Component based design is a new paradigm to build distributed systems and applications. The problem of compositional verification of such systems is however still open. We investigate methods and concepts for the provision of “sound” assemblies. We define a behavioural interface type language endowed with a (decidable) set of interface compatibilty and subtyping rules. We define an abstract, dy...

The non-uniqueness of geodesics joining two given points in universal Teichm uller space is proved in the previous paper 7]. The purpose of the present paper is to discuss the non-uniqueness of geodesics in any innnite-dimensional Teichm uller space. It is proved that if 1 and 2 are two extremal Beltrami diierentials belonging to a point ] of a Teichm uller space and 1 ? 2 does not belong to N-...

A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the 3D incompressible Euler equations in bounded cylindrical domains. The fast singular oscillating limits of the 3D Euler equations are investigated for parametrically resonant cylinders. Resonances of fast oscillating swirling Beltrami waves deplete the Euler nonlinearity. These waves are ex...

Abstract Applying very small purely radial strains on amorphous solids in geometry one observes elastic responses that break the symmetry. Without any plasticity involved, indicate mode coupling contributions even for minute strains. We show these symmetry-breaking are due to disorder, typical configurations. The quantitatively explained using classical Michell solutions which excited by coupli...

In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the only other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformal...

The Laplace Beltrami operator is one of the essential tools in geometric processing. It allows us to solve numerous partial differential equations on discrete surface meshes, which a fundamental building block many computer graphics applications. Discrete Laplacians are typically limited standard elements like triangles or quadrilaterals, severely constrains tessellation mesh. But recent years,...

In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by differential equations (SDEs). Our is based on splitting method to solve corresponding SDEs deterministic subproblem discretized using while random Euler-Maruyama scheme. We obtain sharp...