Main Ideas

Insufficient information about the properties, layout pattern of small defects, potential for their growth in time, usually leads either to an unjustified rejection (repair) or to underestimation of the importance of the defect and, as aconsequence, construction failure. Use of automated computerised means of control allows safe service of the old constructions, periodically repeating the UT and monitoring the development of discontinuities in the metal. The main idea of such policy is periodical UT of development of discontinuities or, in a more general form, monitoring of the metal condition. 

Based on the polarization curves of figure C2.8.4 tliere are several possibilities for reducing or suppressing tire corrosion reaction. The main idea behind every case is to shift tire corroding anode potential away from E. This can be done in tire following ways. 

Obviously, one test example is not enough to illuminate all the effects pointed out previously. Thus, we have to concentrate herein on some main ideas. An extensively example-based comparison is in preparation [18]. 

The main idea of research is application of accessible, simple and express methods that don t need expensive reagent techniques for analysis of phanuaceutical products based on bischofite. The determination of metal ions such as Mg, Zn, Cu, Fe by complex-formation titrations using a widely applicable chelating agent, EDTA, have been studied as a function of pH, complexing agents and indicators. The analysis consists of four parts ... 

By observing the system, you can calculate the NPSHa within a one or two point margin. The main idea is to be sure the NPSHa is greater than the NPSHr of the pump. Remember that the NPSHa only deals with the suction side of the pump. Let s go back to that formula ... 

A successful method to obtain dynamical information from computer simulations of quantum systems has recently been proposed by Gubernatis and coworkers [167-169]. It uses concepts from probability theory and Bayesian logic to solve the analytic continuation problem in order to obtain real-time dynamical information from imaginary-time computer simulation data. The method has become known under the name maximum entropy (MaxEnt), and has a wide range of applications in other fields apart from physics. Here we review some of the main ideas of this method and an application [175] to the model fluid described in the previous section. 

In this chapter we ll examine the confonnations of various alkanes and cycloalkanes, focusing most of our attention on three of them ethane, butane, and cyclohexane. A detailed study of even these three will take us a long way towar d understanding the main ideas of conformational analysis. 

By adopting a perspective from the philosophy of science I will attempt to cross levels of complexity from the most elementary chemical explanations based on electron shells to those based on ab initio methods. Such a juxtaposition is seldom contemplated in the chemical literature. Textbooks provide elementary explanations which necessarily distort the full details but allow for a more conceptual or qualitative grasp of the main ideas. Meanwhile the research literature focuses on the minute details of particular methods or particular chemical systems and does not typically examine the kind of explanation that is being provided. To give a satisfactory discussion of explanation in the context of the periodic table we need to consider both elementary and deeper explanations within a common framework. 

The last chapter in this introductory part covers the basic physical chemistry that is required for using the rest of the book. The main ideas of this chapter relate to basic thermodynamics and kinetics. The thermodynamic conditions determine whether a reaction will occur spontaneously, and if so whether the reaction releases energy and how much of the products are produced compared to the amount of reactants once the system reaches thermodynamic equilibrium. Kinetics, on the other hand, determine how fast a reaction occurs if it is thermodynamically favorable. In the natural environment, we have systems for which reactions would be thermodynamically favorable, but the kinetics are so slow that the system remains in a state of perpetual disequilibrium. A good example of one such system is our atmosphere, as is also covered later in Chapter 7. As part of the presentation of thermodynamics, a section on oxidation-reduction (redox) is included in this chapter. This is meant primarily as preparation for Chapter 16, but it is important to keep this material in mind for the rest of the book as well, since redox reactions are responsible for many of the elemental transitions in biogeochemical cycles. 

The seeond step is the investigation of students eoneeptions. Here, the model foeuses on the basie conceptions and not on isolated ideas eoneeming singular phenomena. The main questions here coneem (1) the nature of basic conceptions, (2) the use of seientifie language and terminology, (3) students ideas about seience and (4) possible eorrespondences and/or cfilferenoes between students ideas and scientific conceptions. One of the main ideas of the model is to confront students conceptions in a positive way. The cracial point is to eonsider their explanatory potential rather than their limitations. 

The main idea here is connected with the design of a new difference scheme of second-order approximation for which the maximum principle would be in full force for any step h. The meaning of this property is that we should have (see Chapter 1, Section 1)... 

The main idea behind the Ritz method is to take into consideration... 

