Simplicity, principle

Any procedure for generating hypotheses is based on the simplicity principle. Because of this, we are justified in using the mechanistic hierarchy and in evaluating quantitatively the mechanistic complexity. It is instructive to examine skeletal schemes... 

The relative simplicity of tlie method and the penetrative nature of the x-rays, yield a technique that is sensitive to elements with Z > 10 down to a few parts per million (ppm) and can be perfonued quantitatively from first principles. The databases for PIXE analysis programs [21, 22 and 23] are typically so well developed as to include accurate fiindamental parameters, allowing the absolute precision of the technique to be around 3% for major elements and 10-20% for trace elements. A major factor m applying the PIXE teclmique is that the bombardmg energy of the... 

It is useful to represent the polyelectronic wave function of a compound by a valence bond (VB) structure that represents the bonding between the atoms. Frequently, a single VB structure suffices, sometimes it is necessary to use several. We assume for simplicity that a single VB stiucture provides a faithful representation. A common way to write down a VB structure is by the spin-paired determinant, that ensures the compliance with Pauli s principle (It is assumed that there are 2n paired electrons in the system)... 

We choose 2x2 matrices for simplicity, but we appreciate that the principle applies in general. The (noncommutative) products are... 

Now, in principle, the angle of contact between a liquid and a solid surface can have a value anywhere between 0° and 180°, the actual value depending on the particular system. In practice 6 is very difficult to determine with accuracy even for a macroscopic system such as a liquid droplet resting on a plate, and for a liquid present in a pore having dimensions in the mesopore range is virtually impossible of direct measurement. In applications of the Kelvin equation, therefore, it is almost invariably assumed, mainly on grounds of simplicity, that 0 = 0 (cos 6 = 1). In view of the arbitrary nature of this assumption it is not surprising that the subject has attracted attention from theoreticians. 

Mercury porosimetry is generally regarded as the best method available for the routine determination of pore size in the macropore and upper mesopore range. The apparatus is relatively simple in principle (though not inexpensive) and the experimental procedure is less demanding than gas adsorption measurements, in either time or skill. Perhaps on account of the simplicity of the method there is some temptation to overlook the assumptions, often tacit, that are involved, and also the potential sources of error. 

Principles in Processing Materials. In most practical apphcations of microwave power, the material to be processed is adequately specified in terms of its dielectric permittivity and conductivity. The permittivity is generally taken as complex to reflect loss mechanisms of the dielectric polarization process the conductivity may be specified separately to designate free carriers. Eor simplicity, it is common to lump ah. loss or absorption processes under one constitutive parameter (20) which can be alternatively labeled a conductivity, <7, or an imaginary part of the complex dielectric constant, S, as expressed in the foUowing equations for complex permittivity ... 

The reduction of dimensions also reduces volumes which are accessible to the detector. Thus, detection principles related to geometric dimensions of the detector cell ai e not ideally suited for coupling to microsystems, whereas surface sensitive principles, such as electrochemical methods or optical methods utilizing the evanescent field of a waveguide, or methods which can be focussed on a small amount of liquid, such as electrochemiluminescence (ECE), ai e better suited. This is why electrochemiluminescence detectors ai e combined to microsystems. Moreover ECE has found wide applications in biochemistry because of its high sensitivity, relatively simplicity and feasibility under mild conditions. 

As with any constitutive theory, the particular forms of the constitutive functions must be constructed, and their parameters (material properties) must be evaluated for the particular materials whose response is to be predicted. In principle, they are to be evaluated from experimental data. Even when experimental data are available, it is often difficult to determine the functional forms of the constitutive functions, because data may be sparse or unavailable in important portions of the parameter space of interest. Micromechanical models of material deformation may be helpful in suggesting functional forms. Internal state variables are particularly useful in this regard, since they may often be connected directly to averages of micromechanical quantities. Often, forms of the constitutive functions are chosen for their mathematical or computational simplicity. When deformations are large, extrapolation of functions borrowed from small deformation theories can produce surprising and sometimes unfortunate results, due to the strong nonlinearities inherent in the kinematics of large deformations. The construction of adequate constitutive functions and their evaluation for particular... 

