Variables spacing between

Figure 6.24 Calculation of versus emitter stripe width, 5 with a variable spacing between emitter mesa and the base contact, 5 -...

For systems where there is variable spacing between absorption bands, it would, of course, be necessary to include anhar-monicity corrections. 

Zirconocene dichlorides having the ether functionality at the Cp substituents with variable spacing between the oxygen donor and metal center, such as complexes 603 (n = 2, 4, 6, 8) shown in Scheme 136,435 were prepared to elucidate how that spacing affects their catalytic behavior. The presence of the oxygen atom close to the metal center severely reduced the olefin polymerization activity, whereas such activity increased as the distance between... 

Quahtative description of physical behaviors require that each continuous variable space be quantized. Quantization is typically based on landmark values that are boundary points separating qualitatively distinct regions of continuous values. By using these qualitative quantity descriptions, dynamic relations between variables can be modeled as quahtative equations that represent the struc ture of the system. The... 

Discretization of the governing equations. In this step, the exact partial differential equations to be solved are replaced by approximate algebraic equations written in terms of the nodal values of the dependent variables. Among the numerous discretization methods, finite difference, finite volume, and finite element methods are the most common. Tlxe finite difference method estimates spatial derivatives in terms of the nodal values and spacing between nodes. The governing equations are then written in terms of... 

Here, (7 + V2, 7) represents the region centered between the nodal blocks in question, (7, J) and (7 + 1, J), and A.v is the block spacing along x. The first derivative of concentration, in other words, is taken as the amount the variable changes between two nodal blocks, divided by the block spacing. As Ax becomes smaller, the approximation more closely reflects the actual derivative. 

A fundamental idea in multivariate data analysis is to regard the distance between objects in the variable space as a measure of the similarity of the objects. Distance and similarity are inverse a large distance means a low similarity. Two objects are considered to belong to the same category or to have similar properties if their distance is small. The distance between objects depends on the selected distance definition, the used variables, and on the scaling of the variables. Distance measurements in high-dimensional space are extensions of distance measures in two dimensions (Table 2.3). 

The Mahalanobis distance considers the distribution of the object points in the variable space (as characterized by the covariance matrix) and is independent from the scaling of the variables. The Mahalanobis distance between a pair of objects xA and xB is defined as... 

Principal component analysis (PCA) can be considered as the mother of all methods in multivariate data analysis. The aim of PCA is dimension reduction and PCA is the most frequently applied method for computing linear latent variables (components). PCA can be seen as a method to compute a new coordinate system formed by the latent variables, which is orthogonal, and where only the most informative dimensions are used. Latent variables from PCA optimally represent the distances between the objects in the high-dimensional variable space—remember, the distance of objects is considered as an inverse similarity of the objects. PCA considers all variables and accommodates the total data structure it is a method for exploratory data analysis (unsupervised learning) and can be applied to practical any A-matrix no y-data (properties) are considered and therefore not necessary. 

The direction in a variable space that best preserves the relative distances between the objects is a latent variable which has maximum variance of the scores (these are the projected data values on the latent variable). This direction is called by definition the first principal component (PCI). It is defined by a loading vector... 

Cjk Covariance between variables j and k C is the covariance matrix. d Distance between two objects in multivariate variable space for instance... 

The basal conglomerate unit shows high and variable copper concentrations (142 ppm to >5,000 ppm). The high concentrations are due to the presence of copper oxides in fractures filling spaces between clasts. Copper oxides are observed where white, mineralised dolomite overlies the conglomerate. 

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