This paper concerns a new type of approximant for series analysis. By incorporating linear recurrence techniques, such as are involved with second order di erential approximants, algebraic approximants can be extended to nonlinear di erential approximants. The discussion of nonlinearities is constrained by discussing approximants just one step removed from second order algebraic approximants. T...

A new hybrid controller has been applied for feedback stabilization of a Pendubot, whose dynamics show second order nonholonomic properties. Experimental results for di erent test cases show that hybrid control outperforms the existing control algorithm. This successful implementation provides a novel alternative for the control of under-actuated mechanical systems. Many such systems are subjec...

We extend Ehrhard Regnier's di erential linear logic along the lines of Laurent's polarization. We provide a denotational semantics of this new system in the well-known relational model of linear logic, extending canonically the semantics of both di erential and polarized linear logics: this justi es our choice of cut elimination rules. Then we show this polarized di erential linear logic re ne...

We survey some constructive aspects of di erential Galois theory and indicate some analogies between ordinary Galois theory and di erential Galois theory in characteristic zero and nonzero.

this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.

In this paper we present a new symbolic approach to hybrid systems Hybrid systems are systems con taining both continuous and discrete changing quantities We model hybrid systems using hybrid automata Hybrid automata extend the classical notion of nite state machines by combining di erential equations to model the dynamic behavior of systems with a nite control In contrast to other approaches w...

We describe a MIMD parallel code to solve a general class of ordinary di erential equations, with particular emphasis on the large, sparse systems arising from space discretization of systems of parabolic partial di erential equations. The main goals of this work are sharp bounds on the accuracy of the computed solution and exibility of the software. We discuss the sources of error in solving d...

The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by di erential equations with discontinuous right{hand sides. In this paper we analyze the behavior of three di erent Lotka{Volterra predator{prey systems with opt...

Novel computing devices are exploited for numerical computation. The solution of a numerical problem is sought, which has been solved many times before, but this time with a di erent set of input data. A table is a classical way to collect the old solutions in order to exploit them to nd the new one. This process is extended to more general problems than the usual function value approximation. ...

In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...