We demonstrate an automated method for proving statements in temporal logic about continuous systems, even in the face of incomplete knowledge. The method combines an implemented, on-they , model-checking algorithm for statements in the temporal logic CTL* 3, 4, 5] with the output of the qualitative simulation algorithm QSIM 10, 12]. Based on the QSIM Guaranteed Coverage Theorem, we prove that ...

We present Signal Spatio-Temporal Logic (SSTL), a modal logic that can be used to specify spatio-temporal properties in linear time and for a discrete space. The logic is equipped with a Boolean and a quantitative semantics, and with accompanying monitoring algorithms. As such, it is suitable for real-time verification of both white box and black box complex systems. It can also be integrated i...

We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension, also known as stable norm (or minimal action) in Weak KAM theory. In particular we investigate its strict convexity and differentiability properties.

Richard Levins has advocated the scientific merits of qualitative modeling throughout his career. He believed an excessive and uncritical focus on emulating the models used by physicists and maximizing quantitative precision was hindering biological theorizing in particular. Greater emphasis on qualitative properties of modeled systems would help counteract this tendency, and Levins subsequentl...

The basic requirement of numerical methods is convergence. However, from the practical point of view, it is generally not sufficient to construct convergent numerical methods for the solutions of partial differential equations. The qualitative adequateness of the methods is also an issue. The numerical solutions should mirror the characteristic properties of the original physical process that i...

Let n be a positive integer and let 0 < α < n. In this paper, we continue our study of the integral equation u(x) = ∫ R 1 |x− y|n−α u(y)dy. (0.1) We mainly consider singular solutions in subcritical, critical, and super critical cases, and obtain qualitative properties, such as radial symmetry, monotonicity, and upper bounds for the solutions. AMS Subject Classification 2000 35J99, 45E10, 45G05

We consider multirate digital control systems which consist of an interconnection of a continuous-time non-linear plant (described by ordinary diierential equations), a digital controller (described by ordinary difference equations) which has quantizers (but is otherwise linear), along with the required interface elements (A/D and D/A converters). The input to the digital controller consists of...

– This paper proposes that the concept of ‘qualitative’ developed around the qualitative theory of nonlinear dynamical systems be applied to the field of system dynamics in order to provide a more solid foundation for the use of the qualitative in this field. The advantages of the use of qualitative concepts are analyzed both from a conceptual and an operational point of view. A preliminary sta...

We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of sesquilinear mappings. We apply our results to parabolic problems of different nature: a coupled diffusive system arising in neurobiology, a strongly damped wave equati...

Dealing with service composition is an important and challenging issue of distributed systems. Existing works investigate mechanisms for analyzing and synthesizing a composition based on qualitative properties which characterize operations and/or messages choreography constraints. Apart from these qualitative properties, quantitative properties such as time related features are a crucial settin...