Results 21 to 30 of about 19,164 (129)
Sultan Qaboos University Journal for Science, 2016 We describe an extension of the pyritohedral symmetry in 3D to 4-dimensional Euclidean space and construct the group elements of the 4D pyritohedral group of order 576 in terms of quaternions. It turns out that it is a maximal subgroup of both the rank-4
Nazife O. Koca +2 more
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New Calabi–Yau manifolds from genetic algorithms
Physics Letters BCalabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm.
Per Berglund +5 more
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Projective geometry of Wachspress coordinates
, 2019 We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress in 1975.
Kohn, Kathlén, Ranestad, Kristian
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Minkowski Polynomials and Mutations
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Given a Laurent polynomial f, one can form the period of f: this is a function of one complex variable that plays an important role in mirror symmetry for Fano manifolds.
Mohammad Akhtar +3 more
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The covariogram determines three-dimensional convex polytopes
Advances in Mathematics, 2009 The cross covariogram g_{K,L} of two convex sets K, L in R^n is the function which associates to each x in R^n the volume of the intersection of K with L+x. The problem of determining the sets from their covariogram is relevant in stochastic geometry, in probability and it is equivalent to a particular case of the phase retrieval problem in Fourier ...
openaire +3 more sources
Three-dimensional lattice polytopes with two interior lattice points
, 2016 16 pages, 5 figures, 5 ...
Balletti, Gabriele +1 more
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Extremal properties for dissections of convex 3-polytopes [PDF]
, 1999 A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices forms a ...
Bruns Winfried +6 more
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Families of lattice polytopes of mixed degree one
, 2020 It has been shown by Soprunov that the normalized mixed volume (minus one) of an $n$-tuple of $n$-dimensional lattice polytopes is a lower bound for the number of interior lattice points in the Minkowski sum of the polytopes.
Balletti, Gabriele, Borger, Christopher
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Journal of Institute of Control, Robotics and Systems, 2009 This article describes the analysis of stable grasping for multi-fingered robot. An analysis method of stable grasping, which is based on the three-dimensional acceleration convex polytope, is proposed. This method is derived from combining dynamic equations governing object motion and robot motion, force relationship and acceleration relationship ...
Myeong-Eon Jang, Ji-Hong Lee
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Risk‐aware safe reinforcement learning for control of stochastic linear systems
Asian Journal of Control, EarlyView.Abstract This paper presents a risk‐aware safe reinforcement learning (RL) control design for stochastic discrete‐time linear systems. Rather than using a safety certifier to myopically intervene with the RL controller, a risk‐informed safe controller is also learned besides the RL controller, and the RL and safe controllers are combined together ...
Babak Esmaeili +2 more
wiley +1 more source