Results 111 to 120 of about 5,495,109 (374)
Lines Missing Every Random Point
, 2014 We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time ...
A.S. Besicovitch +19 more
core +1 more source
First eigenvalue of submanifolds in Euclidean space
International Journal of Mathematics and Mathematical Sciences, 2000 We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely.
Kairen Cai
doaj +1 more source
On two mathematical representations for “semantic maps”
Zeitschrift für Sprachwissenschaft, 2022 We describe two mathematical representations for what have come to be called “semantic maps”, that is, representations of typological universals of linguistic co-expression with the aim of inferring similarity relations between concepts from those ...
Croft William
doaj +1 more source
Metric Foliations on the Euclidean Space [PDF]
arXiv, 2018 We complete a minor gap in Gromoll and Walschap classification of metric fibrations from the Euclidean space, thus completing the classification of Riemannian foliations on Euclidean spaces.
arxiv
Embedding dimensions of matrices whose entries are indefinite distances in the pseudo-Euclidean space [PDF]
arXiv, 2022 A finite set of the Euclidean space is called an $s$-distance set provided the number of Euclidean distances in the set is $s$. Determining the largest possible $s$-distance set for the Euclidean space of a given dimension is challenging. This problem was solved only when dealing with small values of $s$ and dimensions.
arxiv
Simulation of Inhomogeneous Refractive Index Fields Induced by Hot Tailored Forming Components
Advanced Engineering Materials, EarlyView.This article presents a simulation model for simulating inhomogeneous refractive index fields (IRIF) in hot‐forged components, accounting for thermal influences and complex geometries. Through this simulation, a priori knowledge about the propagation of the IRIF can be obtained, allowing for the positioning of the component or an optical measurement ...
Pascal Kern +3 more
wiley +1 more source
Kinematic Mapping in Semi-Euclidean 4-Space
Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2015 We study the some algebraic properties of matrix associated to Hamilton operators is defined for semi-quaternions. The kinematic mapping corresponding to these operators in semi-Euclidean 4-space is same as the kinematic mapping of Blaschke and Grünwald ...
Mehdi JAFARI
doaj +4 more sources
Dimension of a snowflake of a finite Euclidean subspace [PDF]
arXiv, 2017 Let $X$ be an $n$-point subset of a Euclidean space and $0 < a < 1$. The classical theorem of Schoenberg implies that the snowflake space $X^a$ can be isometrically embedded into Euclidean space. In the paper we show that points in the image of such an embedding always are in general position. As application we prove the analogue of Schoenberg's result
arxiv
Beyond Order: Perspectives on Leveraging Machine Learning for Disordered Materials
Advanced Engineering Materials, EarlyView.This article explores how machine learning (ML) revolutionizes the study and design of disordered materials by uncovering hidden patterns, predicting properties, and optimizing multiscale structures. It highlights key advancements, including generative models, graph neural networks, and hybrid ML‐physics methods, addressing challenges like data ...
Hamidreza Yazdani Sarvestani +4 more
wiley +1 more source
The r-mean curvature and rigidity of compact hypersurfaces in the Euclidean space [PDF]
arXiv, 2020 In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.
arxiv