Dominance order

By the induction on the length and the dominance order of partitions, we immediately get the following... 

Competition between conspecifics of the same sex may either lead to spacing, often as territorial behavior, or dominance orders among animals that stay together, at least temporarily. 

The bulk properties of these temporal dissipative structures also differ from those of the thermodynamic solution. The time average of the concentrations at a given point in space is only a second-order correction (but spatially dependent). The spatial average, as in the stationary dissipative structures, varies even to the dominant order. 

Substituting into equation (12) one then obtains a system of linear equations for xj which incorporate the effect of the imperfection already at the dominant order. By working out these relations one finally arrives at the bifurcation equations for the amplitude of the dominant part of the solution, exi. 

Fig.3. Schematics of the evolution of equilibrium segregation with temperature in alloys with order-segregation competition (a) dominant surface segregation tendency (Langmuir-McLean behaviour), (b) dominant ordering tendency. Signs of enthalpy and entropy of segregation are indicated.

The necessity for a proper averaging over a multitude of conformations remains when the protein is partially ordered. The power of the matrix methods can still be utilized if the dominant ordering interactions are of relatively short range, as they are in helix formation (6). The conformational partition function, Z, for a chain of n residues is formulated as shown in Equation 1. 

Fielder DR (1965) A dominance order for shelter in the spiny lobster Jasus lalandei (H. Milne-Edwards). Behaviour 24 236-245... 

The smallest natural number where the dominance order is not a total order of its partitions is n = 6. Below is the Hasse diagram [206] of the poset of number partitions of M = 6, together with the dominance order ... 

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