In this paper, the classic straightening out theorem from di erential geometry is used to derive necessary and su cient conditions for locally converting rectangular di erential inclusions to constant rectangular di erential inclusions. Both scalar and coupled di erential inclusions are considered. The results presented in this paper have use in the area of computer aided veri cation of hybrid ...

One of the most important theorems in Ordinary Di↵erential Equations is Picard’s Existence and Uniqueness Theorem for first-order ordinary di↵erential equations. Why is Picard’s Theorem so important? One reason is it can be generalized to establish existence and uniqueness results for higher-order ordinary di↵erential equations and for systems of di↵erential equations. Another is that it is a g...

This work investigates the problem of state estimation for singular stochastic di®erential systems. A Kalman-Bucy-like ̄lter is proposed, based on a suitable decomposition of the descriptor vector into two components. The ̄rst one is expressed as a function of the observation, and therefore does not need to be estimated, while the second component is described by a regular linear stochastic sys...

The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ productivities does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show ...

There are three di erent actions of the unimodular Lie group SL on a two dimensional space In every case we show how an ordinary di erential equation admitting SL as a symmetry group can be reduced in order by three and the solution recovered from that of the reduced equation via a pair of quadratures and the solution to a linear second order equation A particular example is the Chazy equation ...

in this paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...

Coronal mass ejections (CMEs) can have a profound impact on the interplanetary medium and the near-earth environment. We discuss the feasibility of detecting coronal mass ejections at radio wavelengths with a groundbased instrument. In particular, we explore the possibility that a radio telescope employing Fourier synthesis imaging techniques can detect thermal bremsstrahlung emission from CMEs...

I. Positive energy representations of LSU(N) ................................................................. 477 II. Local loop groups and their von Neumann algebras ................................................. 491 III. The basic ordinary di€erential equation ..................................................................... 505 IV. Vector and dual vector primary ®elds ..................

We study a coupled uid-structure system. The structure corresponds to a part of the boundary of a domain containing an incompressible viscous uid. The structure displacement is modeled by an ordinary di erential equation. We prove the local null controllability of the system when the control acts on a xed subset of the uid domain.

For linear di erential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of both equations are de ned and their relationships are characterized.