The basic idea

The dashed line encloses the internal reactions, labeled J through 75 the processes J, Ji, and J% are transport fluxes that transport material into or out of the 

The GRIND method was developed with the aim of extracting the most relevant information from a MIF and compressing it into a handful of variables. The requirements were challenging  

In greater detail, the procedure for obtaining the GRIND involves three steps, as shown in Fig. 6.1. 

The aim of this work is the preparation of photoconductive compounds with high carrier mobilities. There are a number of indications that the carrier mobility, i.e. the speed of the charge particles within the sample, depends on the geometric arrangement of the photoconductive moieties. 

At room temperature for instance, the mobility in single crystals of aromatic compounds like anthracene or perylene is very high, i.e. in the range of 10 cm A s [5], In amorphous polymers the carrier mobilities are orders of magnitude smaller and typical values are in the range of 10 and 10 cm A s [6]. 

With this in mind we started the synthesis of a series of liquid crystalline model com-poimds and polymers in which the side groups possess both mesogenic and photoconductive properties. 

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The basic idea is to extract firstly "sure" contours contour segment extremities are identified by studying the local neighbourhood of each pixel. The aim of closing contours algorithm is to find the best path between two points that are extremities of the gap to fulfil. 

Some methods that paitly cope with the above mentioned problem have been proposed in the literature. The subject has been treated in areas like Cheraometrics, Econometrics etc, giving rise for example to the methods Partial Least Squares, PLS, Ridge Regression, RR, and Principal Component Regression, PCR [2]. In this work we have chosen to illustrate the multivariable approach using PCR as our regression tool, mainly because it has a relatively easy interpretation. The basic idea of PCR is described below. 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

Although it is now somewhat dated, this book provides one of the best treatments of the Hartree-Fock approximation and the basic ideas involved in evaluating the correlation energy. An especially valuable feature of this book is that much attention is given to how these methods are actually implemented. 

Scaiming probe microscopies have become the most conspicuous surface analysis tecimiques since their invention in the mid-1980s and the awarding of the 1986 Nobel Prize in Physics [71, 72]- The basic idea behind these tecimiques is to move an extremely fine tip close to a surface and to monitor a signal as a fiinction of the tip s position above the surface. The tip is moved with the use of piezoelectric materials, which can control the position of a tip to a sub-Angstrom accuracy, while a signal is measured that is indicative of the surface topography. These tecimiques are described in detail in section BI.20. 

The experimental data and arguments by Trassatti [25] show that at the PZC, the water dipole contribution to the potential drop across the interface is relatively small, varying from about 0 V for An to about 0.2 V for In and Cd. For transition metals, values as high as 0.4 V are suggested. The basic idea of water clusters on the electrode surface dissociating as the electric field is increased has also been supported by in situ Fourier transfomr infrared (FTIR) studies [26], and this model also underlies more recent statistical mechanical studies [27]. 

The treatment of equilibrium solvation effects in condensed-phase kmetics on the basis of TST has a long history and the literature on this topic is extensive. As the basic ideas can be found m most physical chemistry textbooks and excellent reviews and monographs on more advanced aspects are available (see, for example, the recent review article by Tnihlar et al [6] and references therein), the following presentation will be brief and far from providing a complete picture. 

It turns out that one cannot propagate Y using standard numerical methods because Y blows up whenever g is zero. To circumvent this one must propagate Y by invariant imbedding . The basic idea here is to construct a propagator Y which satisfies... 

The basic ideas underlying most, if not all, of tire energy-difference methods follow... 

An alternative, and closely related, approach is the augmented Hessian method [25]. The basic idea is to interpolate between the steepest descent method far from the minimum, and the Newton-Raphson method close to the minimum. This is done by adding to the Hessian a constant shift matrix which depends on the magnitude of the gradient. Far from the solution the gradient is large and, consequently, so is the shift d. One... 

To demonstrate the basic ideas of molecular dynamics calculations, we shall first examine its application to adiabatic systems. The theory of vibronic coupling and non-adiabatic effects will then be discussed to define the sorts of processes in which we are interested. The complications added to dynamics calculations by these effects will then be considered. Some details of the mathematical formalism are included in appendices. Finally, examples will be given of direct dynamics studies that show how well the systems of interest can at present be treated. 

The basic idea of NMA is to expand the potential energy function U(x) in a Taylor series expansion around a point Xq where the gradient of the potential vanishes ([Case 1996]). If third and higher-order derivatives are ignored, the dynamics of the system can be described in terms of the normal mode directions and frequencies Qj and Ui which satisfy ... 

