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We investigate solution techniques for numerical constraint-satisfaction problems and validated numerical set integration methods for computing reachable sets of nonlinear hybrid dynamical systems in the presence of uncertainty. To use interval simulation tools with higher-dimensional hybrid systems, while assuming large domains for either initial continuous state or model parameter vectors, we need to solve the problem of flow/sets intersection in an effective and reliable way. The main idea developed in this paper is first to derive an analytical expression for the boundaries of continuous flows, using interval Taylor methods and techniques for controlling the wrapping effect. Then, the event detection and localization problems underlying flow/sets intersection are expressed as numerical constraint-satisfaction problems, which are solved using global search methods based on branch-and-prune algorithms, interval analysis and consistency techniques. The method is illustrated with hybrid systems with uncertain nonlinear continuous dynamics and nonlinear invariants and guards. 相似文献
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Moussa Maïga Nacim Ramdani Louise Travé-Massuyès Christophe Combastel 《Mathematics in Computer Science》2014,8(3-4):407-423
Computing the reachable set of hybrid dynamical systems in a reliable and verified way is an important step when addressing verification or synthesis tasks. This issue is still challenging for uncertain nonlinear hybrid dynamical systems. We show in this paper how to combine a method for computing continuous transitions via interval Taylor methods and a method for computing the geometrical intersection of a flowpipe with guard sets, to build an interval method for reachability computation that can be used with truly nonlinear hybrid systems. Our method for flowpipe guard set intersection has two variants. The first one relies on interval constraint propagation for solving a constraint satisfaction problem and applies in the general case. The second one computes the intersection of a zonotope and a hyperplane and applies only when the guard sets are linear. The performance of our method is illustrated on examples involving typical hybrid systems. 相似文献
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Czechoslovak Mathematical Journal - We present sufficient conditions for the existence of pth powers of a quasiho-mogeneous Toeplitz operator Teisθφ, where φ is a radial polynomial... 相似文献
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Zouari N Sayari A Miled N Verger R Gargouri Y 《Colloids and surfaces. B, Biointerfaces》2006,49(1):8-14
Using the classical emulsified system and the monomolecular film technique, we compared the interfacial properties of the scorpion digestive lipase (SDL) with those of higher animals'. In the absence of bile slats, SDL does not hydrolyse efficiently pure tributyrin, as well as dicaprin films maintained at low surface pressure. The preincubation of bile salts with tributyrin seems to be a better substrate for SDL than the pure tributyrin. A kinetic study on the surface pressure dependency, stereospecificity and regioselectivity of SDL was performed using monomolecular films of either three dicaprin isomers or three pairs of didecanoyl-deoxyamino-O-methyl glycerol enantiomers (DDG) containing a single hydrolysable decanoyl ester bond. With all diacylglycerol isomers, SDL has a surface pressure threshold of about 15 m Nm(-1), below which enzymatic activity is undetectable. SDL seems to prefer vicinal ester groups of the diacylglycerol isomers, with preference for sn-1 position at both 15 and 23 m Nm(-1). Furthermore, the maximum SDL activity is measured with DDG having a primary ester bond (1,3DDG, SII). This shows that SDL has a preference for the sn-1 position of this diacylglycerol analogue. Moreover, this was in line with the fact that SDL is inactive on sn-2 position of both DDG isomers and a triacylglycerol. With diacylglycerol analogue isomers, SDL shows a preference for distal isomers contrary to what has been observed with diacylglycerol isomers. SDL interacts with egg-phosphatidyl choline (egg-PC) monomolecular films. The critical surface pressure value (13 m Nm(-1)) is comparable to those of pancreatic lipases. 相似文献
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