Involutions and Trivolutions in Algebras Related to Second Duals of Group Algebras

We define a trivolution on a complex algebra $A$ as a non-zero conjugate-linear, anti-homomorphism $\tau$ on $A$, which is a generalized inverse of itself, that is, $\tau^3=\tau$. We give several characterizations of trivolutions and show with examples that they appear naturally on many Banach algebras, particularly those arising from group algebras. We give several results on the existence or non-existence of involutions on the dual of a topologically introverted space. We investigate conditions under which the dual of a topologically introverted space admits trivolutions

Asymptotic oscillations

AbstractGiven a function f:X→R defined on the support of a ballean, we introduce the notion of slow oscillation in direction of a filter on X. We show that there exists a filter on X responsible for the rate of slow oscillation of f at infinity. We apply this result to the Stone–Čech compactifications of discrete groups

Approximable W A P and L U C- interpolation sets

Extending and unifying concepts extensively used in the literature, we introduce the notion of approximable interpolation sets for algebras of functions on locally compact groups, especially for weakly almost periodic functions and for uniformly continuous functions. We characterize approximable interpolation sets both in combinatorial terms and in terms of the LUCLUC- and WAPWAP-compactifications and analyse some of their properties

Interpolation sets and the size of quotients of function spaces on a locally compact group

We devise a fairly general method for estimating the size of quotients between algebras of functions on a locally compact group. This method is based on the concept of interpolation sets and unifies the approaches followed by many authors to obtain particular cases. Among the applications we find, we obtain that the quotients WAP(G)/B(G) (G being a locally compact group in the class [IN] or a nilpotent locally compact group) and CB(G)/LUC(G) (G being any non-compact non-discrete locally compact group) contain a linearly isometric copy of \ell_\infty(\kappa(G)) where \kappa(G) is the compact covering number of G, and WAP(G), B(G) and LUC(G) refer, respectively, to the algebra of weakly almost periodic functions, the uniform closure of the Fourier-Stieltjes algebra and the bounded right uniformly continuous functions.The research of the second author was partially supported by the Spanish Ministry of Science (including FEDER funds), grant MTM2011-23118 and Fundació Caixa Castelló-Bancaixa, grant number P1$⋅$1B2014-35

A transient network of telechelic polymers and microspheres : structure and rheology

We study the structure and dynamics of a transient network composed of droplets of microemulsion connected by telechelic polymers. The polymer induces a bridging attraction between droplets without changing their shape. A viscoelastic behaviour is induced in the initially liquid solution, characterised in the linear regime by a stretched exponential stress relaxation. We analyse this relaxation in the light of classical theories of transient networks. The role of the elastic reorganisations in the deformed network is emphasized. In the non linear regime, a fast relaxation dynamics is followed by a second one having the same rate as in the linear regime. This behaviour, under step strain experiments, should induce a non monotonic behaviour in the elastic component of the stress under constant shear rate. However, we obtain in this case a singularity in the flow curve very different from the one observed in other systems, that we interpret in terms of fracture behaviour.Comment: 9 pages, 4 figure

Formal Architecture Specification for Time Analysis

International audienceWCET calculus is nowadays a must for safety critical systems. As a matter of fact, basic real-time properties rely on accurate timings. Although over the last years, substantial progress has been made in order to get a more precise WCET, we believe that the design of the underlying frameworks deserve more attention. In this paper, we are concerned mainly with two aspects which deal with the modularity of these frameworks. First, we enhance the existing language Sim-nML for describing processors at the instruction level in order to capture modern architecture aspects. Second, we propose a light DSL in order to describe, in a formal prose, architectural aspects related to both the structural aspects as well as to the behavioral aspects

A constraint-based WCET computation framework

National audienceOTAWA is a tool dedicated to the WCET computation of critical real-time systems. The tool was enhanced in order to take into account modern micro-architecture features, through an ADL-based approach. Architecture constraints are expresses such that they can be solved by well known efficient constraint solvers. In this paper, we present how we could describe some complex architecture features using the Sim-nML language. We are also concerned by the validation and the animation point of views

A Mechanized Semantic Framework for Real-Time Systems

International audienceConcurrent systems consist of many components which may execute in parallel and are complex to design, to analyze, to verify, and to implement. The complexity increases if the systems have real-time constraints, which are very useful in avionic, spatial and other kind of embedded applications. In this paper we present a logical framework for defining and validating real-time formalisms as well as reasoning methods over them. For this purpose, we have implemented in the Coq proof assistant well known semantic domains for real-time systems based on labelled transitions systems and timed runs. We experiment our framework by considering the real-time CSP-based language fiacre, which has been defined as a pivot formalism for modeling languages (aadl, sdl, ...) used in the TOPCASED project. Thus, we define an extension to the formal semantic models mentioned above that facilitates the modeling of fine-grained time constraints of fiacre. Finally, we implement this extension in our framework and provide a proof method environment to deal with real-time system in order to achieve their formal certification

Multi-core Code Generation from Polychronous Programs with Time-Predictable Properties (ACVI 2014)

Workshop of ACM/IEEE 17th International Conference on Model Driven Engineering Languages and Systems (MoDELS 2014)International audienceSynchronous programming models capture concurrency in computation quite naturally, especially in its dataflow multi-clock (polychronous) flavor. With the rising importance of multi-core processors in safety-critical embedded systems or cyber-physical systems (CPS), there is a growing need for model-driven generation of multi-threaded code for multi-core systems. This paper proposes a build method of timepredictable system on multi-core, based on synchronous-model development. At the modeling level, the synchronous abstraction allows deterministic time semantics. Thus synchronous programming is a good choice for time-predictable system design. At the compiler level, the verified compiler from the synchronous language SIGNAL to our intermediate representation (S-CGA, a variant of guarded actions) and to multi-threaded code, preserves the time predictability. At the platform level, we propose a time-predictable multi-core architecture model in AADL (Architecture Analysis and Design Language), and then we map the multi-threaded code to this model. Therefore, our method integrates time predictability across several design layers