Two Approaches to Modeling and Solving the Packing Problem for Convex Polytopes
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DOI: 10.1007/s10559-018-0059-3
Abstract: We consider the problem of packing convex polytopes in a cuboid of minimum volume. To describe analytically the non-overlapping constraints for convex polytopes that allow continuous translations and rotations, we use phi-functions and quasi-phi-functions. We… read more here.
Keywords: approaches modeling; two approaches; phi functions; problem ... See more keywords
A MINI element over star convex polytopes
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DOI: 10.1016/j.finel.2019.103368
Abstract: Abstract In this paper, we extend the concept of MINI element over triangles to star convex arbitrary polytopes. This is achieved by employing the volume averaged nodal projection (VANP) method over polytopes in combination with… read more here.
Keywords: mini element; star convex; element star; strain ... See more keywords
Polyrun: A Java library for sampling from the bounded convex polytopes
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DOI: 10.1016/j.softx.2021.100659
Abstract: Abstract Polyrun is a Java library that provides methods for exploiting the bounded convex polytopes. Such polytopes define a space of feasible problem parameters with a set of linear constraints. The software makes available an… read more here.
Keywords: library sampling; java library; bounded convex; polyrun java ... See more keywords
A Gibbs Sampler for a Class of Random Convex Polytopes
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DOI: 10.1080/01621459.2021.1881523
Abstract: Abstract We present a Gibbs sampler for the Dempster–Shafer (DS) approach to statistical inference for categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields… read more here.
Keywords: random convex; gibbs sampler; convex polytopes; class random ... See more keywords
Rejoinder—A Gibbs Sampler for a Class of Random Convex Polytopes
Sign Up to like & getrecommendations! Published in 2021 at "Journal of the American Statistical Association"
DOI: 10.1080/01621459.2021.1945458
Abstract: We are very grateful to all commenters for their stimulating remarks, questions, as well as useful pointers to the literature which span a wide range of statistical methods over decades of research. We have neither… read more here.
Keywords: random convex; gibbs sampler; sampler class; convex polytopes ... See more keywords
Convex Polytopes, Algebraic Geometry, and Combinatorics
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DOI: 10.1090/noti2137
Abstract: In the last several decades, convex geometry methods have proven very useful in algebraic geometry specifically to understand discrete invariants of algebraic varieties. An approach to study algebraic varieties is to assign to a family… read more here.
Keywords: algebraic geometry; polytopes algebraic; geometry combinatorics; geometry ... See more keywords
On the Fractional Metric Dimension of Convex Polytopes
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Problems in Engineering"
DOI: 10.1155/2021/3925925
Abstract: In order to identify the basic structural properties of a network such as connectedness, centrality, modularity, accessibility, clustering, vulnerability, and robustness, we need distance-based parameters. A number of tools like these help computer and chemical… read more here.
Keywords: dimension convex; metric dimension; fractional metric; convex polytopes ... See more keywords
Omnidimensional Convex Polytopes
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DOI: 10.3390/sym15030755
Abstract: The study shows that the volumes and surfaces of n-balls, n-simplices, and n-orthoplices are holomorphic functions of n, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas… read more here.
Keywords: volumes surfaces; convex polytopes; omnidimensional convex;