We show how to calculate the Euler characteristic of an affine Jacobi variety of a spectral curve from its defining equations. 0 Membre du CNRS 1 Laboratoire associé au CNRS.

We consider q-Painlevé equations arising from birational representations of the extended affine Weyl groups of A (1) 4 and (A1+A1) -types. We study their hypergeometric solutions on the level of τ functions.

We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on Z2. The fields are associated to the vertices and an equation Q(x1, x2, x3, x4) = 0 relates four fields at one quad. Integrability of equations is understood as 3Dconsistency. The latter is a possibility to consistently impose equations of the same type on all the faces of a three-dimensional cube. This allows ...

We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(1) and GARCH(1,1) time series models. Our results build upon work of Goldie [Ann. Appl. Probab. 1 (1991) 126–166], who ha...

We introduce a geometric process algebra based on affine geometry, with the aim of describing the concurrent evolution of geometric structures in 3D space. We prove a relativity theorem stating that algebraic equations are invariant under rigid body transformations.

Techniques based on Interval and Affine Arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of Affine Arithmetic called Revised Affine Arithmetic. We extend the range of functions presented in Revised Affi...

We introduce the notion of a nonlinear splitting on fibre bundle as generalization an Ehresmann connection. present its basic properties and we pay attention to special cases affine, homogeneous principal splittings. explain where splittings appear in context Lagrangian systems Finsler geometry show their relation Routh symmetry reduction, submersive second-order differential equations unreduct...

the vibrations produced by trains include two parts which are deterministic and random vibrations. due to variation of dynamic loads and patterns of load-time, the random vibration of moving train is one of the most important issues in the field of railway engineering. one of the important sources in producing the train vibrations is rail roughness and irregularities. in this paper, responses o...

We present communication efficient secure protocols for a variety of linear algebra problems. Our main building block is a protocol for computing Gaussian Elimination on encrypted data. As input for this protocol, Bob holds a k×k matrix M , encrypted with Alice’s key. At the end of the protocol run, Bob holds an encryption of an upper-triangular matrix M ′ such that the number of nonzero elemen...

In this paper, we study a simplified affine motion model based coding framework to overcome the limitation of translational motion model and maintain low computational complexity. The proposed framework mainly has three key contributions. First, we propose to reduce the number of affine motion parameters from 6 to 4. The proposed four-parameter affine motion model can not only handle most of th...