In particular, we obtain that the thermal history encodes small fluctuations around the equilibrium population which are exponentially amplified near the glass transition, which mathematically corresponds to the boundary layer of the master equation.
Swapping identities mathematically corresponds to inverting the sign of s and t values.
The k- genomic table T k (G), which mathematically corresponds to a multiset, is defined by equipping the words of D k (G) with their multiplicities, that is, the number of their respective occurrences in G. Let α(G) denote the multiplicity of α and po s G gives the set of positions of α in a genome G (that is, the positions where the first symbol of α is placed).
Mathematically, this corresponds to the delay effect of the infection (see also [10, 13, 14]).
Mathematically, this corresponds to regressing a mapping between the set of observations and the set of actions.
Mathematically, this corresponds to an application of Bayes' rule in which first-order optic flow information is combined with information about the observer's motion provided by proprioceptive and vestibular signals [6].
Mathematically, this corresponds to the minimization of the functional J over a set of feasible, (u 1 t), u 2 t), u 3 t)), strategies on [0, T].
Mathematically, this corresponds to a bifurcation point at which the system moves from a stable fixed point to a limit cycle.
Mathematically, this corresponds to the representation of the solution by a von Neumann series (cf. [79, Chapter 4]), which can be shown to converge as long as the norm of the operator K is smaller than one, ‖ K ‖ < 1.
Mathematically, this corresponds to minimizing the following quantity for each k: (4) Therefore, our strategy of determining each protein complex's functions is determining { Fc jk} which minimizes either Eq. (4) under the constraint (3), with the given values of { Fp ik} and { U ij}.
Based on the constructed model, characteristics of energy flow behavior, i.e., energy-harvesting rate, energy consumption interval, and state probability of energy, are analyzed mathematically, which correspond to different parts of the system.
