A q-di erence analog of the sixth Painlev e equation is presented. It arises as the condition for preserving the connection matrix of linear q-di erence equations, in close analogy with the monodromy preserving deformation of linear di erential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed. Mathematical Subject Classi cations (19...

The paper describes the aeroelastic analysis of a tiltrotor con guration. The 1/5 scale wind tunnel semispan model of the V-22 tiltrotor aircraft is considered. The analysis is performed by means of a multi-body code, based on an original formulation. The di erential equilibrium problem is stated in terms of rst order di erential equations. The equilibrium equations of every rigid body are writ...

In earlier work we constructed a class of spherically symmetric, ̄uid dynamical shock waves that satisfy the Einstein equations of general relativity. These shock waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure. Our shock waves are determined by a system of ordinary di€erential equations that describe the matching of a FriedmannRobertson-Walker metric (a c...

This special issue is an outgrowth of a minisyposium titled “Mathematics of Social Systems” held at the 9th AIMS Conference on Dynamical Systems, Di↵erential Equations and Applications, held in Orlando, FL in July 2012. Presenters from that session were invited to submit papers that were reviewed using the usual procedures of the DCDS journals, along with additional authors from the field. Math...

The present paper gives a new view point for the di erential operators with respect to the coordinates of the quantum matrix space. A special emphasis is put on an inductive construction of these di erential operators from the q-di erence operators de ned on each columns (resp. rows). This idea for understanding our operators provides us with two important applications: (1) a construction of th...

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-...

We describe a MIMD parallel code to solve a general class of ordinary di erential equations, with particular emphasis on the large, sparse systems arising from space discretization of systems of parabolic partial di erential equations. The main goals of this work are sharp bounds on the accuracy of the computed solution and exibility of the software. We discuss the sources of error in solving d...

We investigate the derivation and the mathematical properties of a Saint-Venant model with an energy equation and with temperature-dependent transport coe±cients. These equations model shallow water °ows as well as thin viscous sheets over °uid substrates like oil slicks, atlantic waters in the Strait of Gilbraltar or °oat glasses. We exhibit an entropy function for the system of partial di®ere...

This paper is concerned with linear uniformly elliptic and par abolic partial di erential equations in divergence form It is assumed that the coe cients of the equations are random variables constant in time The Green s functions for the equations are then random variables Regularity properties for expectation values of Green s functions are obtained In par ticular it is shown that the expectat...

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...