Three-factor model

Existing mathematical models predicting cognitive readiness/performance from sleep/wake history are based on the interaction of three factors. These factors are sleep homeostasis, circadian rhythm, and sleep inertia (12). Three-factor models successfully predict performance effects of acute, total sleep deprivation and... 

The scatter plots are shown in Figure 24. The sums of squares of the residuals for the one, two, and three-factor models are 201,11.53, and 10.64 respectively and the estimated tryptophan concentrations from the test solutions are... 

Figure 3.51. Use of NIR to predict the melt index (MI) of a series of EVA copolymers with differing VA contents. A three-factor model was used to predict In(MI) using the PRESS and the F-statistic criterion (Hansen and Vedula, 1998). Copyright 1998 John Wiley and Sons, Inc. reproduced with permission.

Lin Chen, A Three-Factor Model of the Term Structure of Interest Rates, preprint (Washington Federal Reserve Board, July 1995). 

By contrast with ideal models, practical reactors must consider many factors other than variations in temperature, concentration, and residence time. Practical reactors deviate from the three idealized models but can be classified into a number of common types. 

The computation just outlined is easily extended to any number of factors. For a system with three factors, for example, a 2 factorial design can be used to determine the parameters for the empirical model described by the following equation... 

Three Parameter Models. Most fluids deviate from the predicted corresponding states values. Thus the acentric factor, CO, was introduced to account for asymmetry in molecular stmcture (79). The acentric factor is defined as the deviation of reduced vapor pressure from 0.1, measured at a reduced temperature of 0.7. In equation form this becomes ... 

The known models for describing retention factor in whole variable space ar e based on three-phase model and containing from three to six par ameters and variety combinations of two independent factors (micelle concentration, volume fraction of organic modifier). When the retention models are comparing or the accuracy of fitting establishing, the closeness of correlation coefficient to 1 and the sum of the squared residuals or the sum of absolute deviations and their relative values is taken into account. A number of problems ar e appear in this case ... 

The collision model of reaction rates just developed can be made quantitative. We can say that the rate constant for a reaction, k, is a product of three factors ... 

Stella and Himmelstein [95,97,99] examined mathematical models of several hypotheses and concluded that an additional condition is necessary for transport parent drug site retention. They identified three factors for successful targeting via prodrugs [95] ... 

Following the scheme given in Fig. 5.1, the influence of three factors a, hand c can be studied on the basis of the linear model... 

For 10-fold 13C labelled retinal, it has been shown that the differences between chemical shifts for polyene chain carbons of the chromophore in its native environment and detergent-solubilised system were small67 Analysis of the environment of the Schiff base has supported the model of stabilisation based on the protonation by a complex counterion. Three factors were responsible for the excessive positive charge in polyene (i) electronegative nitrogen, (ii) protonation and (iii) counterion strength. 

A more detailed analysis using multivariable regression of the ibuprofen data demonstrated that a three-parameter model accurately fit the data (Table 7). The Bonding Index and the Heywood shape factor, a, alone explained 86% of the variation, while the best three-variable model, described in what follows, explained 97% of the variation and included the Bonding Index, the Heywood shape factor, and the powder bed density. All three parameters were statistically significant, as seen in Table 7. Furthermore, the coefficients are qualitatively as... 

The factorial approach to the design of experiments allows all the tests involving several factors to be combined in the calculation of the main effects and their interactions. For a 23 design, there are 3 main effects, 3 two-factor interactions, and 1 three-factor interaction. Yates algorithm can be used to determine the main effects and their interactions (17). The data can also be represented as a multiple linear regression model... 

Output includes node displacements, member end forces and support reactions A three-dimensional model would produce more accurate results hut a two-dimensional analysis normally is sufficient for this type of structure. Members will be subjected to loads from both long and short walls. The member capacity used in the mode or the allowable deformation must be limited to account for the fact that the members will be subjected to simultaneous bi-axial loading. A typical capacity reduction factor is 25%. This factor reflects the fact that peak stresses from each direction rarely occur at the same time. 

It was found that fewer PLS factors were needed for process stream samples to yield a decent model. The correlation coefficients were stronger and the SEPs lower in every case. One example is protein add-back r2 = 0.891 using four PLS factors, whereas the process-stream samples enabled a three-factor PLS model to be generated with an r2 = 0.915. The respective SEP for each model was add-back = 4.351 process = 2.343. This paper seems to confirm the idea that samples taken during a process are more representative of that process. 

The Aspt, Ace-K, Caf and Na-Benz contents were determined by using spectra fort he mixtures studied above were registered in the spectral range 190-300 nm using 0.1 N HjPO solution as a reference and the absorbance values were recorded every 5 nm from these spectra. By apphcation of the PLS-2 algorithm a model was optimized using three factors for Aspt, Ace-K, Caf and Na-Benz calculated by analysis of the optimized PLS-2 model. 

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