We address the enumeration of q-coloured planar maps counted by the number of edges and the number of monochromatic edges. We prove that the associated generating function is di erentially algebraic, that is, satis es a non-trivial polynomial di erential equation with respect to the edge variable. We give explicitly a di erential system that characterizes this series. We then prove a similar re...

This paper summarizes recent results on the number and characterization of di erential invariants of transformation groups Generalizations of theorems due to Ovsiannikov and to M Green are presented as well as a new approach to nding bounds on the number of independent di erential invariants Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables th...

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 ...

In this paper we discuss the formulation of the governing equations that describe ow of uids in porous media Various types of uid ow ranging from single phase ow to compositional ow are considered It is shown that all the di erential equations governing these types of ow can be e ectively rewritten in a fractional ow formulation i e in terms of a global pressure and saturation or saturations an...

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 this paper, a strategy based on the Sliding Mode Control(SMC) is used to achieve the Boolean input for DC-DC buck converter. Three di¤erent surfaces are proposed in order to design integer order and fractional order controller. Unlike conventional methods, sliding mode controllers designed through this methodology directly produce Boolean control actions, avoiding the usability of pulse-widt...

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...

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...