Naturalized, defined

If the coupling from and to the waveguide is considered, design-tool interfaees are naturally defined via the spatially discretized optical field. 

Exercise. When Y has r components, which are real, one naturally defines... 

Sources of external potential can be produced in a number of ways in which there is no need for special massive nuclei. As they identify external sources they are classical variables, namely, position coordinates for the sources. There is no quantum dynamics related to them yet. Symmetry constraints can be naturally defined. We formally write He(p a) to distinguish this situation from the standard approach. Since the primacy is given to the electronic wave function, and no Schrodinger equation is available at this point, its existence has to be taken as workinghypotheses. 

Here, we show, in terms of a variational principle of statistical mechanics, that a temperature proportional to Xj-1 can be naturally defined to characterize the first-order feature (fluctuation) around the peak position of a distribution in a state space that is projected onto an appropriate coordinate. It is also shown that the necessity of the so-called prior distribution can naturally result along with its clear physical meaning. Several new features of the linear surprisal theory are uncovered through the analysis. 

The examples shown in Fig. 2 are illustrations of various aspects of the problem in the block copolymer case, shown in Fig. 2a, one of the two sides is typically weaker than the other so the problem can be reduced to the study of the weak side. If the connecting chains are grafted to a non-polymeric substrate or to a crosslinked network on one side, as shown in Fig. 2b, then the problem is more naturally defined. In the case of triblock copolymers, the two sides of the interface are inherently asymmetric through the different architecture of the chain but the reinforcement effect can be treated with the same formalism by de-... 

Clearly, in the subsystem resolution one could also consider all intermediate specifications of the molecular (constrained) equilibria, when only a part of the subsystems remains externally open (characterized by the fixed chemical potentials of a common reservoir) with the remaining, complementary set of subsystems being closed (characterized by the fixed subsystem numbers of electrons) [4,5]. Such mixed representations can be also naturally defined in the CSA approach. We would like to observe, that in the theory of chemical reactivity these partially opened situations do indeed arise, e.g., in the surface reactions, when one adsorbate is opened (chemisorbed) while the other reactant remains externally closed (physisorbed) on the catalyst surface, which acts as the electron reservoir for the reaction. 

We might naturally define the Thiele modulus as In Equation 7.21, but the results for various reaction orders have a common asymptote if we instead defilne... 

For the problems we study, it is impossible to measure or fix the forces acting at the interfaces, and the geometrical approach is the only one that can be used. For instance, as is discussed below, in the contact between a membrane and an inserted peptide, the hydrophobic matching condition naturally defines a displacement mq rather than the shearing force causing that displacement ... 

Euclidean (up to gelation point) to fractal (after it) reduces sharply curing rate of system 2DPP+HCE/DDM. The fact that after the gelation point the plots slope in Fig. 23 is independent on Tcur, indicates unequivocally on spatial (due to diffusion conditions reagents) disorder nature, defining replacement ds on d. ... 

IR spectroscopy is one of the most powerful spectroscopic tools available for the analysis of polymer systems (a.l). IR spectroscopy is molecularly specific with high sensitivity. It is based on the absorption or attenuation by matter of electromagnetic radiation of a specified motion of chemical bonds. Through quantum physics, nature defines the absorption modes, their locations in the frequency spectrum and the amount of energy absorbed by each molecule. The absorbance at a characteristic frequency is a measure of the concentration of the chemical species being probed in the sample. 

Differentiation with respect to the three fields Lo, Li and L2 allows for three susceptibilities to be naturally defined, viz ... 

Perhaps the first demonstration that the PMN respiratory burst activity is critical to normal host defense came from observations of patients with chronic granulomatous disease (CGD). CGD was first established as a clinical entity in 1957 by Brendes, and due to the severity of its nature defined as a fatal disease of childhood. The first understanding of the nature of CGD came in 1966 and 1967 when Holmes was able to show that the neutrophils of CGD patients has normal ingestion but defective intracellular killing with their clinical isolates. In 1967, Holmes revealed that the fundamental abnormality was a complete absence of the neutrophil respiratory burst. The first report of a failure of CGD neutrophils to CL came in 1973 by Stjernholm and has... 

Under the above assumptions there appears a certain vector field naturally defined on the domain D which is described on D by the following system of differential equations x = To( (x), x), where = (x) = —sets the described graph. In small neighbourhoods of the points x and x the integral trajectories of this system tend to x+ as t +oo and to x as t oo (Fig. 71). 

Thus, there was historically concluded how the crystals grow in a perpendicular (normal) direction to its sides at a speed as much lower as the reticular density on tiiat face is higher, naturally defining the crystal face as the reticular plane with maximum density (of its structural points, inhibiting the further advancement of the crystalline form in the normal direction at the plane-face in cause). 

This type of reactor has developed more recertcly. In Europe, the first examples of implementation were designed for tannery and kraft paper pulp water, i,e. less concentrated in S than spent caustic. Operation at atmospheric pressure and at the only temperature allowed by the exothermic nature of the reactions naturally defines longer reaction times. However, the oxidation tanks built for this type of process are less sensitive to the maintenance and corrosion problems which may affect reactors working at high temperature and pressure. 

At a water-solid interface, the position of the interface plane is naturally defined by the surface of the solid. Accordingly, it is no longer possible to define the interface in such a way that the solvent surface excess concentration is zero, as it has been done for the liquid-air interface in Fig. 2. In practice, the situation can be depicted as in Fig. 13. This implies that at the difference of the bulk phase concentrations, a surface excess concentration may very weU be negative. This is the case for water at the interface between an aqueous surfactant solution and a highly polar solid (see Sec. III.C). 

The overall charge balance is expressed as where I is the external current flowing to the eleetrode, Iq the eomponent of I involve in the film growth, and Iq Ihe corrosion current measuring the flux of metal cations released in the solution. Equation (41) must be considered algebraically i.e., a negative (cathodic) value of / will produce film destruction by cathodic reduction and possibly a decrease of the corrosion current. Steady state is naturally defined for a constant film thickness, Iq = 0, and therefore an external current equal to the corrosion current. 

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