The co-equivalence property of homogeneous schemes lies in the main idea behind a new approach to the further estimation of the order of accuracy of a scheme on account of (9) or (10) its coefficients a, d, ip should be compared with coefficients d, d, (p of a simple specimen scheme, the accuracy order of which is well-known (see Section 7). 

The main idea behind regularization of dilference schemes is that the schemes of a desired quality should be sought in the class of stable schemes starting from an original scheme and replacing it, by changing the operator R, by another scheme of a desired quality belonging to the class of stable schemes. 

In order to clarify the main idea behind this approach, we turn to the scheme with weights... 

Apparently, the main idea behind this approach needs certain clarification. For example, formula (38) necessitates imposing a nonzero background temperature prior to the front. In spite of this fact, there are some delays in introducing new intervals, thus causing large deviations of a solution in a vicinity of the front. Formula (37) is useless for very large values of the index cr a > 20). Formula (36) has the best accuracy and reproduces rather accurately without concern of the background temperature. 

The main idea behind this approach is to accelerate and simplify the algorithms by means of the method of. separate or successive eliminations. To that end, the difference equations (60) are divided into the following groups ... 

It is worth recalling here that the first economical schemes were intended for the elimination of intermediate values with no problems. The main idea behind this approach is to involve factorized schemes in integer steps , a key role of which is to relate the values y and in some or other convenient ways. 

As a matter of experience, the estimation of the nearness of a solution of the difference problem amounts to the proximity between a solution of the original problem (5) and a solution of the chain of problems (6)-(7). The main idea behind this approach is connected with the obvious relation... 

LOS for equations with variable coefficients. One way of covering equations with variable coefficients is connected with possible constructions of locally one-dimensional schemes and the main ideas adopted for problem (15). It sufficies to point out only the necessary changes in the formulas for the operators Lc, and Aq., which will be used in the sequel, and then bear in mind that any locally one-dimensional scheme can always be written in the form (21)-(23). Several examples add interest and help in understanding. 

Locally one-dimensional schemes find a wide range of applications in solving the third boundary-value problem. If, for example, G is a rectangle of sides /j and or a step-shaped domain, then equations (21) should be written not only at the inner nodes of the grid, but also on the appropriate boundaries. When the boundary condition du/dx = cr u- -v[ is imposed on the side = 0 of the rectangle 0 < < / , a = 1,2, the main idea... 

Let N2 = 2" for the clarity only. The main idea behind the decomposition method is the further successive elimination from the governing equations of the vectors Yj with odd numbers and, after this, with even numbers divisible 2, 4, 8 etc. Other ideas are connected with setting the following equations for j = 2, 4, 6,.. ., N2 — 2, where N2 = 2 ... 

Factorized iteration schemes and ADM. The main idea behind this approach is connected with the equivalence between ADM from the preceding sections and the two-layer iteration scheme... 

The main idea behind classical molecular (or atom) dynamics (MD) is fairly simple. To illustrate this for the relatively simple case of an ensemble of atoms, let us consider a system of N particles, each having mass m, with Cartesian coordinates r,. The motion of this system of particles can be described by solving a set of equations of the type... 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

The main idea of a lattice model is to assume that atomic or molecular entities constituting the system occupy well-defined lattice sites in space. This method is sometimes employed in simulations with the grand canonical ensemble for the simulation of surface electrochemical proceses. The Hamiltonians H of the lattice gas for one and two adsorbed species from which the ttansition probabilities 11 can be calculated have been discussed by Brown et al. (1999). We discuss in some detail MC lattice model simulations applied to the electrochemical double layer and electrochemical formation and growth two-dimensional phases not addressed in the latter review. MC lattice models have also been applied recently to the study the electrox-idation of CO on metals and alloys (Koper et al., 1999), but for reasons of space we do not discuss this topic here. 

Numerous measurements of the conductivity of aqueous solutions performed by the school of Friedrich Kohhansch (1840-1910) and the investigations of Jacobns van t Hoff (1852-1911 Nobel prize, 1901) on the osmotic pressure of solutions led the young Swedish physicist Svante August Arrhenius (1859-1927 Nobel prize, 1903) to establish in 1884 in his thesis the main ideas of his famous theory of electrolytic dissociation of acids, alkalis, and salts in solutions. Despite the sceptitism of some chemists, this theory was generally accepted toward the end of the centnry. 

The main idea of PCA is to approximate the original data, spectra in our case, by a small number (A < r) of factors, discarding the minor factors ... 

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