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Wireless Sensor Network-Based Rigid Body Localization for NLOS Parameter Estimation
Sensors, 2022 In wireless sensor network (WSN)-based rigid body localization (RBL) systems, the non-line-of-sight (NLOS) propagation of the wireless signals leads to severe performance deterioration.
Pengwu Wan +3 more
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Ellipses surrounding convex bodies
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 If, for a double normal xx* of a convex body K, an ellipse E ∋ x, x* is included in K, we say that E is surrounded by the boundary of K. If, instead, in the plane of E, K is included in the convex hull of E, then we say that E is surrounding K.
Zamfirescu Tudor
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Reduced spherical convex bodies [PDF]
Bulletin of the Polish Academy of Sciences Mathematics, 2018 The aim of this paper is to present some properties of reduced spherical convex bodies on the two-dimensional sphere $S^2$. The intersection of two different non-opposite hemispheres is called a lune. By its thickness we mean the distance of the centers of the two semicircles bounding it.
Lassak, Marek, Musielak, Michał
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RECTILINEAR AND BROWNIAN MOTION FROM A RANDOM POINT IN A CONVEX REGION
Image Analysis and Stereology, 2011 A particle is projected from a point P in a subset E of a convex region H to a point Q in a uniformly random direction. The probability that Q lies in the interior of H at time t is obtained for two types of motion of the particle, rectilinear (i.e ...
Peter Ehlers, Ernest Enns, Tak Fung
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CONVEX BODIES AND GAUSSIAN PROCESSES
Image Analysis and Stereology, 2011 For several decades, the topics of the title have had a fruitful interaction. This survey will describe some of these connections, including the GB/GC classification of convex bodies, Ito-Nisio singularities from a geometric viewpoint, Gaussian ...
Richard A Vitale
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Covering the Boundary of Special Convex Bodies with Smaller Homothetic Copies
Journal of Harbin University of Science and Technology, 2019 For Hadwiger conjecture that the least number c(K) of translates of the interior of K needed to cover K is at most 2n, according to the fact that c(K) equals the least number of smaller homothetic copies of K with the same homothetic ratio needed to ...
JI Dong-hai, Lv De-jing, MA Ze-min
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The heart of a convex body [PDF]
, 2012 We investigate some basic properties of the {\it heart} $\heartsuit(\mathcal{K})$ of a convex set $\mathcal{K}.$ It is a subset of $\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object.
C. Carstensen +19 more
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Competitively Chasing Convex Bodies [PDF]
SIAM Journal on Computing, 2019 Let $\mathcal{F}$ be a family of sets in some metric space. In the $\mathcal{F}$-chasing problem, an online algorithm observes a request sequence of sets in $\mathcal{F}$ and responds (online) by giving a sequence of points in these sets. The movement cost is the distance between consecutive such points.
Sébastien Bubeck +3 more
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COMPARATIVE PRECISION OF THE PIVOTAL ESTIMATORS OF PARTICLE SIZE
Image Analysis and Stereology, 2011 The pivotal estimators of the surface area and the volume of a generic "particle" are based on a point sampled test line on an isotropic pivotal plane through a fixed point called the pivotal point.
Luis M Cruz-Orive
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Correspondences between convex geometry and complex geometry [PDF]
Épijournal de Géométrie Algébrique, 2017 We present several analogies between convex geometry and the theory of holomorphic line bundles on smooth projective varieties or K\"ahler manifolds. We study the relation between positive products and mixed volumes.
Brian Lehmann, Jian Xiao
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