In isopycnal coordinate ocean models, diapycnal diffusion must be expressed as a nonlinear difference equation. This nonlinear equation is not amenable to traditional implicit methods of solution, but explicit methods typically have a time step limit of order (where is the time step, h is the isopycnal layer thickness, and κ is the diapycnal diffusivity), which cannot generally be satisfied sin...

An intrinsic definition of the index for implicit linear time-varying differential systems is proposed. This definition relies on linear algebraic techniques over the noncommutative principal ideal ring of non-constant linear differential operators (noncommutative transfer function or state-variable representation). Accordance with the existing definition for constant coefficient linear systems...

In air traffic management, pairwise coordination is the ability to achieve separation requirements when conflicting aircraft simultaneously maneuver to solve a conflict. Resolution algorithms are implicitly coordinated if they provide coordinated resolution maneuvers to conflicting aircraft when only surveillance data, e.g., position and velocity vectors, is periodically broadcast by the aircra...

By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of the Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly obtained. The ground state and low-lying excited states are studied in the thermodynamic limit. The ground-state energy in the strong coupling limit is obtained...

This work considers a semi-implicit system ∆, that is, a pair (S, y), where S is a explicit system described by a state representation ẋ(t) = f(t, x(t), u(t)), where x(t) ∈ Rn and u(t) ∈ Rm, which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) ∈ Rl. An input candidate is a set of functions v = (v1, . . . , vs), which may depend on time t, on x, and on u and...

We show how the classic BDD-based technique of implicit state enumeration for FSMs can be generalized to an automata-based approach for implicit state enumeration of FSMs interacting with datapaths of unbounded width. We present experimental results showing that our automata representation of an unbounded width datapath can be 10x more compact than the BDD representation of the corresponding 32...

In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target st...

We examine some ways of proving the Implicit Function Theorem and the Inverse Function Theorem within Bishop's constructive mathematics. Section 2 contains a new, entirely constructive proof of the Implicit Function Theorem. The paper ends with some comments on the application of the Implicit Function Theorem in classical mechanics.