Generalized coordinates terms Links

In this section, we begin the description of Brownian motion in terms of stochastic process. Here, we establish the link between stochastic processes and diffusion equations by giving expressions for the drift velocity and diffusivity of a stochastic process whose probability distribution obeys a desired diffusion equation. The drift velocity vector and diffusivity tensor are defined here as statistical properties of a stochastic process, which are proportional to the first and second moments of random changes in coordinates over a short time period, respectively. In Section VILA, we describe Brownian motion as a random walk of the soft generalized coordinates, and in Section VII.B as a constrained random walk of the Cartesian bead positions. 

In ATP, a chain of three phosphate residues is linked to the 5 -OH group of the nucleoside adenosine (see p. 80). These phosphate residues are termed a, p, and y. The a phosphate is bound to ribose by a phosphoric add ester bond. The linkages between the three phosphate residues, on the other hand, involve much more unstable phosphoric add anhydride bonds. The active coenzyme is in fact generally a complex of ATP with an Mg "" ion, which is coordinatively bound to the a and p phosphates (Mg "" ATP ). However, the term ATP is usually used for the sake of simplicity. 

In general terms, both steric effects and electronic factors are expected to play a role in determinating the reactivity of square-planar platinum complexes. The presence of planar amine ligands in cis- or /ran.y-Pt(anion )2 complexes and their orientation with respect to the coordination plane, as well as their substituents, can reduce the rates of DNA binding or thio binding compared to aliphatic ammine and amine complexes. Especially, substituents close to the coordination site should be expected to slow down axial substitution reactions at Pt. As there is now little doubt that DNA platina-tion is a key event (or THE key event) in the mechanism of action of platinum anticancer drugs, attention to the process of formation of the major adduct (GG) as an intrastrand cross-link between N(7) atoms of two adjacent guanine (G) residues, will remain important. 

Solid phosphates show a huge variety of crystal structures, and it is not practical to classify them in terms of structural types as is done with simple oxides, halides, etc. However, some general classes of metal phosphate structures will be considered three-dimensional frameworks of linked phosphate tetrahedra and tetrahedrally or octahedrally coordinated cations, layered phosphates, and phosphate glasses. In all of these materials the size and topology of pores within the structure are of importance, as these determine the ability of ions and molecules to move within the structure, giving rise to useful ion exchange, ionic condnction, or catalytic properties. Ion exchange can also be nsed to modify the properties of the host network, for example, the nonlinear optical behavior of potassium titanyl phosphate (KTP) derivatives. 

It is often necessary to focus on the surroundings of a particular atom or ion in a solid and, for this purpose, structures drawn in terms of polyhedra are helpful. The polyhedra selected are generally metal-nonmetal coordination polyhedra. These are composed of a central metal atom surrounded by nonmetal atoms. By reducing the nonmetal atoms to points and then joining the points by lines one is able to construct the polyhedral shape. These polyhedra are then linked together to build up the complete structure. This representation has aheady been used as a way of describing the structure of diamond (Figure 5.20). 

Synchronized supply chain A general vision of having all links in the supply chain producing at the same rate as customer demand. Obstacles include coordination, batch size limitations in production, and inability to share information. However, synchronization is a useful goal as it is likely to provide high levels of customer service at low cost relative to unsynchronized supply chains. The term is somewhat synonymous with a lean supply chain. 

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