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Geometric illustration

The factorial experiments above can be illustrated geometrically as shown in Fig. 5.1. The experimental domain is a cube spanned by the factor axes. The experiments are located at the comers of the cube. [Pg.93]


It will be useful to give a geometrical illustration of the concepts p. and tr included in Eq. (14.33). First, we will construct a special coordinate system. [Pg.1327]

Geometrically illustrated, clusters are continuous regions of a highdimensional space, each of them containing a relatively high density of points (e.g., objects), separated from each other by regions that are relatively empty (low density of points). The belonging of points (objects) to... [Pg.256]

Figure 5.8 shows the power curve for the standard tank configuration geometrically illustrated in Figure 5.5. Since this is a baffled non-vortexing system, equation 5.20 applies. Figure 5.8 shows the power curve for the standard tank configuration geometrically illustrated in Figure 5.5. Since this is a baffled non-vortexing system, equation 5.20 applies.
Computational modeling can be a very powerful tool to understand the structure and dynamics of complex supramolecular assemblies in biological systems. We need to sharpen the definition of the term model somewhat, designating a procedure that allows us to quantitatively predict the physical properties of the system. In that sense, the simple geometrical illustrations in Fig. 1 only qualify if by some means experimentally accessible parameters can be calculated. As an example, a quantitative treatment of DNA bending in the solenoid model would only be possible if beyond the mechanical and charge properties of... [Pg.398]

FIGURE 19 Geometric illustration of PCA. Each spectrum is plotted as a point, whose coordinates are the intensities collected at three different wavelengths. For a given collection of spectra, the first principal component is the direction in space which covers the greatest variation of the corresponding point set. [Pg.394]

Geometrical illustrations of the efficiency of thermodynamic description of the stationary flow distribution problems as applied to the analysis of closed active and open passive hydraulic circuits were already presented in Section 3.2. The geometrical interpretation of the general models for the nonstationary flow distribution in the hydraulic circuit ((23)—(28)) and chemical systems with the set redundant mechanism of reaction ((29)-(34)) is still to be carried out which will obviously require a number of nontrivial problems to be solved. [Pg.38]

A geometric illustration of the possible variations of a synthetic "theme" is shown in Fig.1.4. The different "axes" of the reaction space and the experimental space can for the moment be regarded just as "variations". In the chapters to follow, we shall see that these "axes" can be quantified to describe multidimensional variations. [Pg.13]

Fig.1.4 Geometric illustration of possible variations of a synthetic reaction. Fig.1.4 Geometric illustration of possible variations of a synthetic reaction.
The method of steepest ascent was the first method by which multivariate experiments could be designed with a view to achieving a systematic improvement of the result. It was described by Box and Wilson[l] as early as 1951, and has been much used over the years, especially in industrial experimentation. The underlying principles are simple as can be seen in the following geometric illustration. [Pg.211]

This example is given to show the geometric illustration of a response surface model. [Pg.250]

Examples of designs matrices are given below and the corresponding geometric illustrations of the distribution of the experimental points are given in Fig. 12.3. [Pg.254]

Geometric illustrations are used to show the mathematical aspects of the modelling process. It is shown that these models are related to eigenvalues and eigenvectors. See Fig 15.10 for the definitions. [Pg.356]

The principles behind PLS are simple and easily understood from a geometrical illustration. The method is based upon projections, similar to principal components analysis. The two blocks of variables are given by the matrices X and Y. The following notations will be used ... [Pg.462]

Figure 1.12. Interference of waves scattered by atoms inside the crystal. Geometrical illustration of Bragg s law... Figure 1.12. Interference of waves scattered by atoms inside the crystal. Geometrical illustration of Bragg s law...
The mechanical operations of finding the differential coefficient of one variable with respect to another in any x expression are no more difficult than ordinary algebraic processes. Before de-scribing the practical methods of differentiation it will be instructive to study a geometrical illustration of the process. Fig. 5. [Pg.31]

The following is a geometrical illustration of one meaning of the different terms in Taylor s development. If four curves Pa, Pb, Pc, Pd,... (Fig. 123) have a common p... [Pg.291]

FIGURE 5.3 Geometrical illustration of representative vectors of a curve, a surface, and a volume (a) Gradient U is orthogonal to a curve defined by the scalar u = C and oriented toward the maximum increase in U. (b) The cross product UxVis defined as the vector )Northogonal to U and V whose modulus is equal to the area of the parallelogram (U,V). (c) The mixed product of U,V,W is defined as the dot product of the cross product U.(V x W) and is equal to the volume of the parallelepiped (U,V,W). [Pg.121]

Let us try to find some geometrical illustration of second-rank symmetrical tensors. For this, let us start by considering an equation of a second-degree surface (quadric) AyXjXj = 1, where the J/, = Ajj are coefficients of the quadric. Let us use an orthogonal transformation Eq. (2.5) and express this equation in the new coordinate system... [Pg.28]

Electrocatalysis - Basic Concepts, Theoretical Treatments in Electrocatalysis via DFT-Based Simulations, Fig. 4 Geometrical illustration of (a) a sphere-like nanoparticle, (b) Pt, (c) PImlIt, and (d) PtMcIrNi. (e) The predicted binding enCTgy of oxygen (BEO) against strain, (f) The correlation of BEO and the d-band center of metals, (g) The specific activity versus BEO of Pti,i ... [Pg.400]

In this section, we give a geometric illustration of how the aBB algorithm works by showing how it would locate all of the solutions of a single equation/(x) = 0 over the interval x [0,4]. The function we use for our illustration is... [Pg.282]


See other pages where Geometric illustration is mentioned: [Pg.21]    [Pg.103]    [Pg.36]    [Pg.53]    [Pg.93]    [Pg.150]   


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