The basic idea of specifying the priority of the atoms around a stereocenter in order to obtain a stereodescriptor is also incorporated into the most widespread structure representations, the Molfile and SMILES (see Sections 2.3.3, and 2.4.6). 

The atom type tlefin es the chemical eii viroiini eii t of an atom. The basic idea is that not all carbon atoms in molecules are the same and can be distinguished by the following ... 

The basic idea of mixed model in MIXDO/3 is the same as that used for CNDO and INDO and corrects appears in the... 

The literature of surface diffusion is now quite extensive. A review of the basic ideas, with reference to many of the earlier papers, is given by Dacey [44], and a good selection of references including more recent work can be found in Aris [45]... 

Note that different spreadsheets and different versions of the same spreadsheet vary in the details of the calculation but that the basic idea for all is to cany out the calculation for the top cell and fill in the remaining cells in the same column with the mouse—a very convenient technique for simple calculations on large data sets. Consult the Help section of your spreadsheet for specific details. 

The basic idea of symmetry analysis is that any basis of orbitals, displacements, rotations, etc. transforms either as one of the irreducible representations or as a direct sum (reducible) representation. Symmetry tools are used to first determine how the basis transforms under action of the symmetry operations. They are then used to decompose the resultant representations into their irreducible components. 

The basic idea of mixed model in MINDO/3 is the same as that used for CNDO and INDO and corrects Y b, which appears in the core Hamiltonian. Because the algorithm in calculating the Coulomb interaction in MINDO/3 is different from that used in CNDO and INDO, the procedure to correct Y b is also different from that in CNDO and INDO. 

The basic ideas of thermoelectricity have been known for nearly two centuries, but until well after the Second World War the primary use was for temperature measurement (qv) using metallic wires. Then, upon improvements in semiconductor technology, thermoelectric power generation and refrigeration came under serious consideration. 

Rules. Rules, first pioneered by early appHcations such as Mycin and Rl, are probably the most common form of representation used in knowledge-based systems. The basic idea of rule-based representation is simple. Pieces of knowledge are represented as IE—THEN rules. IE—THEN rules are essentially association pairs, specifying that IE certain preconditions are met, THEN certain fact(s) can be concluded. The preconditions are referred to as the left-hand side (LHS) of the rule, while the conclusions are referred to as the right-hand side (RHS). In simple rule-based systems, both the... 

Some industrial applications involve the concept outlined here. The basic idea is to test whether or not a group of obseiwations follows a preconceived distribution. In the case cited, the distribution is uniform i.e., each face value should tend to occur with the same frequency. 

Decoupling Control Systems Decoupling control systems provide an alternative approach for reducing control loop interactions. The basic idea is to use additional controllers called decouplers to compensate for undesirable process interactions. 

The basic idea behind the Euler method is to set the change in w per increment of time as... 

The basic idea of adopting to such a control system is... 

The use of a reactor in series with the ctipacitors w ill reduce the harmonic effects in a power network, as well as their effect on other circuits in the vicinity, such as a telecommunication network (see also Section 23.1 1 and Example 23.4). The choice of reactance should be such that it W ill provide the required detuning by resonating below the required harmonic, to provide a least impedance path for that harmonic and filter it out from the circuit. The basic idea of a filter circuit is to make it respond to the current of one frequency and reject all other frequency components. At power frequency, the circuit should act as a capacitive load and improve the p.f. of the system. For the fifth harmonic, for instance, it should resonate below X 50 Hz for a 50 Hz system, say at around 200-220 Hz, to avoid excessive charging voltages w hich may lead to... 

We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

The main experimental techniques used to study the failure processes at the scale of a chain have involved the use of deuterated polymers, particularly copolymers, at the interface and the measurement of the amounts of the deuterated copolymers at each of the fracture surfaces. The presence and quantity of the deuterated copolymer has typically been measured using forward recoil ion scattering (FRES) or secondary ion mass spectroscopy (SIMS). The technique was originally used in a study of the effects of placing polystyrene-polymethyl methacrylate (PS-PMMA) block copolymers of total molecular weight of 200,000 Da at an interface between polyphenylene ether (PPE or PPO) and PMMA copolymers [1]. The PS block is miscible in the PPE. The use of copolymers where just the PS block was deuterated and copolymers where just the PMMA block was deuterated showed that, when the interface was fractured, the copolymer molecules all broke close to their junction points The basic idea of this technique is shown in Fig, I. 

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