They form a set of evolution equations for a local cobasis which is naturally related to the Almansi deformation tensor.
The propagation of a RZ pulse under the action of fiber dispersion, nonlinearity, and various sources of perturbation is represented in terms of a simple set of evolution equations for its parameters.
The integral method and lubrication theory are used to derive a coupled set of evolution equations for the film thickness, radial and azimuthal flow rates and the surface charge density.
171 (2001) 678] and references cited therein, we introduce a mixture type of the model system that consists of the full Euler equations for the basic conserved variables and an additional set of evolution equations for the problem-dependent material quantities and also the approximate location of the interfaces.
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For the Cauchy problems the topological structure of the solution set of evolution inclusions was examined primarily by Papageorgiou and Shahzad [10], Andres and Pavlǎcková [11], Chen et al. [12] and Papageorgiou and Yannakakis [13] in a Banach space.
For Cauchy problems the topological structure of the solution set of evolution inclusions was examined by Bothe [23], Andres-Pavlackova [24], Gabor-Grudzka [25], and Chen-Wang-Zhou [26] in a Banach space, Bakowska-Gabor [27], and O'Regan [28] in Fréchet spaces.
We use the mappings (mathsf{rules}) and (mathsf{priority}) to associate to a membrane label the set of evolution rules and the priority relation over rules (when this exists): (mathsf{rules}(L_i) = R_i), (mathsf{priority}(L_i)=rho _i), and the projections (mathsf{L}) and (mathsf{w}) which return from a membrane its label and its current multiset, respectively.
Discrete models are usually represented by cellular automata of several forms and variable complexity (grids of cells or groups of cells, in which a finite number of states and a set of evolution and interaction rules are defined).
Generally speaking, one can postulate that all kinds of organisms living today on our planet earth dispose of a set of evolution genes that had become fine-tuned in the course of long periods of past evolution for their evolutionary functions.
