Definition nonuniformity

Other less definite yet important effects such as profile changes due to nonlinear refractive index alteration in spatially nonuniform high power beams must be carefully considered. As example, the use of nonidentical liquids and optical paths prior to and in, say, EFISH cells and the usual quartz calibration cells could cause potentially inaccurate x determinations. Obviously these types of considerations are important when precise experimentation to test fine models of molecular behavior are intended, but have not stood as obstacle to uncovering the important general trends in molecular nonlinearity enhancement. 

Equation (83) may also be considered as applicable for a reaction on a nonuniform surface with different stoichiometric numbers of nonequilibrium stages in this case, however, the average stoichiometric number in (83) is determined not by (80), but in a more complicated manner the definition must involve averaging with respect not only to stages, but also to the kinds of the surface sites. 

Since this formulation includes standard values of thermodynamic functions, we shall define the standard state of a particle adsorbed on a nonuniform surface and the standard state of a free site. A uniform surface with one substance adsorbed is at its standard state at coverage 1/2 (Section IV). In order to apply this definition to each site of a nonuniform surface, we shall restate it as follows a surface site is in its standard state if the probability that it is occupied is 1/2 (in other words, if it is occupied and is vacant equally often). 

Line helices (chordal helices) are composed of dimensionless points. A chordal helix is uniform if all points are equivalent such a helix will have a circular cross-section and could be inscribed on a right circular cylinder. A nonuniform chordal helix is regular if it contains motifs repeated in a definite pattern and irregular if the motifs are not so repeated. For our purposes, chordal helices are useful mathematical abstractions. 

Nonuniform Tuning of Mass Spectra (23). 1. Problem Definitions The... 

The primary potential distribution is, by definition, uniform adjacent to the electrode surface, but the current distribution is highly nonuniform (Fig. 10). It is a general characteristic of the primary current distribution that the current density is infinite at the intersection of an electrode and a coplanar insulator. This condition obtains at the periphery of the disk electrode, and the current density becomes infinite at that point. Additional resistance due to kinetic limitations invariably reduces the nonuniformity of the current distribution. In this system the current distribution becomes more uniform as the Wagner number increases. Theoretically, the current distribution is totally uniform as the Wagner number approaches infinity. 

By definition, the area-average term, il/0(z), depends only on the variable, z, and by assumption is considerably larger in magnitude than the nonuniform term, p(r), which depends fully on the three spatial coordinates (x, y, z). 

Vol kenshtein regards these micro-defects as sites for adsorption and is thus free from the basic assumptions of conventional adsorption theories, (1) constancy of number of adsorption centers with temperature and coverage, and (2) immobility of adsorption sites. The presence of defects does not imply that the surface is energetically heterogeneous. Nonuniformity of the surface arises from adsorption sites having different heats of adsorption. Vol kenshtem assumed that only one definite type of defect characterized by the heat of adsorption q is involved in adsorption and that only one adsorbate molecule can be attached to each site. 

Section C.l contains relevant definitions and basic mathematical relations, which will be used in subsequent sections. In Sections C.2, C.3, and C.4 we treat, respectively, the equations for conservation of mass, momentum and energy. The results are shown to be equivalent to the relations obtained from the kinetic theory of nonuniform gas mixtures in Section C.5. 

By carefully tuning and matching the probe and the various stages in the transmitter amplifier chain and by allowing for a wide rf bandwidth, it is possible to reduce phase transients (for a definition, see Haeberlen, 1976, Appendix D) to a level where their effect upon the m.p. spectrum becomes insignificant. We therefore confine ourselves here to study by simulations phase errors, nonuniform pulsewidths, and a power droop of the transmitter. 

Before we discuss the viscoelastic properties of nonuniform fractal structures we shall give some basic definitions from the theory of elasticity. 

Nonuniformity of stabilizer distribution in some cases may facilitate the increase of stabilization efficiency [58]. At nonuniform distribution, connected with crystallinity, lowmolecular stabilizers obtained on the basis of the same monomer as protected polymer [74] get definite advantage. 

To conclude our discussion of the conditions for the origination of DS in catalytic systems, we consider the peculiarities of the process in the region of multiplicity of USS. It is known that in a model with a single equation of thermal conductivity (i.e., for e 1), a perturbation of certain amplitude will switch the system over from one USS to another (for details of the conditions and the dynamics of such a transition, see ). What will then happen in the model considered (e < 1) where nonuniform steady states exist along with uniform ones To which of them will the system transit On which parameters do the dynamics of such transitions depend This complicated, versatile problem will be treated here only at the definition level. 

As might be expected, the model leads to a great simplification over the calculations required for molecules with a continuous potential energy function, as it enables the analysis to be confined to binary collisions and permits the definition of a collision frequency. Because there is no molecular interaction between collisions, the velocity distributions of two colliding molecules may be assumed to be re-established by the time a second collision occurs between them. Thus a Maxwellian distribution around the local mass velocity may be postulated for the calculation of the mean frequency of collision and the average momentum and energy transported per collision in the nonuniform state of the liquid. 

Results similar to those in Fig. 17.65a and b are summarized in Fig. 17.66 for the A-passage model of nonuniformity associated with equilateral triangular passages. In this case, the definition of the channel deviation parameter 8C is modified to... 

The above definition of the external potentials coupled to densities of the nonuniformly scaled electronic charges of subsystems in - (A, A g) again implies for the two extreme imiform scaling points [see Fig. 2 and Eq.(44)] ... 

Most chrom graphic beds arc uniform from top to bottom. But one can also conceive oj beds that are nonuniform. In this case also, the definition of the HETP holps, if we define the slope locally. Mathematically, we formulate this in the form of a differential equation ... 

A more formal definition of FMS is that it consists of a group of programmable production machines integrated with automated material-handbng equipment and under the direction of a central controller to produce a variety of parts at nonuniform production rates, batch sizes, and quantities (Jha 1991). 

In more complicated material models we modify oruse further constitutive principles determinism is enlarged for densities (mass concentrations) in mixtures (cf. Sects. 2.4,3.5,4.5), and the definition of fluid used in this principle is in fact the result of constitutive principle of symmetry (see Rem. 30 in Chap. 3). Another constitutive principle is the objectivity (frame indifference) principle. Here it is trivially satisfied because motion is neglected and all quantities are objective (see Sects. 3.2,3.5). In nonuniform systems the influence of neighborhood is described in the principle of local action (cf. Sect. 3.5). In mixtures, the property of mixture invariance [32] may also be used as a constitutive principle [33]. 

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