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991.
Henrik Schulz 《Discrete Applied Mathematics》2009,157(16):3485-3493
In this paper we introduce an algorithm for the creation of polyhedral approximations for certain kinds of digital objects in a three-dimensional space. The objects are sets of voxels represented as strongly connected subsets of an abstract cell complex. The proposed algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background voxels. The result of this method is a polyhedron which separates object voxels from background voxels. The objects processed by this algorithm and also the background voxel components inside the convex hull of the objects are restricted to have genus 0. The second aim of this paper is to present some practical improvements to the discussed convex hull algorithm to reduce computation time. 相似文献
992.
Giovanna Guidoboni Roland Glowinski Matteo Pasquali 《Journal of Computational and Applied Mathematics》2009,232(1):72-81
Free surface flows are pervasive in engineering and biomedical applications. In many interesting cases—particularly when small length scales are involved—surface forces (capillarity) dominate the flow dynamics. In these cases, computing the flow together with the shape of the surfaces, requires specialized solution techniques. This article investigates the capabilities of an operator splitting/finite elements method at handling accurately incompressible viscous flow with free surfaces at low capillary numbers. The test case of flow in the downstream section of a slot coater is used for three reasons: (1) it is an established benchmark; (2) it represents an idealized, yet industrially relevant flow; (3) high-fidelity results obtained with monolithic algorithms are available in literature. The flow and free surface shape attained with the new operator splitting scheme agree very satisfactorily with the results obtained with monolithic solvers. Because of its inherent computational simplicity, the new operator splitting scheme is attractive for large-scale simulations, three-dimensional flows, and flows of complex fluids. 相似文献
993.
We provide a sharp, sufficient condition to decide if a point y on a convex surface S is a farthest point (i.e., is at maximal intrinsic distance from some point) on S, involving a lower bound π on the total curvature ωy at y, ωy ≥ π. Further consequences are obtained when ωy > π, and sufficient conditions are derived to guarantee that a convex cap contains at least one farthest point. A connection between simple closed quasigeodesics O of S, points y ∈ S\O with ωy > π, and the set ?? of all farthest points on S, is also investigated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
994.
Two well-known results on the unified treatment of finite termination of a class of algorithms for solving convex programming problems and for solving variational inequality problems are reconsidered. In particular, some of the underlying assumptions employed in the existing literature are shown to be redundant. 相似文献
995.
The aim of the present paper is to characterize prime numbers of the form n = x
2 + (x + 1)2 and to obtain certain proper divisors of composite numbers of the same form, i.e. divisors d of n such that 1 < d < n.
相似文献
996.
We generalize some identities and q-identities previously known for the symmetric group to Coxeter groups of type B and D. The extended results include theorems of Foata and Schützenberger, Gessel, and Roselle on various distributions of statistics, like inversion number, major index, and descent number. In order to show our results we provide explicit characterizations of the systems of minimal coset representatives of Coxeter groups of type B and D. 相似文献
997.
The study of mechanical systems with uncertain parameters is gaining increasing interest in the field of system analysis to provide an expedient model for the prediction of the system behavior. Making use of the Transformation Method, the uncertain parameters of the system are modeled by fuzzy numbers in contrast to random numbers used in stochastic approaches. As a result of this analysis, a quantification of the overall uncertainty of the system outputs, including a worst-case scenario, is obtained. The inputs of the resulting fuzzy-valued model are a priori uncorrelated but after the uncertainties are propagated through the model, interdependency (or interaction) between the outputs may arise. If such interdependency is neglected, a misinterpretation of the results may occur. For example, in the case of applying uncertainty analysis in the early design phase of a product to determine the relevant design-parameter space, the interdependency between the design variables may reduce significantly the available part of the design space. This paper proposes a measure of interdependency between the uncertain system outputs. The interdependency index can be derived by a postprocessing of the data gained by the analysis with the Transformation Method. Such information can be obtained by a negligible amount of extra computation time. 相似文献
998.
Abstract. We propose C
1
Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity
or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving
interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates
in the case of interpolation of smooth functions. 相似文献
999.
Dominique Foata 《Journal of Combinatorial Theory, Series A》2008,115(5):726-736
Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with the triplet (fix, des, maj), or the pair (fix, maj), where “fix,” “des” and “maj” denote the number of fixed points, the number of descents and the major index, respectively. 相似文献
1000.
Michael J. Fisher 《Discrete Mathematics》2008,308(11):2240-2246
We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph Ks,t which admits only the identity automorphism. In particular, this allows us to determine the distinguishing number of the Cartesian product of complete graphs. 相似文献