Elaborations

A systematic listing of the topological possibilities for complexes in terms of max-components is conceivable. That is, the conceivable complexes could be identified in terms of the numbers and types of max-segments and max-surfaces. We let c denote a string that is a cycle, Sc denote a generic closed (i.e., edgeless) surface, and 5p denote a punctured surface (i.e., a surface obtained from a closed surface by cutting 

0 1 0 1 1-handled basket fi, possibly with internal linking 

0 2 0 1 2-handled basket, or double-punctured 5p with handle at each puncture 

0 1 1 1 1-handled basket inside S, or 1-handled basket and linked 

There are a number of different fundamental invariants associated with our three-stage description. They relate not only to classical questions of stoichiometry, but also to questions of strain as mediated by some basic differential-geometric theorems involving curvatures. 

The choice of a material fit to be used as a gas sensitive element depends on certain properties, which naturally include sensitivity and selectivity. 

Sensitivity, which is generally given by the expression G-Gq/Gq, where G and Go are the electric response in the presence of gas and air respectively, expresses the relative variation of the signal due to different gases. 

Selectivity, which appears most often as a parameter relative to the desirable level of accuracy, expresses the sensor s capacity to detect different gases. 

The relative nature of this parameter is linked to the fact that the physicochemical interactions between gas and solid are very likely and that only the intensity of the phenomenon can vary. 

there are other criteria that are just as important. 

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Since process design starts with the reactor, the first decisions are those which lead to the choice of reactor. These decisions are among the most important in the whole design. Good reactor performance is of paramount importance in determining the economic viability of the overall design and fundamentally important to the environmental impact of the process. In addition to the desired products, reactors produce unwanted byproducts. These unwanted byproducts create environmental problems. As we shall discuss later in Chap. 10, the best solution to environmental problems is not elaborate treatment methods but not to produce waste in the first place. 

Early decisions made purely for process reasons often can lead to problems of safety and health (and environment) which require complex and often expensive solutions. It is far better to consider them early as the design progresses. Designs that avoid the need for hazardous materials, or use less of them, or use them at lower temperatures and pressures, or dilute them with inert materials will be inherently safe and will not require elaborate safety systems. ... 

The elaborated method of applying elements for calibration of devices composed of the body with a nartensite structure, with elements made of austenite steel placed in it, allows to ensure calibration repeatability,... 

The contribution wws elaborated in frame of complex program of the GA CR No. 101/96/K264 - Limit states of construction materials with utilisation of non-standard test methods. 

The main point of our elaboration is, that the Gibbs measure (4) of the potential lattice under interest ctin be considered as a nontrivial prior in the Bayes formula for the conditional probability, applied to the problem of image restoration ... 

Currently, the elaboration of methods for the objective control of the authenticity of important documents, such as passports, securities, licenses, certificates, identification cards, etc., is being intensively developed. 

A software has been elaborated allowing the automation of this control and the reconstitution of 2D and 3D images of the controlled samples. 

Un logiciel a etd elabore, permettant d automatiser ce controle et de reconstituer des images a deux et trois dimensions des echantillons controles. 

To define a steel, it would be necessary to know its chemical composition, its physicochemical constitution, its metallurgical state (aimealed, hammered) and other parameters (superficial and chemical processing,. ..). The set of structural characters of a metallic alloy is consequently function of the chemical composition, the elaboration processing, the thermal processing, the temperature, etc. 

Elaboration of a Physical Model by Eddy Current and Application in the Characterization of Long Defects in Hollow Cylindrical Products. 

The work on standardisation in Ukraine is led by the State Committee of Ukraine on Standardisation, Metrology and Certification (Gosstandardt), All the USSR standards (GOSTs) are valid in Ukraine, and several dozens of them were elaborated in the NDT field. 

The principal point of interest to be discussed in this section is the manner in which the surface tension of a binary system varies with composition. The effects of other variables such as pressure and temperature are similar to those for pure substances, and the more elaborate treatment for two-component systems is not considered here. Also, the case of immiscible liquids is taken up in Section IV-2. 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

This approach, much used by Guggenheim [190], seems elaborate, but in the case of more complex situations than the above, it can be a very powerful one. 

