Explanations functional

Since the view I m proposing meets both characteristics of emergence, and is made possible by the existence of functional properties, I will call it functional emergence. The use of the term emergence is appropriate because the existence of functional properties in chemistry supports the layered view of the world characteristic of emergentism. The sui generis chemical properties, laws and explanations function at a higher level than the physical properties, laws and explanations they depend on the physical level, but they do not reduce to it. 

Up to now, we have reflected upon a family of partly competing and partly complementary theses about the metaphysics of the mind, and on how these theses can be illustrated by reference to the explication of reduction. These theses remain silent about the epistemic or procedural character of reductions (except for the highly implausible idea that the relevant identity-statements express a priori tmths) and about explanatory aspects of reduction. In the philosophy of mind, the dominant view about the link between reduction and explanation is that functional reduction somehow goes together with functional or mechanistic explanation. Functionalism also yields a theory of the metaphysics of mental properties and, contrary to ordinary type-identity theories, it explicitly employs the term reduction . 

We used the concept of sound velocity dispersion for explanation of the shift of pulse energy spectrum maximum, transmitted through the medium, and correlation of the shift value with function of medium heterogeneity. This approach gives the possibility of mathematical simulation of the influence of both medium parameters and ultrasonic field parameters on the nature of acoustic waves propagation in a given medium. 

We have seen various kinds of explanations of why may vary with 6. The subject may, in a sense, be bypassed and an energy distribution function obtained much as in Section XVII-14A. In doing this, Cerefolini and Re [149] used a rate law in which the amount desorbed is linear in the logarithm of time (the Elovich equation). 

This algebra implies that in case of Eq. (111) the only two functions (out of n) that flip sign are and because all in-between functions get their sign flipped twice. In the same way, Eq. (112) implies that all four electronic functions mentioned in the expression, namely, the jth and the (j + 1 )th, the th and the (/c -h 1 )th, all flip sign. In what follows, we give a more detailed explanation based on the mathematical analysis of the Section Vin. 

The following sections give an overview of the functional form of the PFF and a short explanation of the various contributions to the total force field energy of a molecule or molecular system. 

Families of finite elements and their corresponding shape functions, schemes for derivation of the elemental stiffness equations (i.e. the working equations) and updating of non-linear physical parameters in polymer processing flow simulations have been discussed in previous chapters. However, except for a brief explanation in the worked examples in Chapter 2, any detailed discussion of the numerical solution of the global set of algebraic equations has, so far, been avoided. We now turn our attention to this important topic. 

Tlie next section of the patent is tided "The Detailed Description of the Preferred Embodiment", Q (Fig. lb), often a multipage work serving several functions. First, the detailed description should provide an illustration of the invention in both its broadest or simplest sense and in its most preferred sense. Any elements of the invention that the inventor beheves are crucial to the success or performance of the invention must also be included within this description. Further, tbi< description should provide an explanation of the invention that is definite and illustrative, so as to allow persons having nothing but die patent before diem to practice or use die invention in the manner intended. This description should be understood by those who work in the area that covers the subject matter of the patent. 

Here it can be seen that the nucleation rate is a decreasing function of growth rate (and supersaturation). The physical explanation is believed to be the mechanical influence of the crystallizer on the growing suspension and/or the effect of Bujacian behavior. 

As in any new field, new structures demand novel names. As the variety of structures has increased, the names have kept pace. Although some may be dismayed by this, the different names connote not only different structural types or functional groups, but conceptual differences among the various classes as well. In order to introduce the novitiate and perljaps remind the journeyman, we provide a few definitions and explanations herewith. 

These explanations do not exhaust the possibilities with regard to underlying causes, but they do illustrate an important point the analysis of human error purely in terms of its external form is not sufficient. If the underlying causes of errors are to be addressed and suitable remedial strategies developed, then a much more comprehensive approach is required. This is also necessary from the predictive perspective. It is only by classifying errors on the basis of underlying causes that specific types of error can be predicted as a function of the specific conditions under review. 

We must now consider the choice of a basis set. I have already made reference to hydrogenic orbitals and Slater orbitals without any real explanation. I have also hinted at the integrals problem variational calculations almost always involve the calculation of a number of two-electron integrals over the basis functions... 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

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