2, though detailed results are also available for the hydroxides of certain other divalent cations. Several summaries of the mechanistic deductions obtained from such work, including literature sources, were presented at a conference at Dijon in 1974 [87]. The extensive literature concerned with the thermal analysis of hydroxides has been reviewed by Dollimore [79] who has also included the behaviour of oxides. Water elimination can be regarded as the first in a sequence of structurally related steps through which the hydroxide is converted into the thermally most stable oxide. 

Numerous and varied conclusions have been stated explicitly or implied in the text of Chaps. 2—5. These include mechanistic deductions, references to inconsistencies or irreconcilable interpretations found in different studies, recommendations for the re-analysis of certain experimental data etc. These will not be repeated in detail in the present chapter, which summarizes only the most significant and general conclusions relating to the kinetics of decompositions and interactions of solids. 

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

Bamford and Dewar have adapted the latter method to the deduction of values for r, and hence to the determination of the individual rate constants kp and kt. They chose to observe the rate of polymerization by measuring the increase in viscosity with time, using for this purpose a specially designed reaction cell equipped with a viscometer. Having established by separate experiments the relation-... 

The formal thermodynamic analogy existing between an ideal rubber and an ideal gas carries over to the statistical derivation of the force of retraction of stretched rubber, which we undertake in this section. This derivation parallels so closely the statistical-thermodynamic deduction of the pressure of a perfect gas that it seems worth while to set forth the latter briefly here for the purpose of illustrating clearly the subsequent derivation of the basic relations of rubber elasticity theory. 

Finally, reductionism is closely tied to the so-called syntactic approach to theories, an approach which treats theories as axiomatic systems expressed in natural or artificial languages. Indeed, closely tied may be an understatement, since deduction is a syntactic affair, and is a necessary component of reduction. Once philosophers of science began to take the semantic approach to theories seriously, the very possibility of reduction became moot. For the semantic approach treats theories as families of models, and models as implicit definitions, about which the only empirical question is whether they are applicable to phenomena. For reduction to be obtained among models semantically characterized requires an entirely different conception of reduction, and whether such a conception would capture anything of interest about inter-theoretical relations is questionable. 

Figure 7.4 presents a sketch for the deduction of the intensity in symmetrical-reflection geometry. F is the footprint area of an incident microbeam on the sample surface, and dlt is the related contribution to intensity. Again utilizing the absorption law Eq. (7.1) we have... 

In the original (22) derivation of Eqn. II.2, Eqn. II.4 was, in effect, used as the starting point for the discussion the logic was accordingly obscured by the fact that Eqn. II.4 already contained all the essentials of the object of derivation. Although these deductions are improper in the classic sense, it is still possible that Eqn. II.4 may be admissible in an extended valence scheme. However, in this situation fundamental difficulties arise in correlating the number of bonds pi and q] (Def. II.9) with the total number of electrons (Defs. II.3 and 11.4). Hence the relations... 

There have been a number of suggestions in the past that an extraterrestrial object impacting on the. earth caused or could cause massive extinctions of life. E. J. Opik [11], for example, discussed the lethal effects which could be caused by the heat generated from such objects striking the earth, and H. C. Urey [12] stated specifically that a comet was probably the cause of the Cretaceous-Tertiary extinctions. There have also been science fiction stories and a movie relating to the effects. The events likely to occur if the sunlight were temporarily "turned off" have also been discussed [13]. Our deduction in contrast to the others is based on physical science data (the iridium anomaly) and is the only explanation we found which explained the Ir anomaloy could cause the massive extinction of life and was likely to occur in a period of 100 million years. 

Extrapolating from prior examples of group formation to future possibilities is a deductive process, and so it is perhaps not so unusual to bring Arthur Conan Doyle s Sherlock Holmes into the discussion. As devoted readers will testify, Conan Doyle s stories are filled with physical details, particularly those relating to the persons and behaviors of his characters. Some of those physical traits are immediately observable to other characters in the stories, whereas other physical traits are apparent only after their logical relation to human actions are made evident by Holmes. 

Pasteur thus made the important deduction that the rotation of polarized light caused by different tartaric acid salt crystals was the property of chiral molecules. The (+)- and ( )-tartaric acids were thought to be related as an object to its mirror image in three dimensions. These tartaric acid salts were dissymmetric and enantiomorphous at the molecular level. It was this dissymmetry that provided the power to rotate the polarized light. 

Corollary means a deduction following on from another, related, fact or series of facts. 

The period-specific throughput share tpPt Vr e R, t e T is the capacity volume normed on the available period time deducted by shut-down hours in relation to the maximum throughput basis. 

There are some scientists and philosophers who still claim that a model by definition "furnishes a concrete image" and "does not constitute a theory." 10 But if the model is the mathematical description, then the question of whether the model is the theory appears to become moot, since most people accept the view that rigorous mathematical deduction constitutes theory. For others, like Hesse and Kuhn, even if the model is a concrete image leading to the mathematical description, it still has explanatory or theoretical meaning, for, as Kuhn put it, "it is to Bohr s model, not to nature, that the various terms of the Schrodinger equation refer." 11 Indeed, as is especially clear from a consideration of mathematical models in social science, where social forces are modeled by functional relations or sets of mathematical entities, the mathematical model turns out to be so much simpler than the original that one immediately sees the gap between a "best theory" and the "real world." 12... 

The table uses a system of symbols for the elements and a system of conventions for atomic weights it employs a classification, or a visual array, that groups the symbols so that their relations and properties are immediately suggested to the viewer who knows the principles of classification and a few facts. Deductions can be made both to the facts that established the table and to the facts that were unknown when the table was first set out. Here is a scheme that is an explanatory and predictive model and an icon in both the semiotic and the popular senses of the word. But its power comes from visual display, from image, not the principles and facts that can be recorded in ordinary or conventional language. 

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