منابع مشابه
Computation of the Perimeter of Measurable Sets via their Covariogram. Applications to Random Sets
The covariogram of a measurable set A ⊂ R is the function gA which to each y ∈ R associates the Lebesgue measure of A ∩ (y + A). This paper proves two formulas. The first equates the directional derivatives at the origin of gA to the directional variations of A. The second equates the average directional derivative at the origin of gA to the perimeter of A. These formulas, previously known with...
متن کاملTransversality and Alternating Projections for Nonconvex Sets
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear convergence. When the two sets are semi-algebraic and bounded, but not necessarily transversal, we nonetheless prove subsequence convergence.
متن کاملThe Hamiltonian Inclusion for Nonconvex Velocity Sets
Since Clarke’s 1973 proof of the Hamiltonian inclusion for optimal control problems with convex velocity sets, there has been speculation (and, more recently, speculation relating to a stronger, partially convexified version of the Hamiltonian inclusion) as to whether these necessary conditions are valid in the absence of the convexity hypothesis. The issue was in part resolved by Clarke himsel...
متن کاملSums, Projections, and Sections of Lattice Sets, and the Discrete Covariogram
Basic properties of finite subsets of the integer lattice Z are investigated from the point of view of geometric tomography. Results obtained concern the Minkowski addition of convex lattice sets and polyominoes, discrete X-rays and the discrete and continuous covariogram, the determination of symmetric convex lattice sets from the cardinality of their projections on hyperplanes, and a discrete...
متن کاملOn Best Approximation by Nonconvex Sets and Perturbation of Nonconvex Inequality Systems in Hilbert Spaces
By virtue of convexification techniques, we study best approximations to a closed set C in a Hilbert space as well as perturbation conditions relative to C and a nonlinear inequality system. Some results on equivalence of the best approximation and the basic constraint qualification are established.
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ژورنال
عنوان ژورنال: Mathematika
سال: 2010
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579310000549