Difference equations in the Lie-admissible formulation

Jannussis, A.

doi:10.1007/bf02748346

Cited by 4 publications

(2 citation statements)

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“…The mathematical background of this qualitative analysis is mathematical models of quantum mechanics (soliton-like solutions) and nonequilibrium thermodynamics (self-organization structures [11,17]). In the general case a new (Lie-admissible non-Hermitian isotopic) non-linear model of quantum mechanics with entropy exchange can be used [7,17] (see Appendix for details). A characteristic feature of this investigations is the study of a cooperative self-organization mechanism for the creation of arti®cial life conditions of a biological MMR on the basis of a soft computing for the control of a correlation between a classical level (Newton mechanics) and a quantum macro-physic level (molecular¯uid medium).…”

Section: Qualitative Description Of Mnr Dynamic Problemmentioning

confidence: 99%

“…(A1) the operatorH is and we obtain Schro Èdinger-type equation i2 oWt ot HWt. De®ne Q-derivative as in[7] i2D Q Wt i2WQt À Wt tQ À 1For the operator i2D Q and t the non-canonical Q-commutation relation is feasiblei2D Q t À QtD Q i2 :Schro Èdinger-type equation with Q-derivative with Hamiltonian H Q i2=t ln Q ln 1 À it 2 Q À 1H À Á is non-Hermitian. This equation is the Lie-admissible representation has the form:Thus a modi®ed Schro Èdinger-type equation with Qderivative has the Lie-admissible isotopic representation.For operators (A1)±(A3) we have a symbolic map…”

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confidence: 99%

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Soft computing simulation design of intelligent control systems in micro-nano-robotics and mechatronics

Panfilov¹,

Ulyanov²,

Kurawaki³

et al. 2000

Soft Computing

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The soft computing simulation design methodology of intelligent control system for mobile micro-nanorobots based on modeling of non-linear dissipative equations of robots motion with a minimum entropy production is described. It includes hierarchical levels for description of dynamic behavior of mobile micro-nanorobots based on laws of microphysics, quantum logic of intelligent dynamic behavior of control objects, optimal control of states and dynamic system theory of mechanical motion. The description of a thermodynamic intelligent behavior (with minimum entropy production) of control objects (robots) and their interrelations with Lyapunov stability conditions are introduced. The role of soft computing on the basis of GA with a ®tness function as a minimum entropy production for intelligent control of mobile micro-nano-robots is discussed.

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Section: Qualitative Description Of Mnr Dynamic Problemmentioning

confidence: 99%

mentioning

confidence: 99%