For example, linear equilibrium equations (for example, obtained when using scaled sum combination functions) in principle can be solved analytically in a generic form, thereby obtaining expressions for the equilibrium values in terms of the parameters of the model, but equilibrium equations involving logistic functions cannot be solved in such a manner.
This 'flat top' version of the ITD retains the key feature of height-structured, density-dependent competition for canopy space, and yet is simple enough to be open to mathematical analysis solving for (for example) the equilibrium Z* in monocultures, and the identity of the late-successional dominant species (Strigul et al. in review; Adams et al. in review; Purves et al. unpublished).
It is well known that many nonlinear problems can be reduced to the search for fixed points of nonexpansive mappings, for example, equilibrium problems, saddle point problems, and variational inequalities.
Indeed, thermodynamics has been found to be a challenging topic for many students, and difficulties related to, for example, equilibrium, reversibility, and Gibbs energy have been reported (Banerjee, 1995; Thomas and Schwenz, 1998).
We observed major differences between our model and the general LG model that reflect different properties and constraints of coiled-coil domains, for example, equilibrium frequencies biased to charged and α-helix promoting amino acids.
For example, equilibrium problems, variational inequalities, convex optimization, split feasibility problems, and inclusion problems are equivalent to relatively fixed point problems.
The theory can be applied to solve many problem in real world, for example: equilibrium problems, variational inequalities and optimization problems.
For example, equilibrium problems [1 6, 10 21], variational inequality problems [22 24], variational relation problems [7, 25], optimization problems [22, 26] and the references therein.
The use of more dynamic economic modelling approaches have been identified as the best means of estimating changes in land use, for example, equilibrium and agent-based modelling [116 118].
For example, the equilibrium dissociation constant (KD) of the Fab fragment of bevacizumab (Fab-12) for VEGF-A has been variously reported as 1.8 and 20 nM, as determined by surface plasmon resonance (SPR) technology (Biacore) [ 28, 36], while the binding characteristics of the full bivalent bevacizumab molecule have not been reported.
