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 study a singular di$usion on Euclidean space which is characterized by the solution of a classical Itô stochastic di$erential equation in which the di$usion coe2cient is not necessarily of full rank. Our motivation is in earlier results of Basak (J. Multivariate Anal. 39 (1991) 44) and Basak and Bhattacharya (Ann. Probab. 20 (1992) 312), who establish su2cient conditions for singular di$usio...

An individual-based model (IBM) of a spatiotemporal terrestrial ecological population is proposed. This model is spatially explicit and features the position of each individual together with another characteristic, such as the size of the individual, which evolves according to a given stochastic model. The population is locally regulated through an explicit competition kernel. The IBM is repres...

Many mathematical problems such as existence questions are studied by using an appropriate realization process either iteratively or continuously In this article di erential equation techniques are used as a special continuous realization process for linear algebra problems The matrix di erential equations are cast in fairly general frameworks of which special cases have been found to be closel...

In this paper, a newly proposed analytical scheme by the authors namely the improved di erential transform method is employed to provide an explicit series solution to the Thomas Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with di erentiation, and ends up in a recursive formula involving the Adomian polynomials to a ord the unk...

Currently, clusters of Personal Computers (PCs) with sharing Fast Ethernet may o er a signi cant price/performance ratio in parallel processing. This paper presents a study of the promising possibilities of parallelism in this environment, using both a classical numerical method to solve a di erential equation and an innovative algorithm to solve the statistical problem of density estimation. I...

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 considers two related problems of state estimation and model validation for a class of uncertain linear systems. The main contribution of the paper is that it considers a general information structure which allows for discrete and continuous measurements as well as missing data. The results are given in terms of a recursive state estimator involving a jump Riccati di€erential equatio...

Here, we do not have to solve any recursion relation or di erential equation explicitly to obtain critical exponents. one has to only diagonarize the scaling matrix at the xed point of RG. On the other hand, in an in nite-order phase transition, the free energy has an essential singularity, and any order derivative of the free energy does not diverge. The correlation length shows strong diverge...

The in ltration process is generally described by a nonlinear di erential equation, which can be solved by iteration methods such as a Newton-Raphson method. In this paper we propose a Discrete Event System Speci cation(DEVS) model for Green-Ampt in ltration. We show that this model can be approximated using Genetic Algorithm optimization of a fuzzy system. The fuzzy approximation is shown to b...