Dual Description

If the overlap of the functions is not large, A and a are both nearly 1v 2 and so the equivalent orbitals approximate to the atomic orbitals for the isolated atoms. The complete equivalence of the two configurations 2bonnding and A2 B2 is the simplest example of the dual description of a molecular system. 

This work includes three main contributions to the modeling and computer simulation of porous materials. First, the Dual Description (DD) of Mayagoitia [3] is extended as to self-consistently embody not only size heterogeneity and spatial correlation but also non-uniform connectivity and geometrical restrictions in the network. More precisely, the input of the model will be the size distributions of sites (pore cavities) and bonds (throats) then Co, C and... 

The neighborhood complex of a graph is an example in which this dual description is not useful. On the other hand, the matroid complex is an example in which both descriptions are frequently used, depending on the circumstances. The dual presentation in this case uses the term circuits, which play the role of the minimal nonsimplices, and goes as follows. 

In glassy polymers tire interactions of tire penetrant molecules witli tire polymer matrix differ from one sorjDtion site to anotlier. A limiting description of tire interaction distribution is known under tire name of tire dual-soriDtion model [, 60]. In tliis model, tire concentration of tire penetrant molecules consists of two parts. One obeys Henry s law and tire otlier a Langmuir isotlienn ... 

Silicates in Solutions. The distribution of sdicate species in aqueous sodium sdicate solutions has long been of interest because of the wide variations in properties that these solutions exhibit with different moduli (23—25). Early work led to a dual-nature description of sdicates as solutions composed of hydroxide ions, sodium ions, coUoidal sdicic acid, and so-called crystaHoidal sdica (26). CrystaHoidal sdica was assumed to be analogous to the simple species then thought to be the components of crystalline sdicate compounds. These include charged aggregates of unit sdicate stmctures and sdica (ionic micelles), and weU-defined sdicate anions. 

Figure 3 Mutation of a ligand Asp into Asn in solution and bound to a protein, (a) Thermodynamic cycle, (b) Dual topology description a hybrid ligand with two side chains. Blocks are used to define the hybrid energy function [Eq. (14)]. Only the ligand is shown the environment is either solvent or the solvated protein, (c) Single-topology description.

An interesting description of a commercial tin-plate installation appears in a special issue of the Norelco Reporter Each side of the coated steel strip can be traversed continuously by a separate measuring head, and the results appear on a two-pen strip-chart recorder located near the 4 x 2 x 9-foot dual electronic rack that energizes and regulates the two measuring heads some 100 feet away. 

The amino acids, basic building blocks of proteins, all share this dual acid-base character. See Chapter 13 for a description of the amino acids and their biological chemistry. Organic bases also have a long and varied history as painkillers and narcotics, as our Chemishy and Life Box on the next page describes. 

In the following, after a brief description of the experimental setup and procedures (Section 13.2), we will first focus on the adsorption and on the coverage and composition of the adlayer resulting from adsorption of the respective Cj molecules at a potential in the Hup range as determined by adsorbate stripping experiments (Section 13.3.1). Section 13.3.2 deals with bulk oxidation of the respective reactants and the contribution of the different reaction products to the total reaction current under continuous electrolyte flow, first in potentiodynamic experiments and then in potentiostatic reaction transients, after stepping the potential from 0.16 to 0.6 V, which was chosen as a typical reaction potential. The results are discussed in terms of a mechanism in which, for methanol and formaldehyde oxidation, the commonly used dual-pathway mechanism is extended by the possibility that reaction intermediates can desorb as incomplete oxidation products and also re-adsorb for further oxidation (for the formic acid oxidation mechanism, see [Samjeske and Osawa, 2005 Chen et al., 2006a, b Miki et al., 2004]). 

