We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary di erential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary di erential equations. Since they generate systems of algebraic equations in at most n unknowns, where n is the order...

This paper introduces a new estimation method of Luby-Racko 's pseudorandomness and maximum average of di erential probability of block ciphers with SPN(Substitution and Permutation Network)structures like E2. In this paper, we analyze the pseudorandomness of the SPN-structure and E2-like transformations and show that this can be easily calculated by simple matrix calculation, and clarify that ...

We consider a system of ordinary di erential equations consisting of a singularly perturbed scalar di erential equation of second order and a scalar di erential equation of rst or second order and study a Neuman-Cauchy or a Neuman-Dirichlet problem. We assume that the degenerate equation has two intersecting solutions such that the standard theory for systems of Tichonov's type cannot be applie...

We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...

We design here a primary platform for computing the basic homological information of Commutative Di erential Graded Algebras (brie y, CDGAs), endowed with linear di erential. All the algorithms have been implemented in the framework settled by Mathematica, so that we can take advantage of the use of symbolic computation and many other powerful tools this system provides. Working in the context ...

In a series of papers, starting with [Fully nonlinear stochastic partial di¤erential equations. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 9] Lions and Souganidis proposed a (pathwise) theory for fully non-linear stochastic partial di¤erential equations. We present here a (partial) extension towards certain spatial dependence in the noise term. The main novelty is the use of rough path...

We suggest two algorithms that allow e cient timing recovery for MSK based on the computation of the Fourier spectrum of the absolute value of the di erential phases. One is suited for parallel frequency estimation while the second is less complex but requires previous frequency correction. The algorithms are investigated using both analysis and simulation. The two algorithms approximately lead...

Hybrid action systems extend a conventional action system with a guarded di erential equation | a di erential action | that de nes evolution of continuous variables while the guard remains true. The new action is given a weakest liberal precondition semantics, which is illustrated by examples from a train model. The example motivates a discussion of priorities in a system of iterated di erentia...

We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...