Multimode, definition

Give definitions for the following maximum, minimum, optimum, unimodal, multimodal, local optimum, global optimum, continuous, discrete, constraint, equality constraint, inequality constraint, lower bound, upper bound, natural constraint, artificial constraint, degree of freedom, feasible region, nonfeasible region, factor tolerance. 

From the wealth of observations on catalyst preformation and catalyst aging reported in the literature it is extremely difficult to draw definitive conclusions about the nature of the reactions which occur during this process step. Nevertheless, it is rather evident that contrary to metallocene catalysts, the majority of Nd-based catalyst systems do not exhibit the features of single site catalysts (SSC). As bimodal and multimodal MMDs are observed for Nd-based catalyst systems various active species (or active sites) are present... 

An important feature of atmospheric aerosol size distributions is their multimodal character. Mass distributions, measured in urban centers, are characterized by three modes with a minimum between 1.0 and 3 The size range of particles larger than the minimum (supermicron particles) is termed coarse, while the smaller particles are called fine. The three modes present in the mass distribution of Figure 7.14 correspond to the nuclei mode (particles below 0.1 /zm), accumulation mode (0.1 < Dp < /.tm), and coarse mode Dp > )Lim) (Whitby and Sverdrup, 1980). Thus the fine particles include both accumulation and nuclei modes. The boundaries between these sections are not precise (recall in Chapter 2 that we divided fine and coarse modes at 2.5 /zm diameter). Note that our definition of modes has been based on the mass (or volume distribution). The location of modes may be different if they are based on the number or surface distribution. 

Give definitions for the following terms unimodal multimodal replication of experiments factor level coding of factors local and global optimum randomization screening designs factor effects. 

Without frequency-selective elements inside the laser resonator, the laser generally oscillates simultaneously on many resonator modes within the spectral gain profile of the active medium (Vol. 1, Sect. 5.3). In this multimode operation no definite phase relations exist between the different oscillating modes, and the laser output equals the sum intensities L of all oscillating modes, which are more... 

For instance, in order to increase the polymer concentration of polymer latexes, multimodal and/or broad PSDs may be required [47]. It must also be stressed that the PSD and the polymerization rates are coupled in many heterogeneous polymerizations. This leads to the definition of the fifth classical control problem, which is the control of some features of the PSD of the final polymer material. 

On a multimode fiber, with fiber parameter F oo, virtually all modes satisfy rij = 1, and thus P, of Eq. (20-37) varies with the number of modes. We show in Section 36-13 that M = F V2 for the step-profile fiber, and, from the definition of F inside the back cover, is proportional to 0, where 6 is the complementary critical angle. Apart from... 

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