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...

We consider the e cient solution of partial di↵erential equations for strongly elliptic operators with constant coe cients and stochastic Dirichlet data by the boundary integral equation method. The computation of the solution’s twopoint correlation is well understood if the two-point correlation of the Dirichlet data is known and su ciently smooth. Unfortunately, the problem becomes much more ...

A simpli ed box ocean model for the North Atlantic is used to study the in uence of multiplicative short-term climate variability on the stability and long-term dynamics of the North Atlantic thermohaline circulation. A timescale separation between fast temperature ans slow salinity uctuations is used to decouple the dynamical equations resulting in a multiplicative stochastic di erential equat...

For evaluating a hedging strategy we have to know at every instant the solution of the Cauchy problem for a parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to nd these magnitudes by Monte Carlo simulation of the corresponding system of stochastic di erential equations using weak solution schemes. It turns out that with one and the same contro...

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.

This paper is concerned with the numerical solution of a system of ordinary di erential equations ODEs y Sy t f t y p on an inter val b subject to boundary conditions g y y b p The ODEs have a coe cient that is singular at t but it is assumed that the boundary value problem BVP has a smooth solution Some popular methods for BVPs evaluate the ODEs at t This paper deals with the practical issues ...

This paper reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible ow. The theory is applied to a system de ned by the partial di erential equations of the ow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adj...

This paper is concerned with linear uniformly elliptic and par abolic partial di erential equations in divergence form It is assumed that the coe cients of the equations are random variables constant in time The Green s functions for the equations are then random variables Regularity properties for expectation values of Green s functions are obtained In par ticular it is shown that the expectat...