Description of a class of multivalued differential equations with almost weakly stable trivial solution
Design of unknown input fractional-order observers for fractional-order systems
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the...
Desingularization of a Hyperelliptic Curve Associated with a Doubly Periodic Dirac Potential
Déterminants et intégrales de Fresnel
On présente ici une approche directe et géométrique pour le calcul des déterminants d’opérateurs de type Schrödinger sur un graphe fini. Du calcul de l’intégrale de Fresnel associée, on déduit le déterminant. Le calcul des intégrales de Fresnel est grandement facilité par l’utilisation simultanée du théorème de Fubini et d’une version linéaire du calcul symbolique des opérateurs intégraux de Fourier. On obtient de façon directe une formule générale exprimant le déterminant en terme des conditions...
Determination of coupled sway, roll, and yaw motions of a floating body in regular waves.
Determination of the diffusion operator on an interval
The inverse problem of spectral analysis for the diffusion operator with quasiperiodic boundary conditions is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solvability of the inverse problem are obtained.
Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions in a rational functional form approximating a maximal Lyapunov function that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions for a class of hybrid (piecewise...
Deterministic and stochastic vector differential equations applied in technical systems theory
Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model
An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling...
Deterministic homogenization of parabolic monotone operators with time dependent coefficients.
Deterministic minimax impulse control in finite horizon: the viscosity solution approach
We study here the impulse control minimax problem. We allow the cost functionals and dynamics to be unbounded and hence the value functions can possibly be unbounded. We prove that the value function of the problem is continuous. Moreover, the value function is characterized as the unique viscosity solution of an Isaacs quasi-variational inequality. This problem is in relation with an application in mathematical finance.
Devil's staircase route to chaos in a forced relaxation oscillator
We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameter values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by Kennedy, Krieg and Chua (in [10]) related with the appearance of...
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
Die algebraische Struktur der allgemeinen Kummerschen Transformationen
Die allgemeine Lösung einer zylindrischen Differentialgleichung vierter Ordnung nullten Parameterwertes
Die Anwendung der Quasilinearisation auf gewisse Probleme aus der Theorie der gewöhnlichen Differentialgleichungen 3. Ordnung
Die asymptotischen Formeln für die Lösungen der kanonischen Differentialgleichung 3. Ordnung
Die Determinantenmethode zur Berechnung des charakteristischen Exponenten der endlichen Hillschen Differentialgleichung.
Die Eindeutigkeit des Grenzzyklus bei der Liénardschen Differentialgleichung.
Die Entwicklungen nach Eigenfunktionen irregulärer Eigenwertprobleme mit zerfallenden Randbedingungen. II.