scholarly journals SIMPLE MOTION PURSUIT DIFFERENTIAL GAME OF MANY PURSUERS AND ONE EVADER ON CONVEX COMPACT SET

2015 ◽  
Vol 102 (4) ◽  
Author(s):  
I.A. Alias ◽  
R.N.R. Ramli ◽  
G. Ibragimov ◽  
A. Narzullaev
Keyword(s):  
Differential Game ◽  
Convex Compact ◽  
Compact Set ◽  
Simple Motion ◽  
Convex Compact Set

scholarly journals Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry

2021 ◽  
Author(s):  
Andrei Ardentov ◽  
Lev Lokutsievskiy ◽  
Yuri Sachkov
Keyword(s):  
Optimal Control Problems ◽  
Convex Compact ◽  
Control Problems ◽  
Compact Set ◽  
Dimensional Control ◽  
Rolling Ball ◽  
Dynamic Motion ◽  
Convex Compact Set ◽  
Motion Problem ◽  
Arbitrary Convex

We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set Ω. The considered problems are well studied for the case when Ω is a unit disc, but barely studied for arbitrary Ω. We derive extremals to these problems in general case by using machinery of convex trigonometry, which allows us to do this identically and independently on the shape of Ω. The paper describes geodesics in (i)  the Finsler problem on the Lobachevsky hyperbolic plane; (ii) left-invariant sub-Finsler  problems on all unimodular 3D Lie groups (SU(2), SL(2), SE(2), SH(2)); (iii) the problem of rolling ball on a plane with distance function given by Ω;  (iv) a series of "yacht problems" generalizing Euler's elastic problem, Markov-Dubins problem, Reeds-Shepp problem and a new sub-Riemannian problem on SE(2); and (v)  the plane dynamic motion problem.

Measurability problems in a metrizable convex compact set

1972 ◽  
Vol 12 (2) ◽  
pp. 201-203 ◽  
Author(s):  
Jens Peter Reus Christensen
Keyword(s):  
Convex Compact ◽  
Compact Set ◽  
Convex Compact Set

CR-MEROMORPHIC EXTENSION AND THE NONEMBEDDABILITY OF THE ANDREOTTI–ROSSI CR STRUCTURE IN THE PROJECTIVE SPACE

1999 ◽  
Vol 10 (07) ◽  
pp. 897-915 ◽  
Author(s):  
FRÉDÉRIC SARKIS
Keyword(s):  
Type Theorem ◽  
Extension Theorem ◽  
Convex Compact ◽  
Projective Manifold ◽  
Compact Set ◽  
Cr Structure ◽  
Convex Compact Set ◽  
Meromorphic Maps ◽  
Extension Result ◽  
Meromorphic Map

Let [Formula: see text] be a polynomially convex compact set and let M be a (2p-1) dimensional (p ≥ 2) maximally complex bounded scarred C1 submanifold of [Formula: see text], irreducible in the current sense. According to Harvey–Lawson [14] and Chirka [4], there exists a bounded irreducible analytic set [Formula: see text] such that [M]=±d[T]. In this paper, we prove that every CR-meromorphic map carrying M into a projective manifold V extends to a meromorphic map F:T → V. We extend the notion of CR-meromorphic maps to CR submanifolds of [Formula: see text] and give another proof of our extension theorem which extends to the greater codimensional case. We also apply our extension result to prove a Lewy type extension theorem for CR-meromorphic maps, a Hartogs type theorem in [Formula: see text] and the non embedding of the Andreotti–Rossi CR structure in [Formula: see text].

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