The discussion so far has been confined to systems in which the solute species are dilute, so that adsorption was not accompanied by any significant change in the activity of the solvent. In the case of adsorption from binary liquid mixtures, where the complete range of concentration, from pure liquid A to pure liquid B, is available, a more elaborate analysis is needed. The terms solute and solvent are no longer meaningful, but it is nonetheless convenient to cast the equations around one of the components, arbitrarily designated here as component 2. 

There has been considerable elaboration of the simple Girifalco and Good relationship, Eq. XII-22. As noted in Sections IV-2A and X-6B, the surface ftee energies that appear under the square root sign may be supposed to be expressible as a sum of dispersion, polar, and so on, components. This type of approach has been developed by Dann [70] and Kaelble [71] as well as by Schonhom and co-workers (see Ref. 72). Good (see Ref. 73) has preferred to introduce polar interactions into a detailed analysis of the meaning of in Eq. IV-7. While there is no doubt that polar interactions are important, these are orientation dependent and hence structure sensitive. 

This is useful since c can be estimated by means of the BET equation (see Section XVII-5). A number of more or less elaborate variants of the preceding treatment of lateral interaction have been proposed. Thus, Kiselev and co-workers, in their very extensive studies of physical adsorption, have proposed an equation of the form... 

The general approach goes back to Frenkel [63] and has been elaborated on by Halsey [64], Hill [65], and McMillan and Teller [66]. A form of Eq. XVII-78, with a = 0,... 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E ... 

A more elaborate theoretical approach develops the concept of surface molecular orbitals and proceeds to evaluate various overlap integrals [119]. Calculations for hydrogen on Pt( 111) planes were consistent with flash desorption and LEED data. In general, the greatly increased availability of LEED structures for chemisorbed films has allowed correspondingly detailed theoretical interpretations, as, for example, of the commonly observed (C2 x 2) structure [120] (note also Ref. 121). 

There are many large molecules whose mteractions we have little hope of detemiining in detail. In these cases we turn to models based on simple mathematical representations of the interaction potential with empirically detemiined parameters. Even for smaller molecules where a detailed interaction potential has been obtained by an ab initio calculation or by a numerical inversion of experimental data, it is usefid to fit the calculated points to a functional fomi which then serves as a computationally inexpensive interpolation and extrapolation tool for use in fiirtlier work such as molecular simulation studies or predictive scattering computations. There are a very large number of such models in use, and only a small sample is considered here. The most frequently used simple spherical models are described in section Al.5.5.1 and some of the more common elaborate models are discussed in section A 1.5.5.2. section Al.5.5.3 and section Al.5.5.4. 

Many other mles, some of which are rather more elaborate, have been proposed [HI], but these mles have insubstantial theoretical imderpiimings and they continue to be used only because there is often no better way to proceed. 

Modem versions of diis approach use a more elaborate exponential fiinction for the repulsion, more dispersion tenns, induction tenns if necessary, and individual damping fiinctions for each of the dispersion, and sometimes induction, tenns as in equation (Al.5.37). 

Claverie P 1978 Elaboration of approximate formulas for the interactions between large molecules applications in organic chemistry Intermolecular Interactions From Diatomics to Biopolymers ed B Pullman (New York Wiley) p 69... 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

This is the factor by which the echo magnetization is attenuated as a result of difhision. More elaborate calculations, which account for phase displacements due to difhision occurring during the application of the gradient pulses yield... 

In the previous chapters experiments have been discussed in which one frequency is applied to excite and detect an EPR transition. In multiple resonance experiments two or more radiation fields are used to induce different transitions simultaneously [19, 20, 21, 22 and 23], These experiments represent elaborations of standard CW and pulsed EPR spectroscopy, and are often carried out to complement conventional EPR studies, or to refine the infonnation which can in principle be obtained from them. 

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