Linear General

In polymer processing, the mathematical models are by and large deterministic (as are the processes), generally transport based, either steady (continuous process, except when dynamic models for control purposes are needed) or unsteady (cyclic process), linear generally only to a first approximation, and distributed parameter (although when the process is broken into small, finite elements, locally lumped-parameter models are used). 

Differently from the previous case (CO-Mb), the reaction path associated to such a tautomeric process may be less intuitive. For this reason we calculated the intrinsic reaction coordinate (IRC) [61] in vacuum which provided a linear generalized degree... 

Th and Th, e.g., would tend to cancel each other out. Because of variations in seawater chemistry over time, it is not likely that the assumption of constant Nq, or of the initial ratios, is strictly true, but the linearity generally observed in In N versus z plots indicates that it is a sufficiently good approximation that valid estimates of average accretion rates over long time intervals can be obtained. 

Linear, Generalized Linear, and Nonlinear Mixed Effects Models... 

LINEAR, GENERALIZED LINEAR, AND NONLINEAR MIXED EFFECTS MODELS... 

When reliable O are available, the adjustable parameters may be obtained from Equation (3.27), but the derivation is more involved than the simpler case of uniform variance. More information regarding the full derivation is provided by Press et al. [10]. The remainder of this section focuses on regression analyses with the assumption of constant variance, with separate discussions of simple linear, generalized multiple linear, and nonlinear regression. 

Sawaya N.W. and Grossmann I.E. 2004. A cutting plane method for solving linear-generalized disjunctive programming problems (submitted). 

In relation to Methods IV and V, the instantaneous MMDs were simulated with the aim of calculating the (noise-free) calibrations log M V) and log M (V) (Fig. IB). These functions were obtained from the (noise-free or non-truncated) mass chromatogram in order to illustrate their true shapes in the complete range of the measured chromatogram. The resulting ad hoc calibrations are non-linear, generally less steep than log M(V), and close to the effective linear calibration log Af(V)liv (Fig. IB). 

In an isothermal, isobaric, isotropic, and single-phase system of components, the flux equations for neutral particles can be expressed in a linearized general formulation as ... 

In the area of hydroformylation of linear higher alkenes, applications as detergent alcohol dominate (mainly C12-C16) [76]. The market size for detergent alcohols was ca. 1200 kt/a in 1995 [73]. Linearity (generally in the range 40- 100%) relates to the need for detergency (micelles) and... 

The wear coefficient varies with slurry concentration. Figure 5 shows the variation of the wear coefficient with slurry concentration for POM. A linear relation exists for 2 N and slurry concentrations below 600 g/1, whereas at a normal load of 0.5 N the relation is clearly non-linear. Generally, the erosive wear rate increases with an increase in particle concentration (or the number of particles). However, for polymers, this linear relation of erosive wear with particle concentration is less obvious [9-11]. 

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