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Various augmented Lyapunov Krasovskii functionals (LKFs) with triple-integral terms are constructed for the two delay subintervals.

The diffusion and reaction terms are constructed using the flame speed and flame thickness, and the flame speed is taken as a function of the local stretch rate to incorporate the stretch effect.

In the mass fraction (MF) formulation, only the reaction rate for the progress variable is stored, and mean species source terms are constructed to relax the mean mass fractions towards the value stored in the look-up table.

Schemes of up to fifth order of accuracy in space and time for the two-dimensional compressible Euler equations and the shallow water equations with source terms are constructed.

Those GO terms are constructed in trees under three categories, Biological Process (BP), Molecular Function (MF), and Cellular Component (CC).

Prony series models with various terms were constructed for each mixture type; the parameters of these Prony series models were all positive.

A new Lyapunov Krasovskii functional (LKF) with some new terms is constructed, which can use more information of the activation function at the dynamic partitioning point.

Based on the hybrid uncertain model, the hybrid uncertain dynamic response equilibrium equation, in which different random and interval parameters are simultaneously included in input and output terms, is constructed.

Then, a novel Lyapunov Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived.

A novel Lyapunov-Krasovskii functional decomposing the delay in all integral terms was constructed.

A newly augmented Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed by decomposing integral interval, in which the relationships between the augmented state vectors are fully taken into account.