One of the major uses of molecular simulation is to provide useful theoretical interpretation of experimental data. Before the advent of simulation this had to be done by directly comparing experiment with analytical (mathematical) models. The analytical approach has the advantage of simplicity, in that the models are derived from first principles with only a few, if any, adjustable parameters. However, the chemical complexity of biological systems often precludes the direct application of meaningful analytical models or leads to the situation where more than one model can be invoked to explain the same experimental data. 

Simplicity in design is preferred. The modified KISS principle Keep It Simple and Safe is applicable. 

For simplicity, the basic theoretical considerations of electrostatic precipitation are given in terms of cylindrical geometry, i.e., pipe-type electrostatic precipitation. This makes it possible to show most of the basic principles without numerical modeling. 

While it is impossible to describe a system of storekeeping and distribution suitable for every site, there are certain essential principles which should be adhered to if cleanliness, order and economy are to be maintained. How these principles should be applied is for individual management to decide. The keynote, however, should be simplicity. A storekeeper familiar with both grades and needs should control distribution. While the lubrication schedule for any particular unit is generally the concern of the operator, the storekeeper must equally be aware of it and have a comprehensive list of the different grades, their applications, quantities, daily and other periodic needs. On such a basis he will be able to requisition and store the necessary lubricants in the most convenient and economic quantities and packages, and ensure that supplies are used on a first in, first out basis. 

As a first approach to the principles which govern the behaviour of metals in specific environments it is preferable for simplicity to disregard the detailed structure of the metal and to consider corrosion as a heterogeneous chemical reaction which occurs at a metal/non-metal interface and which involves the metal itself as one of the reactants (cf. catalysis). Corrosion can be expressed, therefore, by the simple chemical reaction ... 

The complexity of the systems to be protected and the variety of techniques available for cathodic protection are in direct contrast to the simplicity of the principles involved, and, at present the application of this method of corrosion control remains more of an art than a science. However, as shown by the potential-pH diagrams, the lowering of the potential of a metal into the region of immunity is one of the two fundamental methods of corrosion control. 

This method has very little other than its simplicity to recommend it in the form just described. But when a binary base is used, the corresponding procedure is to bisect the interval successively. Each bisection determines one additional binary digit to the approximation, it requires only the evaluation of the function, and the method is often efficient and accurate. The principle is used by Givens (Section 2.3) in finding the roots of a tridiagonal symmetric matrix. 

In principle all methods except viscosity measurement can be used to obtain absolute values of molar mass. Viscosity methods, by contrast, do not give absolute values, but rely on prior calibration using standards of known molar mass. The relationship between polymer solution viscosity and molar mass is merely empirical but the techniques are widely used because of their simplicity. All of the absolute methods are time-consuming and laborious and are not used on a routine basis. As well as the techniques already mentioned, there is the size-exclusion method of chromatography known as Gel-Permeation Chromatography (GPC). All of these methods are discussed in detail in the sections that follow. 

In order to explain the linkages between strategy and stress response reference will be made to Fig. lb which depicts the patterns of seasonal change in shoot biomass associated with the full spectrum of primary strategies (Fig. la). For simplicity, this diagram refers to the patterns observed in herbaceous plants in a temperate zone situation with a sharply defined growing season. However, the principles adduced can be applied to any life-form or biome. 

The advantage of the dispersing principle is related to the relatively low technical expenditure to achieve dispersion, i.e. the simplicity of the concept. However, as flow patterns may change and are not known for new systems, they have to be identified, documented as flow-pattern maps and controlled. Thus, some analytical characterization has to be done in advance of the experiment. Hence inspection windows again are essential (for the first prototype they may be eliminated later). 

Among the many ways to go beyond the usual Restricted Hartree-Fock model in order to introduce some electronic correlation effects into the ground state of an electronic system, the Half-Projected Hartree-Fock scheme, (HPHF) proposed by Smeyers [1,2], has the merit of preserving a conceptual simplicity together with a relatively straigthforward determination. The wave-function is written as a DODS Slater determinant projected on the spin space with S quantum number even or odd. As a result, it takes the form of two DODS Slater determinants, in which all the spin functions are interchanged. The spinorbitals have complete flexibility, and should be determined from applying the variational principle to the projected determinant. 

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