Integral representation of dominated operations on spaces of continuous vector fields

1967 ◽  
Vol 173 (2) ◽  
pp. 147-180 ◽  
Author(s):  
N. Dinculeanu
Keyword(s):  
Integral Representation ◽  
Vector Fields ◽  
Continuous Vector

scholarly journals Quasi-Continuous Vector Fields on RCD Spaces

2020 ◽  
Vol 54 (1) ◽  
pp. 183-211
Author(s):  
Clément Debin ◽  
Nicola Gigli ◽  
Enrico Pasqualetto
Keyword(s):  
Vector Fields ◽  
Continuous Vector

MULTIPERIODIC SOLUTIONS OF SECOND-ORDER SYSTEMS WITH DIFFERENTIATION OPERATOR ON THE LYAPUNOV'S VECTOR FIELD

2020 ◽  
Vol 69 (1) ◽  
pp. 155-163
Author(s):  
B.Zh. Omarova ◽  
Keyword(s):  
Integral Representation ◽  
Vector Fields ◽  
Homogeneous System ◽  
Differentiation Operator ◽  
Second Order ◽  
Inhomogeneous System ◽  
Representation Of Solutions ◽  
Real Analytic ◽  
Time Variables ◽  
Second Order Systems

The problem of the existence and integral representation of a unique multiperiodic solution of a second-order linear inhomogeneous system with constant coefficients and a differentiation operator on the direction of the main diagonal of the space of time variables and of the vector fields in the form of Lyapunov systems with respect to space variables were considered. The multiperiodicity of zeros of this operator and the condition for the absence of a nonzero multiperiodic and real-analytic solution of the homogeneous system corresponding to the given system are established. An integral representation of solutions of an inhomogeneous linear autonomous system that multiperiodic in time variables and realanalytic in space variables is obtained. The existence theorem of a unique multiperiodic in time variables and real-analytic in space variables solutions of the original linear system in terms of the Green's function under sufficiently general conditions is substantiated.

N-DIMENSIONAL CANONICAL CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 239-258 ◽  
Author(s):  
LJ. KOCAREV ◽  
LJ. KARADZINOV ◽  
L. O. CHUA
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Measure Zero ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Continuous Vector ◽  
Linear Vector ◽  
Linear Dynamic ◽  
Canonical Chua’S Circuit

In this paper we present an n-dimensional canonical piecewise-linear electrical circuit. It contains 2n two-terminal elements: n linear dynamic elements (capacitors and inductors), n - 1 linear resistors and one nonlinear (piecewise-linear) resistor. This circuit can realize any prescribed eigenvalue pattern, except for a set of measure zero, associated with (i) any n-dimensional two-region continuous piecewise-linear vector fields and (ii) any n-dimensional three-region symmetric (with respect to the origin) piecewise-linear continuous vector fields. We also proved a theorem that specifies the conditions for a vector field, realized with our canonical circuit, to have two or three equilibrium points.

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