We propose a new method for evaluating the security of block ciphers against di erential cryptanalysis and propose new structures for block ciphers. To this end, we de ne the word-wise Markov (Feistel) cipher and random output-di erential (Feistel) cipher and clarify the relations among the di erential, the truncated di erential and the impossible di erential cryptanalyses of the random output-...

In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary di erential equation systems, based on robust mathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for...

This paper describes a new symmetry-based approach to solving a given ordinary di¬erence equation. By studying the local structure of the set of solutions, we derive a systematic method for determining one-parameter Lie groups of symmetries in closed form. Such groups can be used to achieve successive reductions of order. If there are enough symmetries, the di¬erence equation can be completely ...

This review focusses on modelling of signal transduction pathways. It will introduce the general concepts of modelling and signal transduction, and then proceed with presenting the two most common approaches: Ordinary Di erential Equations (ODE) and Petri Nets (PN). Including an overview about some of the PN upgrades, such as Timed or Coloured Petri Nets, this review will show the major di eren...

We prove that the solution of a system of random ordinary di erential equations dX(t) dt = V(t;X(t)) with di usive scaling, X"(t) = "X( t " ), converges weakly to a Brownian Motion when " # 0. We assume that V(t;x), t 2 R, x 2 R is a d-dimensional, random, incompressible, stationary Gaussian eld which has mean zero and decorrelates in nite time.

During the last few years, di erent approaches for integrating ordinary di erential equations on manifolds have been published. In this work, we consider two of these approaches. We present some numerical experiments showing bene ts and some pitfalls when using the new methods. To demonstrate how they work, we compare with well known classical methods, e.g. Newmark and Runge-Kutta methods. AMS ...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

This paper is concerned with time-stepping numerical methods for computing sti semi-discrete systems of ordinary di erential equations for transient hypersonic ows with thermo-chemical nonequilibrium. The sti ness of the equations is mainly caused by the viscous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are needed ...

The paper is devoted to the study of the relationship between integral manifolds of ordinary di erential equations and duck trajectories. We derive su cient conditions for the existence of continuous slow integral surfaces that are devided into stable and unstable parts and propose a method of construction of surfaces consisting of duck trajectories.

A detailed description is given of the parallel algorithms used in AUTO94P, an experimental parallel version of the software AUTO for the numerical bifurcation analysis of systems of ordinary di erential equations. Timing results and user instructions for the Intel Delta are included. The sequential version of the software, AUTO94, is fully described in [8]. For a related tutorial paper see [5,...