Marine Anoxia and Ocean Acidification During the End‐Permian Extinction
Geophysical Monograph Series, Page 325-340., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Ying Cui +4 more
wiley +5 more sources
High‐Pressure Na‐Ca Carbonates in the Deep Carbon Cycle
Geophysical Monograph Series, Page 127-136., 2020 This book is Open Access. A digital copy can be downloaded for free from Wiley Online Library.
Explores the behavior of carbon in minerals, melts, and fluids under extreme conditions
Carbon trapped in diamonds and carbonate-bearing rocks in subduction zones are examples of the continuing exchange of substantial carbon ...
Sergey Rashchenko +2 more
wiley +6 more sources
A Sobolev space and a Darboux problem [PDF]
Pacific Journal of Mathematics, 1977 M. B. Suryanarayana
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Solid State Self-Assembly of an Extended Curved-Arm Nickel(II) Macrocycle with Fullerene C<sub>60</sub>. [PDF]
Chem Asian JThree co‐crystalline structures that contain fullerene C60 and (5,14‐dihydro‐6,8,15,17‐tetrabenzyl‐2,3,11,12‐tetramethyldibenzo[b,i][1,4,8,11]tetraazacyclotetradecine)nickel(II) show the formation discrete one‐dimensional hollow channels as a results of 1 : 1 interplay and 1 : 2 dimeric interplay with the fullerenes arranged in hexagonal arrays ...
Ling I +4 more
europepmc +2 more sources
Lifting in Sobolev spaces [PDF]
Journal d'Analyse Mathématique, 2000 We characterize the couples $(s,p)$ with the following property: if $u$ is a complex-valued unimodular map in $W^{s,p}$, then $u$ has (locally) a phase in $W^{s,p}$.
Jean Bourgain +2 more
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Equivalent Norms for Sobolev Spaces [PDF]
Proceedings of the American Mathematical Society, 1970 where ...
Robert Adams
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Topology and Sobolev Spaces [PDF]
Journal of Functional Analysis, 2001 Let two compact connected oriented smooth Riemannian manifolds \(M\) and \(N\) (with or without boundary) be given. It is supposed that \(\dim M\geq 2\); the example \(N=S^1\) is of importance. Let \(W^{1,p}(M,N)\) be the Sobolev space of functions \(u\in W^{1,p} (M,\mathbb{R}^k)\) with \(u(x)\in N\) a.e.
Haïm Brézis, Yanyan Li
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On anisotropic Sobolev spaces [PDF]
Communications in Contemporary Mathematics, 2019 We investigate two types of characterizations for anisotropic Sobolev and BV spaces. In particular, we establish anisotropic versions of the Bourgain–Brezis–Mironescu formula, including the magnetic case both for Sobolev and BV functions.
Hoai-Minh Nguyen, Marco Squassina
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On fractional Orlicz–Sobolev spaces [PDF]
Analysis and Mathematical Physics, 2021 AbstractSome recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings.
Angela Alberico +3 more
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AIMS Mathematics, 2022 This paper considers a simplified three dimensional Ericksen-Leslie System for nematic liquid crystal flows in the unbounded domain $ \Omega: = \mathbb R^+\times \mathbb R^2 $ or the smooth bounded domain $ \Omega $.
Junling Sun, Xuefeng Han
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