The quantum deformation of the group of motions of the plane and its Pontryagin dual are described in details. It is shown that the Pontryagin dual is a quantum deformation of the group of transformations of the plane generated by translations and dilations. An explicite expression for the unitary bicharacter describing the Pontryagin duality is found. The Heisenberg commutation relations are w...

This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is curvilinear functional defined by given differential one-form, while the optimal state be determined curve connecting two points, among all curves satisfying some primal feasibility conditions. resulting outcome an invariant Frit...

J. Dugundji Department of Mathematics, University of So. Cal., Los Angeles, CA. 90007, USA Z. Naturforsch. 37 b, 1205-1215 (1982); received April 5, 1982 Chemical Topology, Structure Correlation, Measure of Chemical Similarity, Quality of Syntheses, Shortest Reaction Pathways The principle of minimum chemical distance (PMCD) is derived from the general theory of the BEand R-matrices, and makes ...

An optimal control problem modeling the economic behavior of a representative household is studied. The existence its solution proved, necessary optimality conditions in form Pontryagin–Clarke maximum principle are obtained, and an synthesis constructed. model identified against Russian statistical data. used to analyze consumer crediting Russia influence on economy under COVID-19 pandemic cond...

Abstract A sequentialquadratic Hamiltonian schemefor solving open-loop differential Nash games is proposed and investigated. This method formulated in the framework of Pontryagin maximum principle represents an efficient robust extension successive approximations strategy for optimal control problems. Theoretical results are presented that prove well-posedness scheme, numerical experiments repo...

In this note we announce preliminary results obtained by applying the methodology of Sussmann [4, 5, 6, 7, 8] to the problem studied by Ledzewicz and Schättler (cf. [1, 2]), of deriving high-order necessssary conditions for a minimum in optimal control theory, extending the classical Pontryagin Maximum Principle (abbr. MP) of [3]. The work of [1, 2] uses high-order generalizations of the theore...

<p style='text-indent:20px;'>In this paper, we consider an optimal control problem in which a dynamical system is controlled by nonlinear Caputo fractional state equation. The investigated the case when Pontryagin maximum principle degenerates, that is, it satisfied trivially. Then second order optimality conditions are derived for considered problem.</p>