We observe that the exactly solved eight-vertex solid-on-solid model contains an hitherto unnoticed arbitrary field parameter, similar to the horizontal field in the six-vertex model. The parameter is required to describe a continuous spectrum of the unrestricted solid-onsolid model, which has an infinite-dimensional space of states even for a finite lattice. The introduction of the continuous ...

Claude Itzykson was fascinated (among other things) by the mathematics of integrable billiards (see [AI]). This paper is devoted to new results about the chaotic regime. It is an extended version of the talk of one of us (M.K.) on the conference " The Mathematical Beauty of Physics " , Saclay, June 1996, dedicated to the memory of C. Itzykson. We started from computer experiments with simple on...

Mathematical morphology is a useful theory of nonlinear operators widely used for image processing and analysis. Despite the successful application morphological binary gray-scale images, extending them to vector-valued images not straightforward because there are no unambiguous orderings vectors. Among many approaches multivalued mathematical morphology, those based on total orders particularl...

This is the first one of a series of papers on Minkowski algebra. One of purposes of this paper is to set up a general framework so that the mixed volume theory and integral geometry can be developed algebraically in subsequent papers. The so called Minkowski algebra of convex sets is the vector space generated by indicator functions of closed convex sets and relatively open convex sets, where ...

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

The dynamics of an electron in a one-dimensional superlattice is investigated under the action of a THz electric field. The density matrix equations of motion within a single miniband are solved using a relaxationtime approximation for scattering. The electronic response to THz radiation is obtained by calculating the dipole moment, whence we compute the power dissipated, the THz reflection coe...

We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is independent of the sequence index. The problem is hard because it involves possibly multivalued mappings at each vector in the sequence, where the missing variabl...