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Metric Entropy of Homogeneous Spaces
, 1997 For a (compact) subset $K$ of a metric space and $\varepsilon > 0$, the {\em covering number} $N(K , \varepsilon )$ is defined as the smallest number of balls of radius $\varepsilon$ whose union covers $K$.
Szarek, Stanislaw J.
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Six mathematical gems from the history of distance geometry [PDF]
International Transactions in Operational Research, 2015 This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics.
Leo Liberti, C. Lavor
semanticscholar +1 more source
Effective metric in fluid-gravity duality through parallel transport: A proposal [PDF]
Physical Review D, 2019 The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics.
Shounak De, S. Dey, B. R. Majhi
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Geometric Meanings of Curvatures in Finsler Geometry [PDF]
, 2000 In Finsler geometry, we use calculus to study the geometry of regular inner metric spaces. In this note I will briefly discuss various curvatures and their geometric meanings from the metric geometry point of view, without going into the forest of ...
Shen, Zhongmin
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Advanced Engineering Materials, EarlyView.Laser surface texturing significantly improves the corrosion resistance and mechanical strength of 3D‐printed iron polylactic acid (Ir‐PLA) for marine applications. Optimal laser parameters reduce corrosion by 80% and enhance tensile strength by 25% and ductility by 15%.
Mohammad Rezayat +6 more
wiley +1 more source
Advanced Engineering Materials, EarlyView.Additive manufacturing technologies like laser powder‐bed fusion offer great design freedom and individualization of products down to a batch size of one. However, parts fabricated with this technology suffer from poor quality. Acoustic assistance during the build process can minimize these drawbacks.
Oliver Maurer, Dirk Bähre
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A Coding Theoretic Study on MLL proof nets
, 2010 Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area of mathematics,
Girard +4 more
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Advanced Engineering Materials, EarlyView.This study presents a 3D representative volume element‐based simulation approach to predict mesoscopic residual stress and strain fields in silicon solid solution‐strengthened ductile cast iron. By modeling phase transformation kinetics with an enhanced Johnson–Mehl–Avrami–Kolmogorov model, the effects of varying cooling rates on residual stresses are ...
Lutz Horbach +6 more
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Advanced Engineering Materials, EarlyView.This study presents a hyperelastic mechanical metamaterial for elastic energy dissipation. Energy is dissipated within its unit cells by friction assisted by material damping. Frictional contact is enhanced when using auxetic unit cells. The load–displacement plot for one compression cycle shows a pronounced hysteresis loop, indicating that a large ...
Eunhyeuk Jeong +2 more
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Preface to: Submanifolds in Metric Manifolds
MathematicsThe present editorial contains 11 research articles, published in the Special Issue entitled “Submanifolds in metric manifolds” of the MDPI mathematics journal, which cover a wide range of topics from differential geometry in relation to the theory and ...
C. Hreţcanu
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