Due to the presence of low-temperature desorption peak a new desorption site was included to phenomenological model of TPD experiments previously used for the description of the Cu-Na-FER samples [5], The fit of experimental TPD curves was performed in order to obtain adsorption energies and populations for individual site types sites denoted A (A1 pair), B (sites in P channel (A1 at T1 or T2)), C (sites in the M channel and intersection (A1 at T3 or T4)) [3] and D (newly introduced site). The new four-site model was able to reproduce experimental TPD curves (Figure 1). The desorption energy of site D is cu. 82 kJ.mol"1. This value is rather close to desorption energy of 84 kJ.mol"1 found for the site B , however, the desorption entropy obtained for sites B and D are rather different -70 J.K. mol 1 and -130 J.K. mol"1 for sites B and D , respectively. We propose that the desorption site D can be attributed to so-called heterogeneous dual-cation site, where the CO molecule is bonded between monovalent copper ion and potassium cation. The sum of the calculated populations of sites B and D (Figure 2) fits well previously published population of B site for the Cu-Na-FER zeolite [3], Because the population of C type sites was... 

Though it is impossible to formulate a complete mathematical representation of the super-rate burning, it is possible to introduce a simplified description based on a dual-pathway representation of the effects of a shift in stoichiometry. Generalized chemical pathways for both non-catalyzed and catalyzed propellants are shown in Fig. 6.26. The shift toward the stoichiometric ratio causes a substantial increase in the reaction rate in the fizz zone and increases the dark zone temperature, a consequence of which is that the heat flux transferred back from the gas phase to the burning surface increases. 

We can also conclude that if we employ the Primal-Dual interior-point method, the dual SDP formulation provides a more reduced mathematical description of the variational calculation of the 2-RDM than employing the primal SDP formulation. The former formulation also allows us to reach a faster computational solution. On the other hand, the number of floating-point operations and the memory storage of RRSDP do not depend on the primal or dual SDP formulations. 

The application of microdosimetry to medical physics derives from biological models of radiation action (primarily, the Theory of Dual Radiation Action [14]) that explicitly utilize for their predictions a microdosimetric description of the radiation field. Specifically, they concern the following two problems ... 

Brown RG, Marsden CD Cognitive function in Parkinson s disease from description to theory. Trends Neurosci 13 21-29, 1990 Brown RG, Marsden CD Dual task performance and processing resources in normal subjects and patients with Parkinson s disease. Brain 114 215-231, 1991 Brown RP, Frances A, Kocsis JH, et al Psychotic vs. nonpsychotic depression comparison of treatment response. J Nerv Ment Dis 170 635-637, 1982 Brown SA, Irwin M, Schuckit MA Changes in anxiety among abstinent male alcoholics. J Stud Alcohol 52 55-61, 1991... 

Materials and instrumentation. Experiments were performed using a special home-made cell coupled to a dual current supply with a maximum output of 10 V/40 mA. A detailed technical description of this system is published elsewhere (10). H NMR spectra were recorded on a Varian Mercury vx300 instrument at 25 °C. GC analysis was performed on an Interscience GC-8000 gas chromatograph with a 100% dimethylpolysiloxane capillary column (DB-1, 30 m x 0.325 mm). GC conditions isotherm at 105 "C (2 min) ramp at 30 °C min to 280 °C isotherm at 280 °C (5 min). Pentadecane was used as internal standard. The ionic liquid [omim] [BF4] was prepared following a published procedure and dried prior to use (8). All other chemicals were purchased from commercial sources (> 98% pure). 

The nature of the dual vector ( ) can be deduced without using any equation of motion, but the dual 4-vector is a fundamental geometric property in the four dimensions of spacetime. The complete description of the electromagnetic field in 0(3) electrodynamics must therefore involve boosts, rotations, and spacetime translations, meaning that is a fundamental geometric property of spacetime. The unit 4-vector i M is orthogonal to the unit 4-vector... 

In the following Check its, dedicated to illustrate the effect of various window functions and to study the influence of the corresponding parameters, store the processed spectra under the same name, but with ascending processing numbers ( 001001.1R, V)01002.1R,. ..). Use the dual/multiple display of ID WIN-NMR to display and plot the whole series. Do not apply the DC Correction at this stage. Use the Help tool for the mathematical description of the various window functions and for more details of how to use them. 

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