We extend a systematic method for the derivation of high order schemes for affinely controlled nonlinear systems to a larger class of systems in which the control variables are allowed to appear nonlinearly in multiplicative terms. Using an adaptation of the stochastic Taylor expansion to control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-...

The current research attempts to offer a new method for solving fuzzy linear Volterra integral equations system. This method converts the given fuzzy system into a linear system in crisp case by using the Taylor expansion method. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example and also results are...

Introduction Diffusion kurtosis imaging is a new method to estimate the non gaussianity of the diffusion process with diffusion weighted MR images (DWIs) [1]. The model of the DWIs suggested in [1] was based on the Taylor series expansion of the logarithm of the DW magnitude. Unfortunately, this Taylor approximation is only valid for small b-values and leads to diverging predicted DW magnitudes...

In this paper we intend to offer a numerical scheme to solve linear Fredholm fuzzy integral equations system of the second kind. For this aim, we apply Taylor expansion method to convert the given fuzzy system into linear system in crisp case. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example. Resul...

In this paper, we propose a wavelet-Taylor–Galerkin method for solving the twodimensional Navier–Stokes equations. The discretization in time is performed before the spatial discretization by introducing second-order generalization of the standard time stepping schemes with the help of Taylor series expansion in time step. WaveletTaylor–Galerkin schemes taking advantage of the wavelet bases cap...

The Krivine machine is an abstract machine implementing the linear head reduction of λ -calculus. Ehrhard and Regnier gave a resource sensitive version returning the annotated form of a λ -term accounting for the resources used by the linear head reduction. These annotations take the form of terms in the resource λ -calculus. We generalize this resource-driven Krivine machine to the case of the...

Asian options belong to the so-called path-dependent derivatives. They are among the most difficult to price and hedge both analytically and numerically. Basket options are even harder to price and hedge because of the large number of state variables. Several approaches have been proposed in the literature, including Monte Carlo simulations, tree-based methods, partial differential equations, a...

Studying a critical value function φ in parametric nonlinear programming, we recall conditions guaranteeing that φ is a C function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of Dφ. Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of f...

For the continuous-time risk model with compound Poisson input, the ((nite-horizont) joint probability P (t; X x; Y y) of ruin time , surplus X just before ruin and deecit Y at ruin time is considered as a function of the arrival rate of claims. It is expanded into a Taylor series at = 0. A certain extension of a corresponding result for innnite-horizont joint probabilities, which previously ha...

We show that every connected Multiplicative Exponential Linear Logic (MELL) proof-structure (with or without cuts) is uniquely determined by a well-chosen element of its Taylor expansion: the one obtained by taking two copies of the content of each box. As a consequence, the relational model is injective with respect to connected MELL proof-structures. 1998 ACM Subject Classification F.4.1 Math...