Fixed-point iterative sweeping methods were developed in the literature to efficiently solve static Hamilton-Jacobi equations. This class of methods utilizes the Gauss-Seidel iterations and alternating sweeping strategy to achieve fast convergence rate. They take advantage of the properties of hyperbolic partial differential equations (PDEs) and try to cover a family of characteristics of the c...

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A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. We say that a sweeping automaton is degenerate if the automaton has no left-moving transitions. We show that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate swee...

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G. S. Collins and Y. Le Manach Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, UK, and Departments of Anesthesia and Clinical Epidemiology and Biostatistics, Michael DeGroote School of Medicine, Faculty of Health Sciences, Population Health Research Institute, McMaster University and the Perioperati...

This paper is devoted to weaken “classical” assumptions and give new arguments to prove existence of sweeping process (associated to the proximal normal cone of sets). Mainly we define the concept of a “directional prox-regularity” and give assumptions about a Banach space to insure the existence of such sweeping process (which permit to generalize the existing results requiring a Hilbertian st...

Given a convex region in the plane, and a sweep-line as a tool, what is best way to reduce the region to a single point by a sequence of sweeps? The problem of sweeping points by orthogonal sweeps was first studied in [2]. Here we consider the following slanted variant of sweeping recently introduced in [1]: In a single sweep, the sweep-line is placed at a start position somewhere in the plane,...

We have applied sweeping micellar electrokinetic chromatography (sweeping-MEKC) to the simultaneous determination of Delta(9)-tetrahydrocannabinol (THC) and its major metabolites, 11-hydroxy-Delta(9)-tetrahydrocannabinol (THC-OH) and 11-nor-9-carboxy-Delta(9)-tetrahydrocannabinol (THC-COOH). We monitored the effects of several of the sweeping-MEKC parameters, including the proportion of organic...

Fast sweeping methods are a class of efficient iterative methods for solving steady state hyperbolic PDEs. They utilize the Gauss-Seidel iterations and alternating sweeping strategy to cover a family of characteristics of the hyperbolic PDEs in a certain direction simultaneously in each sweeping order. The first order fast sweeping method for solving Eikonal equations (Zhao in Math Comput 74:60...