Jensen notation

The Bravais or space lattice does not distinguish between different types of local atomic environments. For example, neighbouring aluminium and silicon both take the same face-centred cubic Bravais lattice, designated cF, even though one is a close-packed twelve-fold coordinated metal, the other 

Crystal system Lattice symbols Relation between cell edges and angles Characteristic symmetry 

Triclinic aP a b c 0 90 1 -fold (identity or inversion) symmetry only 

Cubic cP, cl, cF = b = -0 = = 90° Four 3-fold axes along body diagonals 

There is sometimes ambiguity as to which nearest neighbours to assign to the local coordination polyhedron. This is illustrated by the two different puckered layer structure types which are displayed by the most stable polymorphs of phosphorus and arsenic respectively. They may both be thought of as resulting from the breaking of three bonds about each atom on a simple cubic lattice as shown in Fig. 1.5. The layers then distort Black 

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Local coordination polyhedra the Jensen notation 7 Table 1.2 The fourteen Bravais lattices in three dimensions... 

The notation of Colored Petri Net (CPN) (Jensen and Rozenberg 1991) introduces the notion of token types, namely tokens are differentiated by colors, which may contain arbitrary data values. Each place has an associated type determining the kind of data that the place may contain. A nonhierarchical CPN is defined by the 9tuple (E, P, T, A, N, C, G,E, /) where ... 

Approximate-level scheme for protons. First column level energies of the harmonic oscillator. Second column interpolated level scheme between the harmonic oscillator and square well solutions. Third column splitting of levels after introducing the spin-orbit interaction. Notation of states (n +1)//, where n is the radial quantum number (n = 0,1,2,...]. Fourth column the number of protons on the indicated subshell Nj). Fifth column full number of protons up to the level indicated (XNj). The magic numbers are indicated in frames. Sixth column parity of the level, (-1). The level scheme for neutrons is similar in that case Nj refers to neutrons (Based on Goeppert Mayer and Jensen 1965]... 

The PLSR method to be presented here is formally defined as a predictive two-block regression method based on estimated latent variables. The present orthogonalized multifactor version [2] was primarily developed by Svante Wold. The so-called PLSl version of this PLSR (one single analyte) will be described in detail in this chapter. It was first applied successfully to near-infrared (NIR) data by Martens and Jensen [3], and their algorithmic representation will be used here, although with a more recent notation. 

In this paper, a BN (Jensen, Finn V, 2001) is employed to represent the system structure of space mechanisms. A general BN consists of nodes, and directed arcs between some nodes (Li J, Wilson AG, 2007). Each node A) is a response with random variable. If there is a directed arc from X, to Xj, Xi is called a parent of Xj. There may be no or more than one parents for each node. An arc characterizes the probabilistic dependency of a node on its parent nodes. That is, depending on the values a node s parents take on, the conditional probability distribution of the node may be different. In this paper, a BN is employed to represent the cause-and-effect failure relationship among elements of space mechanisms, in which nodes are components responses of the space mechanisms. Since components are at different levels, a slightly different notation is adopted for nodes. 

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