Normalization, definition

Figure 1.25 shows the boundary layer that develops over a flat plate placed in, and aligned parallel to, the fluid having a uniform velocity upstream of the plate. Flow over the wall of a pipe or tube is similar but eventually the boundary layer reaches the centre-line. Although most of the change in the velocity component vx parallel to the wall takes place over a short distance from the wall, it does continue to rise and tends gradually to the value vx in the fluid distant from the wall (the free stream). Consequently, if a boundary layer thickness is to be defined it has to be done in some arbitrary but useful way. The normal definition of the boundary layer thickness is that it is the distance from the solid boundary to the location where vx has risen to 99 per cent of the free stream velocity v . The locus of such points is shown in Figure 1.25. It should be appreciated that this is a time averaged distance the thickness of the boundary layer fluctuates owing to the velocity fluctuations.

Chemical reactivity has many different names, such as reactive materials, runaway reaction hazards, instability, thermal sensitivity, and incompatibility. Flammability, toxicity, and corrosion are also forms of reactivity. Since these topics are addressed elsewhere, our focus here will be on those reactions that fall outside the normal definitions of flammable or toxic and that generally occur far more rapidly than corrosion. 

Okuda, T., Cai, Z., Yang, S., Lenny, N., Lyu, C., van Deursen, J., Harada, H. and Downing, J. (1998) Expression of a knocked-in AMLl-ETO leukemia gene inhibits the establishment of normal definitive hematopoiesis and directly generates dysplastic hematopoietic progenitors. 

Looking at the definition of the R-group, the inventor was content to apply a normal definition of Ci 6 alkyl. Confirming his hunch by looking up the definition of alkyl in some standard texts, he was confident that his compound of interest was clearly outside the scope of the claimed genus.33 However, had he taken the time to read the entire patent specification, he would have learned that the patentee as lexicographer had a different definition in mind. In the definitions part of the specification, the following definition for Q.6 alkyl was provided ... 

The time-independent probability for the occurrence of a particular collision process is represented by the corresponding scattering cross section. It characterises the scattering process and is well defined in most scattering experiments. There are some situations when a time-dependent probability must be considered and the normal definition of a scattering cross section is not applicable. 

It should be noted that the normal definition of Reynolds number is inadequate since it refers to some characteristic velocity and length of the mean flow. Alternatively, the microscale Reynolds number and the macroscale Reynolds number are used ... 

A. Par ailleurs A est henselien, done Bi tant integre est necessairement local. Par hypothese B est net sur A, done (chap.V Th.1 cor.l), B est quotient d une A-algebre etale C, que l on peut prendre locale, puisque B est local. Comme A est strictement henselien, le morphisme A - C est necessairement un isomorphisme, par suite le morphisme A — Bi est surjectif done le morphisme A/p — B est bijectif, et a/p est normal. Definition 1.— Soit A local, noetherien, reduit, de dimension 1. Si les conditions prece— dentes sont realisees on dit que la singularity de A est non cuspidale. 

Aerosol particles in the atmosphere usually carry with them some moisture. The amount of water associated with the aerosol depends on the relative humidity. Increasing the relative humidity condenses more water onto the particles, until finally, when the vapor pressure of water exceeds the saturation point, a certain number of particles grows into fog or cloud droplets. Meterologists call these particles condensation nuclei, or simply nuclei. Fogs and clouds are treated as separate systems and are not included in the normal definition of the atmospheric aerosol, even though they represent an assembly of particles suspended in air and thus constitute an atmospheric colloid. The smoothness of the transition from an assembly of aerosol particles to one of cloud elements makes it difficult to define a boundary line between both colloids. Due to the overlap of size ranges of the particles in both systems, any division will be rather arbitrary. 

Here the first term on the right of the equals sign represents the useful work done by the pump increasing the pressure, elevation, or velocity of the fluid. The second represents the useless work done in heating either the fluid or the surroundings. The normal definition of pump efficiency is... 

Mo) ions have indicated that the onset of the continuum is at the base of the metal K-absorption edges, and therefore at a lower energy than the normal definition of the edge position.Clearly care must be taken in considerations of absorption edge positions, but in some cases they may provide an indication of oxidation... 

Another departure from the normal definition of variables occurs when two first-order differential equations are combined by division into a single ODE. 

For liquids the situation is different. If we rewrite Eq. 12.30 using the normal definition of activity for the liquid phase, and considering the reaction -butane isobutane, we will have... 

The direction of the fundamental-mode transverse electric field within the core of an arbitrary step-profile fiber is shown schematically in Fig. 12-6. When the nonuniformity of Fig. 18-1 (c) is included, the symmetry of the circular fiber is broken. However, since the nonuniformity is infinitesimal, it is clear that the two fundamentalmode patterns are oriented as shown in Fig. 18-8. The propagation constants associated with Figs. 18-8(a) and 18-8(b) are, and by, respectively. If we substitute Eq. (18-64) into Eq. (18-63) and recall the normalization definition in Table 11-1, page 230, we obtain... 

If we substitute Eqs. (23-4) and (23-10) together with the normalization definition of Table 13-2, page 292, into Eq. (23-11), the fundamental-mode attenuation coefficient for an arbitrary, weakly guiding fiber is given by... 

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