Relaxation concept

Anet F A L and O Leary D J 1992 The shielding tensor. Part II. Understanding its strange effects on relaxation Concepts Magn. Reson. 4 35-52... 

The planning objective is to plan global value chain volumes and values. Initially, the value planning model with the objective function to maximize global profit is presented. The objective function also includes a relaxation concept for hard constraints leading to potential plan infeasibility. The future-oriented inventory value planning concept based on volatile raw material prices is presented at the end of the subchapter. 

The value objective function includes also a relaxation concept introduced in the following. 

Automated relaxation already is an integrated feature of newest version of optimization tools that a manually programmed relaxation concept would not be necessary. However, a problem-specific relaxation concept can control, which constraints are subject to relaxation that are suitable to be relaxed from a planners perspective. Therefore, a manually programmed relaxation concept still will be an important element even if optimization tools provide relaxation as standard feature. 

Sales decision variables are the spot sales quantity xsplt, the spot sales turnover ysplt and the respective total sales quantity x pll, / p,l e Is2, teT. Additionally, the partial spot sales quantities xfplt and the approximated partial spot sales turnovers yfplt are required for turnover approximation V / ./ e Is2, j = l..N-l, teT. Relaxation variables Asp m and A ax, / p.l)e Is2, teT are used for hard constraints to relax them in case of model infeasibility as introduced in the relaxation concept in 0. They represent the sales minimum relaxation quantity and sales maximum relaxation quantity required to open the hard constraints. The binary sales relaxation case variable, / pJ e Is2, te T is 1 if the related constraint is relaxed, otherwise it is 0. 8splt is used to count all sales relaxation cases. 

A. Ariza-Castolo, Beyond Excitation NMR Relaxation , Concepts Magn. Reson., A, 2008, 32A, 168. 

Independently of McClare, similar ideas have been put forward by one of us [1, 2] who elaborated on the concept of molecular machines for enzyme catalysis and energy transduction in chemical and biochemical systems. A central point of this concept was founded on the notion of the crucial role of the conformational relaxation of biopolymers in catalyzing biochemical processes. We will consider the application of this relaxation concept to enzymo-logy and bioenergetics in Chapters 4 and 5. We now focus our attention on the general principles of energy transduction by molecular machines. 

What is the principal idea of the relaxation concept This is not simply a question of the conformational relaxation of the substrate-enzyme complex associated with changing the enzyme catalytic activity. The substrate binding to an enzyme active center initiates the conformational relaxation acting as the driving force that pushes the chemical system substrate molecule attached to the catalytic center) along the reaction coordinate. 

According to the relaxation concept [3, 4, 21, 22], a scheme of an enzyme reaction can be written as following... 

The immediate relation to the relaxation concept of enzyme catalysis [3,4, 20, 21] is the theory of rate processes that has been developed by Fain [35]. In this paper. Fain states that the conventional approach to the kinetics of chemical reactions does not hold true for highly ordered macromolecular structures. The traditional approach to the problem implies that all vibrational modes undergo fast relaxation to thermal equilibrium. In the conventional approach to chemical kinetics, the changes in electronic states and nuclear vibration amplitudes were considered separately. Fain has proposed the self-consistent description of simultaneous changes taking place in the... 

I.5. ATP Synthesis from ADP and Pg as Considered from the Viewpoint of the Relaxation Concept of Enzyme Catalysis... 

The results of experiments on acid-base phosphorylation (the pH jump-induced ATP synthesis) performed by isolated or membrane-bound H ATPases could be interpreted on the basis of the relaxation concept of enzyme catalysis. This concept allows us to suggest a model for ATP synthesis consistent with all the experimental data considered above. It has been proposed, in [182-187, 190, 191], that the fast ionization of certain acid... 

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