A note on orthogonality of subspaces in Euclidean geometry [PDF]
We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.
arxiv
GACNet: Interactive Prediction of Surrounding Vehicles Behavior under High Collision Risk
This study designs a dual‐stage prediction framework and introduces a conflict analysis module. This module refines the initially predicted future trajectories and performs collision detection and behavior analysis on the refined trajectories, thereby learning the true interactive behaviors of multiple agents in high‐collision‐risk scenarios.
Jingzheng Chai+3 more
wiley +1 more source
Optimal deployment of indoor wireless local area networks
Abstract We present a two‐phase methodology to address the problem of optimally deploying indoor wireless local area networks. In the first phase, we use Helmholtz's equation to simulate electromagnetic fields in a typical environment such as an office floor.
Antoine Oustry+4 more
wiley +1 more source
Biopolymer coating synthesized with PLA and TiO2 successfully shows a very good barrier property against water on paper. It is supported by SEM that the coating has a good surface appearance. ABSTRACT Polymer wastes are increasingly threatening the environment.
Serat Kotan, Doğan Tutak
wiley +1 more source
The fourth dimension: from its spatial nature in Euclidean geometry to a time-like component of non-Euclidean manifolds [PDF]
In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries, like those of ...
José Maria Filardo Bassalo+2 more
doaj +3 more sources
High‐order multigrid strategies for hybrid high‐order discretizations of elliptic equations
Abstract This study compares various multigrid strategies for the fast solution of elliptic equations discretized by the hybrid high‐order method. Combinations of h$$ h $$‐, p$$ p $$‐, and hp$$ hp $$‐coarsening strategies are considered, combined with diverse intergrid transfer operators.
Daniele A. Di Pietro+3 more
wiley +1 more source
Riemann’s Philosophy of Geometry and Kant’s Pure Intuition [PDF]
The aim of this paper is twofold: first to explicate how Riemann’s philosophy of geometry is organized around the concept of manifold. Second, to argue that Riemann’s philosophy of geometry does not dismiss Kant’s spatial intuition.
Dinçer Çevik
doaj +1 more source
Book Review: The Elements of Non-Euclidean Plane Geometry and Trigonometry [PDF]
J. L. Coolidge
openalex +1 more source
Axion‐Like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect
This review investigates the connection between chiral anomalies and their manifestation in topological materials, using both perturbative methods based on ordinary quantum field theory and conformal field theory (CFT). It emphasizes the role of CFT in momentum space for parity‐odd correlation functions, and their reconstruction by the inclusion of a ...
Claudio Corianò+4 more
wiley +1 more source
Efficient formulation of a two‐noded geometrically exact curved beam element
Abstract The article extends the formulation of a 2D geometrically exact beam element proposed by Jirásek et al. (2021) to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic relations and sectional equations that link the internal forces to sectional deformation variables.
Martin Horák+2 more
wiley +1 more source